Benchmarking Machine Learning for QSAR: A Practical Guide to Models, Metrics, and Modern Applications in Drug Discovery

Abstract

This article provides a comprehensive guide for researchers and drug development professionals on benchmarking machine learning algorithms for Quantitative Structure-Activity Relationship (QSAR) modeling. It covers foundational principles, from classical statistical methods to advanced deep learning and graph neural networks. The scope extends to practical methodological considerations, including molecular representation selection and task-specific model application for virtual screening or lead optimization. It addresses critical troubleshooting aspects like data quality, feature selection, and tackling dataset imbalance. Finally, the article details rigorous validation protocols, comparative performance analysis across algorithms, and the importance of applicability domain assessment. By synthesizing current best practices and emerging trends, this guide aims to equip scientists with the knowledge to build robust, predictive, and reliable QSAR models that accelerate the drug discovery pipeline.

From Linear Models to Deep Learning: Core Principles of QSAR Modeling

Quantitative Structure-Activity Relationship (QSAR) modeling has undergone a profound transformation, evolving from classical statistical approaches to modern artificial intelligence (AI)-driven paradigms. This evolution has fundamentally reshaped drug discovery, turning it from a trial-and-error process into a sophisticated, data-driven science [1]. The integration of AI has empowered researchers with faster, more accurate, and scalable methods to identify therapeutic compounds, ultimately aiming to reduce the high costs and timelines associated with traditional drug development [1] [2]. This guide objectively compares the performance of classical and modern QSAR methodologies, providing experimental data and benchmarking protocols essential for researchers and drug development professionals.

The Foundations and Evolution of QSAR Modeling

From Classical Descriptors to Deep Learning Representations

The core of QSAR lies in representing chemical structures numerically. The evolution of these representations mirrors the journey of the field itself:

• 1D/2D Descriptors: Classical QSAR relied on numerical encodings of fundamental chemical properties (e.g., molecular weight) or topological indices derived from 2D structures [1].
• 3D/4D Descriptors: These descriptors incorporated molecular shape, electrostatic potentials, and even conformational flexibility, providing a more realistic representation of molecules under physiological conditions [1].
• Quantum Chemical Descriptors: Descriptors such as HOMO-LUMO energy gaps and dipole moments were introduced to model electronic properties influencing bioactivity [1].
• Deep Descriptors: Modern AI, particularly graph neural networks (GNNs) and autoencoders, generates "deep descriptors" directly from molecular graphs or SMILES strings. These are data-driven, hierarchical features that capture complex, abstract molecular patterns without manual engineering [1].

The Progression of Modeling Algorithms

The statistical engines of QSAR have advanced from simple linear models to highly complex nonlinear architectures:

• Classical Era: The foundation was built on Multiple Linear Regression (MLR) and Partial Least Squares (PLS), prized for their simplicity, speed, and interpretability. These models are effective when relationships between descriptors and biological activity are linear [1] [3].
• Machine Learning Rise: Algorithms like Support Vector Machines (SVM), Random Forests (RF), and k-Nearest Neighbors (kNN) became standard tools. They handle high-dimensional data and capture nonlinear relationships without strict assumptions about data distribution. Random Forests, in particular, are favored for their robustness to noisy data and built-in feature selection [1].
• Deep Learning Dominance: The current state-of-the-art employs Graph Neural Networks (GNNs), transformers, and other deep learning architectures. These models learn directly from molecular structure, automatically discovering relevant features and complex structure-activity patterns that are often intractable for earlier methods [1] [4].

Table 1: Evolution of QSAR Modeling Techniques

Era	Representative Algorithms	Key Characteristics	Typical Molecular Representations
Classical	Multiple Linear Regression (MLR), Partial Least Squares (PLS)	Linear, highly interpretable, relies on assumptions of normality and linearity	1D/2D descriptors (e.g., molecular weight, topological indices)
Machine Learning	Support Vector Machines (SVM), Random Forests (RF), k-Nearest Neighbors (kNN)	Can capture non-linear relationships, more robust to noisy data	2D/3D descriptors, fingerprints, quantum chemical descriptors
Deep Learning	Graph Neural Networks (GNNs), Transformers, Directed Message Passing Neural Network (DMPNN)	End-to-end learning, automatically learns features from raw data, high predictive power	Molecular graphs, SMILES strings, "deep descriptors"

Performance Benchmarking: Classical vs. Machine Learning vs. Deep Learning

Predictive Performance on Diverse Tasks

Systematic benchmarking reveals clear performance trends across different modeling eras. A comprehensive benchmark of 13 AI methods for predicting cyclic peptide membrane permeability demonstrated that model performance is strongly dependent on molecular representation and architecture [4]. In this study, which used a large, curated dataset from the CycPeptMPDB database, graph-based models, particularly the Directed Message Passing Neural Network (DMPNN), consistently achieved top performance across regression, binary classification, and soft-label classification tasks [4].

Furthermore, the benchmark showed that regression tasks generally outperformed classification approaches for predicting permeability. While deep learning models led the pack, simpler models like Random Forest and SVM also demonstrated competitive performance, highlighting that the optimal model can be task-dependent [4].

Generalizability and the Scaffold Split Challenge

A critical test for any QSAR model is its ability to generalize to new, structurally distinct chemicals. Benchmarking studies often use a "scaffold split," where the test set contains molecules with core structures not seen during training, to simulate real-world discovery scenarios.

The cyclic peptide permeability study found that models validated via this rigorous scaffold split exhibited substantially lower generalizability compared to random splitting [4]. This performance drop is a recognized challenge in QSAR and underscores the risk of overfitting to local chemical patterns present in the training data, a pitfall that complex deep learning models are particularly susceptible to without proper validation.

Table 2: Benchmarking Model Performance and Generalizability

Model / Approach	Reported Performance (Example)	Interpretability	Generalizability (Scaffold Split)
Classical (e.g., PLS)	Lower predictive power on complex, non-linear relationships	High (Model coefficients are directly interpretable)	Varies, can be good for congeneric series
Machine Learning (e.g., Random Forest)	Competitive performance, often strong for medium-sized datasets	Medium (Feature importance available, but local explanations needed)	Good, but can decrease with high dimensionality
Deep Learning (e.g., DMPNN)	Top performance in systematic benchmarks (e.g., Cyclic Peptide Permeability) [4]	Low (Inherent "black box"; requires post-hoc interpretation tools)	Can be substantially lower than with random splits [4]

Experimental Protocols for Benchmarking QSAR Models

Data Preparation and Splitting Strategies

Robust benchmarking requires careful data curation and splitting to avoid over-optimistic performance estimates.

• Dataset Curation: The CARA (Compound Activity benchmark for Real-world Applications) benchmark emphasizes using data from real-world assays, distinguishing between two primary application categories [5]:
  • Virtual Screening (VS) Assays: Contain compounds with a diffused, widespread distribution of pairwise similarities, mimicking screening from diverse chemical libraries.
  • Lead Optimization (LO) Assays: Contain congeneric compounds with high pairwise similarities, representing a series of structurally related analogs [5].
• Data Splitting:
  • Random Split: The dataset is randomly divided into training, validation, and test sets. This provides a baseline measure of performance but can overestimate real-world applicability.
  • Scaffold Split: Molecules are split based on their Murcko scaffolds, ensuring the test set contains core structures not present in the training set. This is a more rigorous test of a model's ability to generalize to novel chemotypes [4] [5].

Validation and Interpretation Benchmarks

Beyond simple prediction accuracy, a comprehensive benchmark must assess model interpretability and robustness.

• Validation Techniques: Established protocols include internal validation (e.g., cross-validation), external validation with a held-out test set, and Y-scrambling to check for chance correlations [3]. Defining the model's Applicability Domain (AD) is crucial to understand the chemical space where its predictions are reliable [6].
• Interpretability Benchmarks: Synthetic datasets with pre-defined patterns allow for quantitative evaluation of interpretation methods. For example, benchmarks have been developed where the target property is the sum of nitrogen atoms in a molecule. The performance of an interpretation method (e.g., SHAP, LIME) is then measured by its ability to correctly assign positive contributions to nitrogen atoms and zero to others, providing a "ground truth" for validation [7] [8].

The following workflow diagram illustrates the key stages in a robust QSAR benchmarking experiment:

The Scientist's Toolkit: Essential Reagents for QSAR Research

Table 3: Key Software and Databases for Modern QSAR Research

Tool Name	Type	Primary Function in QSAR
RDKit	Cheminformatics Library	An open-source toolkit for cheminformatics, used for descriptor calculation, fingerprint generation, and fundamental molecular operations [4].
scikit-learn	Machine Learning Library	A comprehensive library for Python providing classical ML algorithms (RF, SVM, PLS) and utilities for model evaluation and hyperparameter tuning [1].
DeepChem	Deep Learning Library	An open-source platform that simplifies the development of deep learning models on chemical data, including Graph Neural Networks [7].
ChEMBL	Public Database	A manually curated database of bioactive molecules with drug-like properties, providing a vast source of experimental data for training and testing models [5].
VEGA	QSAR Platform	A platform integrating various (Q)SAR models, particularly useful for regulatory applications like predicting environmental fate and toxicity [6].
SHAP (SHapley Additive exPlanations)	Interpretation Tool	A unified framework for interpreting model predictions by quantifying the contribution of each feature to an individual prediction, crucial for "black box" models [1] [9].

The evolution of QSAR from classical MLR and PLS to modern AI is a journey from interpretable linear models to powerful, non-linear predictors. Benchmarking studies consistently show that modern AI methods, especially graph-based models, deliver superior predictive accuracy [1] [4]. However, this power comes with trade-offs: increased computational complexity, a greater risk of overfitting to training data scaffolds, and reduced inherent interpretability. The choice of model is not a simple declaration of a winner but a strategic decision. Researchers must balance the need for predictive power with the requirements for generalizability, speed, and interpretability based on their specific project phase—whether it's initial high-throughput virtual screening or the detailed, mechanism-driven optimization of lead compounds. The future of QSAR lies not in a single algorithm, but in the continued development and thoughtful application of a diverse, well-understood toolkit.

In Quantitative Structure-Activity Relationship (QSAR) modeling, molecular descriptors are fundamental numerical representations that translate chemical information into a quantifiable format suitable for machine learning algorithms. These descriptors formally represent the final result of a logical and mathematical procedure that transforms chemical information encoded within a symbolic representation of a molecule into a useful number [10]. The selection of appropriate molecular representations significantly impacts model performance in predicting biological activities and physicochemical properties, making descriptor choice a critical consideration in benchmarking studies for drug discovery applications [11] [5].

Molecular descriptors are broadly classified by their dimensionality, which corresponds to the complexity of structural information they encode. This classification system ranges from simple 0D descriptors that require no structural information to sophisticated 4D descriptors that account for conformational flexibility and molecular interactions [1] [10]. As the field of computational drug discovery advances, understanding the strengths, limitations, and appropriate applications of each descriptor type becomes essential for building robust QSAR models that can reliably predict molecular properties in real-world scenarios [5] [12].

Classification and Definitions of Molecular Descriptors

0D and 1D Descriptors

0D descriptors represent the simplest form of molecular representation, requiring no information about molecular structure or atom connectivity. These descriptors are derived directly from the chemical formula and include basic molecular properties such as atom counts, molecular weight, and atom-type frequencies. For example, the chemical formula C₇H₇Cl for p-chlorotoluene provides sufficient information to calculate these descriptors. Other examples include sum or average values of atomic properties such as mass, polarizability, or hydrophobic constants. While 0D descriptors exhibit high degeneracy (equal values for different molecular structures) and contain relatively low chemical information, they provide a valuable foundation for modeling certain physicochemical properties and are computationally efficient to calculate [10].

1D descriptors incorporate substructural information through the identification of functional groups and structural fragments within the molecule. These descriptors include counts of specific functional groups (e.g., hydroxyl, carbonyl, amino groups), hydrogen bond donors and acceptors, rotatable bonds, and ring systems. The substructure list representation forms the basis for molecular fingerprints, which are binary vectors indicating the presence or absence of specific structural patterns. 1D descriptors offer more detailed structural information than 0D descriptors while remaining computationally inexpensive to generate. They are particularly valuable for rapid similarity assessments and initial screening phases in drug discovery pipelines [13] [10].

2D Descriptors

2D descriptors, also known as topological descriptors, are derived from the molecular graph representation that defines atom connectivity without considering spatial coordinates. In this representation, atoms correspond to vertices and bonds to edges in a graph structure. These descriptors are graph invariants that capture structural patterns through mathematical transformations of the molecular connectivity matrix. Common 2D descriptors include connectivity indices, path counts, graph-theoretical indices, and information-theoretic measures that encode molecular branching, shape, and complexity [13] [10].

The advantage of 2D descriptors lies in their ability to discriminate between structural isomers while remaining independent of molecular conformation. They provide a balanced approach between informational content and computational requirements, making them widely applicable across diverse QSAR modeling scenarios. Popular software packages such as Dragon and RDKit can calculate comprehensive sets of 2D descriptors from molecular structure inputs [10] [12].

3D Descriptors

3D descriptors incorporate spatial molecular geometry by utilizing the three-dimensional coordinates of atoms within a molecule. These descriptors capture steric and electronic features that influence molecular interactions and biological activity, including molecular surface area, volume, shape parameters, and electrostatic potential distributions. Unlike 2D descriptors, 3D representations can distinguish between stereoisomers and account for conformational effects that significantly impact biological activity [14] [10].

The calculation of 3D descriptors requires energy-minimized molecular structures, which introduces computational complexity and potential uncertainties related to conformational sampling. Despite these challenges, 3D descriptors provide enhanced performance for modeling endpoints strongly influenced by molecular shape and steric factors. Common approaches for 3D similarity assessment include volume overlap methods (e.g., ROCS), surface-based comparisons, and field-based techniques that evaluate molecular interaction potentials [14].

Graph-Based Representations

Graph-based representations directly utilize the molecular graph structure as input for machine learning algorithms, particularly graph neural networks (GNNs). In this approach, atoms are represented as nodes (with features such as element type, hybridization, and charge), while bonds are represented as edges (with features such as bond type and conjugation). Message Passing Neural Networks (MPNNs) and other GNN architectures then learn molecular representations by iteratively exchanging information between connected atoms, effectively capturing complex structural patterns without manual feature engineering [11] [15].

Graph-based methods have demonstrated state-of-the-art performance across various molecular property prediction benchmarks, as they naturally represent molecular topology and can learn task-specific representations directly from data. The directed message passing neural network (D-MPNN) architecture has shown particular promise in molecular property prediction challenges, often outperforming traditional descriptor-based approaches when sufficient training data is available [16] [15].

Performance Benchmarking Across Descriptor Types

Comparative Performance in ADME-Tox Prediction

Recent benchmarking studies provide quantitative comparisons of descriptor performance across critical ADME-Tox (Absorption, Distribution, Metabolism, Excretion, and Toxicity) endpoints. These evaluations reveal consistent patterns in descriptor effectiveness for different prediction tasks, highlighting the importance of strategic descriptor selection based on the specific modeling objective and available data characteristics [12].

Table 1: Performance Comparison of Descriptor Types Across ADME-Tox Targets

ADME-Tox Target	Best Performing Descriptor	Algorithm	Key Performance Metric
Ames Mutagenicity	2D Descriptors	XGBoost	Superior to combined descriptors
P-glycoprotein Inhibition	2D Descriptors	XGBoost	Superior to combined descriptors
hERG Inhibition	2D Descriptors	XGBoost	Superior to combined descriptors
Hepatotoxicity	2D Descriptors	XGBoost	Superior to combined descriptors
Blood-Brain Barrier Permeability	2D Descriptors	XGBoost	Superior to combined descriptors
CYP 2C9 Inhibition	2D Descriptors	XGBoost	Superior to combined descriptors
General ADMET	3D Descriptors + Morgan Fingerprints	Optimized Models	Best overall performance [11]

A comprehensive assessment of descriptor performance across six ADME-Tox targets revealed that traditional 2D descriptors consistently outperformed fingerprint-based representations and their combinations when used with the XGBoost algorithm. Surprisingly, 2D descriptors achieved better performance than models using all examined descriptor sets combined for almost every dataset, challenging the conventional practice of concatenating multiple representations without systematic optimization [12].

For specific ADMET prediction tasks, optimized combinations of descriptors and algorithms have demonstrated superior performance. A recent benchmarking study highlighted that careful feature selection and model optimization can significantly enhance prediction accuracy, with 3D descriptors and Morgan fingerprints contributing to top-performing models for various ADMET endpoints [11].

Performance Across Machine Learning Algorithms

Descriptor performance exhibits significant dependence on the machine learning algorithm employed, with different algorithms showing distinct preferences for specific descriptor types based on their underlying learning mechanisms and the characteristics of the chemical space being modeled.

Table 2: Algorithm-Descriptor Performance Interactions

Algorithm	Best Performing Descriptor Type	Application Context	Performance Notes
XGBoost	2D Descriptors	ADME-Tox Classification	Consistent superiority across targets [12]
RPropMLP	3D Descriptors	Specific ADME-Tox Targets	Competitive with 2D descriptors [12]
Random Forest	Morgan Fingerprints	General Molecular Properties	Robust performance [16]
Graph Neural Networks	Graph Representations	Binding Affinity Prediction	State-of-the-art with sufficient data [16]
k-Nearest Neighbors	Compression-Based (MolZip)	Limited Data Scenarios	Competitive with fingerprints [16]
Support Vector Machines	Extended Connectivity Fingerprints	Various Molecular Properties	Good performance with balanced data [16]

The interaction between algorithm choice and descriptor selection highlights the importance of considering both components simultaneously during model optimization. Tree-based methods like XGBoost and Random Forest demonstrate robust performance with traditional 2D descriptors and fingerprints, while neural network architectures often achieve superior results with learned representations from graph-based inputs or specialized descriptor sets [12] [16].

Experimental Protocols and Benchmarking Methodologies

Standardized Benchmarking Workflow

Robust evaluation of molecular descriptors requires carefully designed experimental protocols that account for dataset characteristics, model selection, and performance validation. The following workflow diagram illustrates a comprehensive benchmarking methodology derived from recent ADMET prediction studies:

This systematic approach ensures fair comparison between descriptor types by controlling for confounding factors such as data quality, model architecture, and evaluation metrics. The workflow emphasizes the importance of statistical hypothesis testing alongside conventional performance metrics to establish significant differences between descriptor combinations [11].

Data Curation and Preprocessing Protocols

High-quality data curation forms the foundation of reliable descriptor benchmarking. Standardized protocols include:

• Salt Removal and Standardization: Extraction of parent organic compounds from salt complexes using tools like the standardisation tool by Atkinson et al. with modifications to include boron and silicon as organic elements [11].
• Tautomer Normalization: Consistent representation of tautomeric forms to ensure standardized descriptor calculation [11].
• Duplicate Handling: Removal of inconsistent duplicate measurements while retaining consistent duplicates based on predefined criteria (exact match for classification, within 20% IQR for regression) [11].
• Structural Filtering: Application of heavy atom and element filters (C, H, N, O, S, P, F, Cl, Br, I) to ensure chemical relevance and computational stability [12].
• Geometry Optimization: Generation of 3D structures using tools like Macromodel (Schrödinger suite) followed by energy minimization to ensure physiologically relevant conformations [12].

These preprocessing steps address common data quality issues in public chemical databases, including inconsistent SMILES representations, fragmented structures, duplicate measurements with conflicting values, and inconsistent labeling across training and test sets [11].

Evaluation Metrics and Validation Strategies

Comprehensive benchmark studies employ multiple evaluation metrics to assess different aspects of model performance:

• Classification Tasks: Accuracy, sensitivity, specificity, Matthews Correlation Coefficient (MCC), AUC-ROC
• Regression Tasks: R², Mean Absolute Error (MAE), Root Mean Square Error (RMSE)
• Model Robustness: Q² (cross-validated R²), external validation performance, learning curves

Advanced validation strategies include scaffold splitting to assess generalization to novel chemotypes, temporal splitting to simulate real-world application scenarios, and cross-validation with statistical testing to establish significant performance differences [11] [5]. The integration of hypothesis testing with conventional cross-validation provides enhanced reliability in model selection, particularly in noisy domains like ADMET prediction [11].

Essential Research Reagents and Computational Tools

Software and Libraries for Descriptor Calculation

Table 3: Essential Computational Tools for Molecular Descriptor Research

Tool Name	Descriptor Types	Primary Function	Application Context
RDKit	2D, 3D, Fingerprints	Cheminformatics Platform	Standard for descriptor calculation [11] [12]
Dragon	1D, 2D, 3D	Comprehensive Descriptor Calculation	Gold standard for traditional descriptors [10]
PaDEL	1D, 2D	Descriptor Calculation	Alternative to Dragon [1]
Chemprop	Graph Representations	Message Passing Neural Networks	State-of-the-art GNN implementation [11]
Schrödinger Suite	3D	Molecular Modeling & Optimization	Industry-standard for 3D structure preparation [12]
scikit-learn	NA	Machine Learning Algorithms	Standard ML implementations [16]
MolZip	Compression-Based	Novel Representation Learning	Alternative approach for limited data [16]

These tools represent the essential software infrastructure for calculating molecular descriptors and building predictive QSAR models. RDKit has emerged as the de facto standard for open-source cheminformatics, providing comprehensive implementation of 2D descriptors, 3D descriptors, and molecular fingerprints. Commercial packages like Dragon offer the most extensive collections of molecular descriptors, with thousands of calculated parameters spanning multiple dimensions of chemical information [10] [12].

Specialized implementations like Chemprop provide optimized graph neural network architectures that directly learn from molecular graph representations, while novel approaches like MolZip explore alternative paradigms using compressed molecular representations that can achieve competitive performance without extensive training [11] [16].

Benchmark Datasets and Chemical Spaces

Robust evaluation of molecular descriptors requires diverse chemical benchmarks that represent real-world application scenarios:

• Therapeutics Data Commons (TDC): Curated ADMET benchmarks with standardized splits and evaluation protocols [11]
• MoleculeNet: Comprehensive collection of molecular property datasets for benchmarking machine learning algorithms [16]
• ChEMBL: Large-scale bioactivity data from scientific literature, enabling practical benchmark construction [5]
• PubChem: Publicly available screening data for specific targets like CYP isoforms [12]

The CARA (Compound Activity benchmark for Real-world Applications) framework addresses important distinctions between virtual screening (VS) and lead optimization (LO) scenarios, which present different compound distribution patterns and modeling challenges [5]. This differentiation is crucial for meaningful descriptor evaluation, as performance characteristics may vary significantly between these distinct application contexts.

The benchmarking evidence consistently demonstrates that 2D descriptors provide robust performance across diverse ADME-Tox prediction tasks, particularly when paired with tree-based algorithms like XGBoost. Their computational efficiency, structural interpretability, and strong predictive performance make them a practical choice for many QSAR applications. However, 3D descriptors and graph-based representations offer complementary advantages for specific endpoints influenced by molecular shape and stereochemistry, particularly as data availability increases [12] [11].

Future research directions include the development of optimized descriptor selection methodologies that move beyond conventional concatenation approaches, adaptive representation strategies that dynamically adjust to specific prediction tasks and data characteristics, and integrated multi-scale representations that combine the strengths of different descriptor types while mitigating their individual limitations [11] [15]. The integration of domain knowledge with data-driven representation learning continues to offer promising pathways for enhancing molecular property prediction in real-world drug discovery applications.

Quantitative Structure-Activity Relationship (QSAR) modeling represents a cornerstone of modern computational drug discovery and toxicology, enabling researchers to predict the biological activity or toxicity of compounds from their chemical structures. Over recent decades, the field has undergone a significant evolution, transitioning from classical statistical approaches to increasingly sophisticated machine learning (ML) algorithms. Among these, Random Forest and Support Vector Machines (SVM) have established themselves as reliable, high-performing classical methods. More recently, Graph Neural Networks (GNNs) have emerged as a powerful deep learning approach capable of learning directly from molecular graph structures. This guide provides an objective comparison of these algorithms' performance, experimental protocols, and applicability within QSAR modeling, framed within the broader context of benchmarking for pharmaceutical and toxicological research.

Algorithm Performance Comparison in QSAR Tasks

The performance of machine learning algorithms varies significantly across different QSAR tasks, dataset sizes, and evaluation metrics. The tables below summarize quantitative performance data from recent studies, providing a benchmark for algorithm selection.

Table 1: Overall Performance Comparison Across Diverse QSAR Tasks

Algorithm	Best Reported R² (Regression)	Key Strengths	Common Challenges	Ideal Use Cases
Random Forest	0.835 [17]	Robust to noise, provides feature importance, handles non-linear relationships	Can overfit on noisy data, less interpretable than linear models	Lead optimization, medium-sized datasets, feature selection [17] [1]
SVM	0.862 (Accuracy) [18]	Effective in high-dimensional spaces, strong theoretical foundations	Performance depends on kernel choice; memory-intensive for large datasets	Virtual screening, binary classification tasks [18] [1]
GNN	High Explainability & Predictivity scores [19]	Learns molecular representations directly from graphs, superior for activity cliffs	"Black-box" nature, high computational resource demand, requires large data	Complex pattern recognition, explainable AI tasks, activity cliff prediction [19]

Table 2: Performance on Specific QSAR Benchmarks

Algorithm	Dataset / Task	Performance Metric	Result	Context & Notes
Random Forest	Anticancer Flavones (MCF-7 Cell Line) [17]	R² (Test Set)	0.820	Superior performance vs. XGBoost and ANN on this dataset
Random Forest	Anticancer Flavones (HepG2 Cell Line) [17]	R² (Test Set)	0.835	Demonstrated consistent accuracy across cell lines
SVM	World Happiness Index (Classification) [18]	Accuracy	86.2%	Tied with Logistic Regression, Decision Tree, and Neural Network for top performance
Consensus Model	Rat Acute Oral Toxicity (CCM) [20]	Under-prediction Rate	2%	Most health-protective model; combines multiple models
GNN (ACES-GNN)	30 Pharmacological Targets [19]	Improved Explainability	28/30 datasets	Framework integrates explanation supervision into training
GNN (ACES-GNN)	30 Pharmacological Targets [19]	Improved Predictivity & Explainability	18/30 datasets	Shows positive correlation between prediction accuracy and explanation quality

Experimental Protocols and Methodologies

Benchmarking Frameworks and Data Sourcing

Robust benchmarking of QSAR models requires carefully designed frameworks that reflect real-world challenges. The CARA (Compound Activity benchmark for Real-world Applications) benchmark addresses this by distinguishing between two primary drug discovery tasks: Virtual Screening (VS) and Lead Optimization (LO) [5]. VS assays involve screening large, diverse compound libraries, resulting in datasets with "diffused" molecular patterns. In contrast, LO assays involve optimizing a lead compound, resulting in datasets with "aggregated" patterns of highly similar, congeneric compounds [5]. This distinction is critical, as an algorithm may excel in one task but underperform in the other. Performance evaluation must also adapt to the task: for VS, the Positive Predictive Value (PPV)—the hit rate within the top-ranked compounds—is often more relevant than balanced accuracy, as it reflects the practical constraint of being able to test only a limited number of compounds experimentally [21].

Algorithm Training and Validation Protocols

• Data Preprocessing and Feature Selection: For classical ML algorithms like Random Forest and SVM, molecular structures are typically converted into numerical descriptors (e.g., physicochemical properties, topological indices) or fingerprints (e.g., ECFP). Dimensionality reduction techniques like Principal Component Analysis (PCA) are often applied to avoid overfitting [1]. For GNNs, this step is automated, as the model learns features directly from the graph representation of the molecule, where atoms are nodes and bonds are edges [19].

• Model Validation and Performance Metrics: Rigorous validation is essential. Standard practice involves splitting data into training, validation, and external test sets. For regression tasks (e.g., predicting IC₅₀ values), common metrics include the coefficient of determination (R²) and Root Mean Square Error (RMSE). For classification tasks (e.g., active/inactive), metrics include accuracy, precision, recall, and the area under the receiver operating characteristic curve (AUROC) [17] [1]. As previously mentioned, PPV is gaining traction for evaluating virtual screening performance [21].

The following workflow diagram illustrates a standardized protocol for developing and benchmarking QSAR models.

The Scientist's Toolkit: Essential Research Reagents & Platforms

Successful QSAR modeling relies on a suite of software tools, databases, and computational platforms. The following table details key resources used in the field.

Table 3: Essential Research Reagents & Computational Platforms

Tool / Resource Name	Type	Primary Function in QSAR	Relevance to Algorithms
ChEMBL [5]	Public Database	Curated database of bioactive molecules with drug-like properties	Primary source of training data for all algorithms.
CARA Benchmark [5]	Benchmarking Framework	Provides a standardized benchmark for VS and LO tasks	Critical for objective, real-world performance comparison of RF, SVM, and GNN.
SHAP [1]	Interpretation Library	Explains output of ML models by computing feature importance	Commonly applied to interpret Random Forest and SVM models.
ACES-GNN Framework [19]	Specialized GNN Architecture	Enhances GNN interpretability and accuracy for Activity Cliffs (ACs)	Specific implementation for GNNs, addressing the "black-box" issue.
OpenML [22]	Open-Science Platform	Enables sharing of datasets, tasks, and model evaluations in uniform standards	Supports reproducible benchmarking and meta-learning for all algorithms.
OCHEM [23]	Online Modeling Environment	Platform for building QSAR models with various descriptor packages	Used for developing consensus models; cited in large-scale toxicity prediction challenges.

The benchmarking data and experimental protocols outlined in this guide demonstrate that there is no single "best" algorithm for all QSAR modeling scenarios. Random Forest remains a highly robust and effective choice for many standard classification and regression tasks, particularly with structured molecular descriptors. Support Vector Machines continue to offer strong performance, especially in classification tasks. The rise of Graph Neural Networks represents a significant shift, offering superior capability in learning complex structure-activity relationships directly from molecular graphs and providing insights into challenging phenomena like activity cliffs.

Future progress in the field will likely be driven by hybrid and consensus approaches that leverage the strengths of multiple algorithms [20] [23], a stronger emphasis on explainable AI (XAI) to build trust and provide actionable insights [19] [1], and the development of more sophisticated benchmarking platforms like CARA that closely mimic real-world discovery pipelines [5]. As datasets continue to grow and algorithms evolve, the objective comparison of their performance will remain fundamental to advancing QSAR research and accelerating drug discovery.

Quantitative Structure-Activity Relationship (QSAR) modeling stands as a cornerstone of modern computational drug discovery. These models mathematically link the structural and physicochemical properties of chemical compounds to their biological activity, enabling the prediction of properties for novel compounds and guiding the design of new therapeutics [24]. As chemical datasets grow in size and complexity, and machine learning (ML) algorithms become increasingly sophisticated, a rigorous and well-defined workflow is paramount for developing robust, predictive, and reliable QSAR models. This guide provides a comparative examination of the key stages in the QSAR pipeline—data curation, model building, and validation—synthesizing insights from contemporary benchmarking studies to inform researchers and drug development professionals.

Data Curation: The Foundation of Predictive Models

The adage "garbage in, garbage out" is acutely relevant to QSAR modeling. The quality of the input data directly dictates the performance and reliability of the final model [25]. Data curation is the critical first step to ensure the dataset is valid, consistent, and ready for computational analysis.

A typical curation pipeline involves several standardized steps [26] [25] [27]:

• Validation: Checking SMILES strings for syntactic and semantic correctness to ensure they represent valid chemical structures.
• Cleaning: Removing salts, neutralizing charges, and standardizing tautomeric forms to create a consistent molecular representation.
• Normalization: Applying standardized rules to handle stereochemistry and other structural features.
• Duplicate Removal: Identifying and aggregating or removing duplicate molecular structures to prevent bias. Conflicting activity values for the same structure are often resolved by removal [26].
• Activity Data Standardization: Converting all biological activities to a common unit and scale (e.g., log-transform IC50 values) [24].

Specialized tools like the MEHC-Curation Python framework have been developed to automate this intricate process, transforming it into a standardized and user-friendly operation that significantly enhances downstream model performance [25].

The Critical Role of Data Splitting

Once curated, the dataset must be split into training, validation, and test sets. Benchmarking studies reveal that the splitting strategy profoundly impacts the perceived generalizability of a model. Two common approaches are [4]:

• Random Splitting: Compounds are assigned randomly to training and test sets. This often leads to optimistic performance estimates, as the test set molecules are likely structurally similar to those in the training set.
• Scaffold Splitting: The dataset is split based on molecular scaffolds (core structures), ensuring that molecules in the test set have different core frameworks from those in the training set. This is a more rigorous test of a model's ability to extrapolate to truly novel chemotypes.

A comprehensive benchmark of 13 ML models for predicting cyclic peptide permeability demonstrated that scaffold splitting "yields substantially lower model generalizability compared to random splitting," highlighting the importance of using a rigorous splitting scheme to avoid overestimating real-world performance [4].

QSAR Model Building: A Comparative Look at Algorithms and Representations

The model-building stage involves selecting molecular representations, calculating descriptors, and choosing machine learning algorithms to establish the structure-activity relationship.

Molecular Representations and Descriptors

Molecules can be represented numerically in several ways, which in turn influences the choice of ML algorithm [4] [28]:

• Molecular Descriptors/Fingerprints: Hand-crafted numerical representations based on physicochemical knowledge (e.g., molecular weight, logP, topological indices). Morgan Fingerprints (ECFP) are a widely used type that encodes circular substructures [4] [29].
• SMILES Strings: A text-based representation of the molecular structure, allowing the application of Natural Language Processing (NLP) models like RNNs and Transformers [4].
• Molecular Graphs: Atoms are represented as nodes and bonds as edges. This representation is the foundation for Graph Neural Networks (GNNs), which have shown superior performance in recent benchmarks [4].
• 2D Molecular Images: A less common approach where SMILES strings are converted into 2D images, enabling the use of Convolutional Neural Networks (CNNs) [4].

Benchmarking Machine Learning Algorithms

The choice of algorithm depends on the problem's complexity, dataset size, and desired interpretability. A systematic benchmark of 13 AI methods for predicting cyclic peptide membrane permeability provides critical insights [4]. The study evaluated models across four representation types and three prediction tasks (regression, binary classification, and soft-label classification).

Performance Comparison of Select Model Architectures (Cyclic Peptide Permeability Prediction) [4]

Model Category	Example Algorithms	Key Findings
Graph-based	DMPNN, GNNs	"Consistently achieve top performance across tasks." [4]
Fingerprint-based (Classical ML)	Random Forest (RF), Support Vector Machine (SVM)	"Can achieve comparable performances" to more complex models, offering a strong baseline [4].
SMILES-based (NLP)	RNN, Transformer	Performance is generally lower than graph and fingerprint-based models in this specific benchmark [4].
Image-based	CNN	A less explored approach; performance can be competitive but is often outmatched by other methods [4].

The study concluded that graph-based models, particularly the Directed Message Passing Neural Network (DMPNN), consistently achieved top performance [4]. Furthermore, it found that framing the problem as a regression task generally outperformed classification approaches [4].

Another benchmarking effort, the CARA benchmark, highlighted that optimal training strategies can differ based on the drug discovery task. For Virtual Screening (VS) assays with structurally diverse compounds, meta-learning and multi-task learning were effective. In contrast, for Lead Optimization (LO) assays involving congeneric series, training separate QSAR models on individual assays already yielded decent performance [5].

QSAR Model Validation: Assessing Predictive Power and Utility

Robust validation is non-negotiable for assessing a model's true predictive power and applicability domain. This involves both internal and external validation techniques [24].

Internal and External Validation

• Internal Validation: Uses only the training data to estimate performance, typically through k-fold Cross-Validation or Leave-One-Out Cross-Validation (LOO-CV). This helps prevent overfitting during model tuning but may yield optimistic performance estimates [24].
• External Validation: The gold standard for evaluating model performance. A fully independent test set, not used in any part of model development, is used to assess the model's ability to generalize to new data [24].

Performance Metrics: Beyond Balanced Accuracy

The choice of performance metric must align with the model's intended application. A paradigm shift is occurring, particularly for models used in virtual screening [21].

• Balanced Accuracy (BA): The average of sensitivity and specificity. Traditionally, maximizing BA has been a key objective, often leading to the practice of balancing imbalanced training datasets (where inactive compounds far outnumber actives) through down-sampling [21].
• Positive Predictive Value (PPV or Precision): The proportion of predicted active compounds that are truly active. In virtual screening of ultra-large libraries, where only a tiny fraction of top-ranked compounds can be tested experimentally, PPV is a more relevant and critical metric than BA [21].

A recent study demonstrated that models trained on imbalanced datasets and selected for high PPV achieved a hit rate at least 30% higher than models trained on balanced datasets for the same number of tested compounds. This finding strongly advocates for a shift in best practices when developing QSAR models for virtual screening over lead optimization [21].

Experimental Protocol: Benchmarking Model Performance

To objectively compare different QSAR methodologies, as done in the cyclic peptide permeability study, a standard protocol can be followed [4]:

• Dataset Curation: Obtain a high-quality, curated dataset with reliable experimental data (e.g., from CycPeptMPDB or ChEMBL).
• Data Splitting: Apply both random and scaffold splitting strategies (e.g., 80/10/10 for train/validation/test) to assess generalizability.
• Model Training: Train a diverse set of models spanning different representations and architectures (e.g., RF, SVM, DMPNN, RNN) on the training set.
• Hyperparameter Tuning: Optimize model hyperparameters using the validation set, often via cross-validation.
• Performance Evaluation: Use the held-out test set to calculate key metrics. For classification, use Balanced Accuracy (BA), Area Under the ROC Curve (AUC-ROC), and Positive Predictive Value (PPV). For regression, use R² and Root Mean Square Error (RMSE).

The Scientist's Toolkit: Essential Research Reagents

Tool / Resource	Function / Description	Examples
Descriptor Calculation Software	Generates numerical descriptors from molecular structures.	PaDEL-Descriptor, DRAGON, RDKit, Mordred [24]
Curation & Workflow Platforms	Automates data cleaning, validation, and machine learning pipelines.	MEHC-Curation (Python) [25], KNIME workflows [26] [27]
Public Bioactivity Databases	Sources of experimentally measured compound activities for training and testing.	ChEMBL [30] [5], BindingDB [30], PubChem [5]
Machine Learning Libraries	Provides implementations of algorithms for model building.	scikit-learn (RF, SVM), Deep Graph Library (GNNs), TensorFlow/PyTorch

The integrated QSAR workflow, from rigorous data curation to thoughtful model building and stringent validation, is essential for developing predictive computational tools in drug discovery. Benchmarking studies consistently show that graph-based models like DMPNN are top performers, and that regression can be more effective than classification for certain tasks. Most importantly, the field is moving towards application-specific validation; prioritizing Positive Predictive Value (PPV) over Balanced Accuracy is crucial for virtual screening applications where the goal is to maximize the yield of true active compounds from a small set of experimental tests. By adhering to these principles and leveraging the growing toolkit of automated workflows and benchmarks, researchers can more reliably harness QSAR modeling to accelerate drug discovery.

Building and Applying Robust QSAR Models: Methods and Real-World Use Cases

The selection of molecular feature representations is a critical first step in building Quantitative Structure-Activity Relationship (QSAR) models for drug discovery. These representations transform chemical structures into numerical vectors that machine learning algorithms can process. The three primary categories of molecular features include expert-designed fingerprints, molecular descriptors, and deep-learned embeddings, each with distinct strengths and limitations. For researchers and drug development professionals, understanding the performance characteristics of these representations across various benchmarking scenarios is essential for developing predictive and robust models. This guide provides a comprehensive comparison based on current experimental studies to inform optimal feature selection for QSAR research.

Molecular Feature Representation Types

Expert-Described Fingerprints

Molecular fingerprints are bit or count vectors that encode the presence or absence of specific structural patterns or substructures within a molecule. They are categorized based on their algorithmic foundations:

• Circular Fingerprints (e.g., ECFP, FCFP, Morgan): Generate molecular features by considering the circular neighborhood around each atom at different radii, dynamically creating fragment identifiers without relying on a predefined fragment list [31] [32].
• Substructure-based Fingerprints (e.g., MACCS, PubChem): Use a predefined dictionary of structural fragments or keys; each bit in the fingerprint corresponds to the presence or absence of one of these specific substructures [33] [32].
• Path-based Fingerprints (e.g., AtomPair, Daylight): Analyze linear paths or the shortest distances between pairs of atoms in the molecular graph, hashing these paths into a fixed-size vector [12] [32].
• Pharmacophore Fingerprints (e.g., PH2, PH3): Encode atoms based on pharmacophore features (e.g., hydrogen bond donor/acceptor) and capture pairs or triplets of these features, representing potential molecular interaction patterns [32].

Molecular Descriptors

Molecular descriptors are numerical values representing theoretical or experimental physicochemical properties of a compound. They are traditionally categorized by dimensionality [12]:

• 1D Descriptors: Global molecular properties such as molecular weight, atom count, and logP.
• 2D Descriptors: Topological descriptors derived from the molecular graph, including connectivity indices and topological surface area.
• 3D Descriptors: Geometrical descriptors based on the three-dimensional conformation of a molecule, such as steric or electrostatic field values as used in 3D-QSAR approaches [34].

Deep-Learned Embeddings

Deep-learned embeddings are continuous vector representations of molecules generated by deep learning models, often in a task-specific or self-supervised manner:

• Graph Neural Networks (GNNs): Learn directly from the molecular graph structure, where nodes represent atoms and edges represent bonds. GNNs update atom representations by aggregating information from their neighbors [33] [31].
• SMILES-Based Embeddings: Models like BERT or CNNs process Simplified Molecular-Input Line-Entry System (SMILES) strings as textual data, learning representations either from the character sequence or tokenized substructures [31] [35].
• Unsupervised Embeddings (e.g., Mol2vec): Generate continuous vectors for molecules by applying word embedding algorithms like Word2vec to molecular substructures, creating representations independent of downstream prediction tasks [31].

The following diagram illustrates the workflow for generating and utilizing these different representations in a QSAR modeling pipeline.

Performance Comparison in QSAR Modeling

Benchmarking on Diverse Molecular Property Prediction Tasks

Extensive benchmarking studies across various molecular property prediction tasks reveal how representation choice impacts model performance. The table below summarizes key findings from large-scale comparative analyses.

Table 1: Performance Comparison of Molecular Representations Across Benchmarking Studies

Representation Category	Specific Type	Reported Performance Advantages	Key Limitations
Traditional Fingerprints	MACCS Keys	Competitive performance in many classification tasks, high interpretability [36].	Limited structural resolution due to small size (166 bits).
	Circular (ECFP)	Considered state-of-the-art for drug-like molecules, strong in virtual screening [36] [32].	May underperform on complex natural products [32].
	Path-based (AtomPair)	Good performance in specific ADME-Tox targets [12].	Performance varies significantly with dataset and target [12].
Molecular Descriptors	1D & 2D Descriptors	Superior for predicting physical properties (e.g., solubility, melting point) [36].	Require careful curation and removal of correlated descriptors [12].
	3D Descriptors	Provide complementary information on shape and electrostatics for binding affinity prediction [34].	Computationally intensive, conformation-dependent [34].
Deep-Learned Embeddings	Graph Neural Networks (GNNs)	Outperform other methods in taste prediction tasks; learn rich structural features directly from graphs [33].	Data-hungry; can be outperformed by simpler methods on small datasets [31].
	SMILES-Based (e.g., BERT)	Can capture contextual semantic information from SMILES strings [35].	Performance highly dependent on pre-training corpus and tokenization strategy [35].
	Unsupervised (e.g., Mol2vec)	Competitive performance in some regression and classification tasks [31].	Tend to underperform supervised embeddings and traditional representations [37] [31].

Impact of Dataset Size and Composition

The optimal choice of molecular representation is highly dependent on the size and nature of the training dataset:

• Low-Data Regimes: In scenarios with limited training data (e.g., fewer than 5,000 compounds), traditional fingerprints and molecular descriptors typically outperform deep-learned representations. For instance, one benchmarking study noted that "traditional fingerprints tend to outperform learned representations in low data scenarios" [31]. Similarly, quantum machine learning classifiers have shown advantages over classical ones specifically when the number of training samples and features is limited [38].

• High-Data Regimes: With larger datasets (e.g., >20,000 compounds), the performance gap narrows, and deep learning methods often become competitive. End-to-end deep learning models demonstrate "comparable performance to, and at times surpass, that of models trained on molecular fingerprints" when sufficient data is available [31].

• Specialized Chemical Spaces: Representation performance can vary significantly across different chemical domains. For natural products, which possess distinct structural characteristics (e.g., higher stereochemical complexity), certain path-based and pharmacophore fingerprints can match or exceed the performance of ECFP, the de facto standard for drug-like compounds [32].

Consensus and Hybrid Modeling

Combining different feature representations seems intuitively beneficial, but experimental evidence presents a nuanced picture:

• Limited Consensus Benefits: A comprehensive comparison concluded that "combining different molecular feature representations typically does not give a noticeable improvement in performance compared to individual feature representations" [36]. This suggests significant information overlap between different representation types.

• Notable Exceptions: In specific applications, carefully designed hybrid models can yield benefits. For taste prediction, a "molecular fingerprints + GNN consensus model" emerged as the top performer, indicating the complementary strengths of expert-designed features and learned representations in this domain [33].

Experimental Protocols for Performance Evaluation

Standardized Benchmarking Methodology

To ensure fair and reproducible comparison of molecular representations, researchers should adhere to a standardized experimental protocol:

• Data Curation and Splitting

  • Source: Utilize standardized public datasets like ChemTastesDB [33], ChEMBL [31], or MoleculeNet benchmarks [36].
  • Preprocessing: Apply consistent structure standardization (salt removal, neutralization, stereochemistry handling) using toolkits like RDKit or the ChEMBL structure pipeline [31] [32].
  • Splitting: Implement rigorous train/validation/test splits (common ratios: 70/10/20 or 80/20) with stratification to maintain class distribution, particularly for imbalanced datasets [33].

• Feature Generation

  • Fingerprints: Generate with consistent parameters (e.g., ECFP4 with radius=2, 1024 bits) [31].
  • Descriptors: Calculate comprehensive sets (e.g., using PaDEL software) followed by removal of constant and highly correlated descriptors [12] [39].
  • Deep Embeddings: Use established architectures (GNNs, BERT) with standardized hyperparameters and, where applicable, leverage publicly available pre-trained models [33] [35].

• Model Training and Evaluation

  • Algorithms: Employ diverse algorithms including Random Forests, XGBoost, and neural networks to ensure robustness across model types [12] [36].
  • Validation: Use nested cross-validation to prevent data leakage and overfitting [36].
  • Metrics: Report multiple performance metrics (e.g., AUC-ROC, accuracy, RMSE) appropriate for classification and regression tasks [12].

Table 2: Key Research Reagents and Software for Molecular Representation

Category	Tool Name	Primary Function	Application in Research
Fingerprint Generation	RDKit	Open-source cheminformatics toolkit; generates multiple fingerprints (Morgan, RDKitFP, AtomPair) and descriptors [31] [32].	Standard for molecular representation calculation; used in most benchmarking studies.
Descriptor Calculation	PaDEL-Descriptor	Calculates 1D, 2D descriptors and fingerprints from molecular structures [39].	Used in QSAR studies for comprehensive descriptor generation [39].
Deep Learning Frameworks	DeepChem	Deep learning library for drug discovery; implements GNNs, transformers, and various molecular featurizers [31].	Provides standardized implementations of deep learning models for fair comparison.
3D-QSAR	OpenEye Orion	Implements 3D-QSAR using shape and electrostatic featurizations for binding affinity prediction [34].	Specialized tool for 3D molecular representation and activity modeling.
Benchmarking Platforms	DeepMol	Python package for benchmarking compound representations on drug sensitivity prediction [31].	Enables systematic comparison of representations on standardized tasks.

Case Study: Taste Prediction Benchmarking

A comprehensive 2023 study provides a detailed protocol for comparing representations on taste prediction [33]:

• Dataset: 2,601 molecules from ChemTastesDB with sweet, bitter, and umami classifications.
• Representations: Compared Morgan, PubChem, Daylight, RDKit, ESPF, and ErG fingerprints against CNN and GNN models.
• Model Training: Split data 7:1:2 (train:validation:test), using DeepPurpose package for implementation.
• Key Finding: GNN-based models outperformed other approaches, with the combination of molecular fingerprints and GNNs achieving best performance, demonstrating hybrid potential in specific domains.

The benchmarking evidence clearly indicates that no single molecular representation consistently outperforms all others across every QSAR task. Traditional fingerprints like ECFP and MACCS remain strong, computationally efficient baselines, particularly for drug-like molecules and in low-data scenarios. Molecular descriptors, especially 2D ones, excel at predicting physicochemical properties, while 3D descriptors provide unique value for binding affinity prediction. Deep-learned embeddings show remarkable promise, with GNNs achieving state-of-the-art performance in specific domains like taste prediction, though they typically require larger datasets to reach their full potential.

For researchers building QSAR models, the selection strategy should be guided by the specific problem context: the target property, dataset size and composition, and available computational resources. Empirical validation on representative data remains the gold standard for identifying the optimal molecular representation for any given drug discovery application.

In modern computer-assisted drug discovery, the one-size-fits-all approach to Quantitative Structure-Activity Relationship (QSAR) modeling is increasingly being replaced by task-specific strategies. The performance requirements for machine learning models differ significantly depending on whether they are used for virtual screening of massive chemical libraries or the lead optimization of smaller, focused compound series [21]. Virtual screening aims to identify novel hit compounds from millions of candidates, while lead optimization refines a small set of promising compounds to enhance their activity and properties. This guide examines the distinct objectives, optimal performance metrics, dataset preparation strategies, and experimental protocols for each task, providing researchers with a framework for selecting and benchmarking appropriate QSAR methodologies.

Table 1: Core Objectives and Challenges in QSAR Applications

Aspect	Virtual Screening	Lead Optimization
Primary Goal	Identify novel hit compounds from ultra-large libraries [21]	Enhance potency and properties of a congeneric series [21]
Chemical Space	Broad and diverse exploration [40]	Focused, local exploration [21]
Key Challenge	Managing extreme dataset imbalance (>99% inactives) [21]	Achieving balanced predictive performance for similar compounds
Practical Constraint	Only a small fraction of top-ranked compounds can be tested experimentally [21]	Accurate prediction of small potency changes

Performance Metrics: Selecting the Right Benchmark

The evaluation metrics that best indicate model utility vary dramatically between virtual screening and lead optimization tasks. For virtual screening, where the goal is to select a small number of compounds for experimental testing from billions of candidates, positive predictive value (PPV), also known as precision, is the most critical metric [21]. PPV measures the proportion of true actives among those predicted as active, directly determining the experimental hit rate. In contrast, for lead optimization, where models must reliably predict activity for all compounds in a series, balanced accuracy (BA) remains the preferred metric as it ensures equal performance in predicting both active and inactive compounds [21].

Table 2: Key Performance Metrics for Virtual Screening vs. Lead Optimization

Metric	Virtual Screening Priority	Lead Optimization Priority	Rationale
Positive Predictive Value (PPV)	Critical [21]	Secondary	Directly impacts experimental hit rate in early discovery
Balanced Accuracy (BA)	Less relevant [21]	Critical [21]	Ensures reliable prediction across all compounds in a series
Sensitivity/Recall	Moderate	High	Important for finding all potential actives in a focused series
Area Under ROC Curve (AUROC)	Limited value [21]	Valuable	Measures overall ranking ability without focusing on top predictions
Enrichment Factor (EF)	Useful early enrichment	Limited value	Measures concentration of actives in top fraction

Dataset Preparation: Balancing Act vs. Real-World Imbalance

Dataset preparation strategies fundamentally differ between these applications. For lead optimization, best practices traditionally recommend dataset balancing through techniques like down-sampling the majority class to create models with high balanced accuracy [21]. However, for virtual screening, maintaining real-world imbalance in training datasets produces superior results. Studies demonstrate that training on imbalanced datasets achieves a hit rate at least 30% higher than using balanced datasets when evaluating top-scoring compounds in batch sizes relevant to experimental high-throughput screening (e.g., 128 molecules) [21].

This paradigm shift acknowledges that both training and virtual screening sets are highly imbalanced in favor of inactive compounds. Models trained on balanced datasets, while achieving higher balanced accuracy, typically show lower PPV, making them less effective for the primary goal of virtual screening: to maximize the number of true actives in the small subset of compounds selected for experimental testing [21].

Experimental Protocols and Workflow Design

Virtual Screening Protocol for Ultra-Large Libraries

The massive scale of make-on-demand chemical libraries containing billions of compounds necessitates specialized workflows that combine machine learning with traditional structure-based methods [40].

Machine Learning-Guided Docking Workflow:

• Initial Docking: Perform molecular docking on a structurally diverse subset (e.g., 1 million compounds) from the ultra-large library [40].
• Classifier Training: Train a classification algorithm (CatBoost with Morgan2 fingerprints recommended) to identify top-scoring compounds based on docking results [40].
• Conformal Prediction: Apply the conformal prediction framework to select compounds from the multi-billion-scale library for docking, controlling the error rate of predictions [40].
• Focused Docking: Dock only the selected subset (typically 1-10% of the full library) to identify final candidates for experimental testing [40].

This protocol reduces computational cost by more than 1,000-fold while maintaining high sensitivity (0.87-0.88), enabling practical virtual screening of billion-compound libraries [40].

Diagram 1: ML-guided virtual screening workflow for ultra-large libraries.

Lead Optimization Protocol Using Consensus QSAR

For lead optimization, consensus modeling with ensemble approaches has demonstrated superior performance for predicting activity and optimizing molecular structures within a congeneric series [41].

Consensus QSAR Modeling Protocol:

• Descriptor Calculation and Selection: Calculate molecular descriptors and fingerprints, followed by feature selection using methods like Classification and Regression Trees (CART) to identify key molecular descriptors [41] [42].
• Multiple Model Development: Develop individual QSAR models using diverse algorithms including Support Vector Machine (SVM), Artificial Neural Network (ANN), and Random Forest (RF) [41] [42].
• Consensus Prediction: Combine predictions from multiple models through consensus or majority voting approaches [41].
• Validation: Validate models using 5-fold cross-validation, y-randomization, and external test sets to ensure robustness and generalizability [41].

This approach has achieved remarkable predictive performance with R²Test > 0.93 for regression models and accuracy up to 92% for classification tasks in optimizing dual 5HT1A/5HT7 serotonin receptor inhibitors [41].

Diagram 2: Consensus QSAR modeling workflow for lead optimization.

The Scientist's Toolkit: Essential Research Reagents and Solutions

Table 3: Essential Computational Tools for QSAR Modeling Tasks

Tool/Resource	Function	Virtual Screening Utility	Lead Optimization Utility
Morgan Fingerprints [40]	Molecular representation using circular substructures	High-performance feature for classifiers [40]	Useful for capturing local molecular features
RDKit Descriptors [11]	Calculation of 2D molecular descriptors	Baseline feature set	Interpretable molecular properties
Conformal Prediction Framework [40]	Provides valid confidence measures for predictions	Critical for error rate control in imbalanced data [40]	Limited application
Consensus Modeling [41]	Combines predictions from multiple algorithms	Moderate utility	Critical - boosts accuracy and robustness [41]
Molecular Docking Software	Structure-based binding affinity prediction	Initial screening and training data generation [40]	Limited to target structure availability
Applicability Domain Assessment [41]	Defines model's reliable prediction space	Moderate utility for diverse libraries	Critical for interpolating within chemical series

The benchmarking data and experimental protocols presented demonstrate that optimal QSAR model performance requires strategic alignment between methodology and application context. Virtual screening campaigns benefit from models trained on imbalanced datasets and evaluated by positive predictive value, leveraging machine learning-guided workflows to navigate billion-compound libraries efficiently. Conversely, lead optimization requires models with high balanced accuracy built on balanced training sets, often achieved through consensus modeling approaches. By adopting these task-specific paradigms, researchers can significantly improve the efficiency and success rates of their drug discovery pipelines.

The integration of machine learning (ML) into Quantitative Structure-Activity Relationship (QSAR) modeling has revolutionized drug discovery, shifting the paradigm from traditional trial-and-error approaches to data-driven predictive science [43] [1]. This transformation is particularly evident in critical discovery areas, including the prediction of Absorption, Distribution, Metabolism, Excretion, and Toxicity (ADMET) properties, assessment of endocrine disruption potential via estrogen receptor alpha (ERα) binding, and identification of inhibitors for intricate signaling targets such as Nuclear Factor kappa B (NF-κB) [43] [44] [45]. Accurately predicting these endpoints in the early stages of drug development is crucial for reducing late-stage attrition, which remains a primary challenge in pharmaceutical R&D [46] [47].

Benchmarking studies reveal that the performance of ML models is highly dependent on the choice of molecular representations and feature selection techniques, often more so than the underlying algorithm itself [11]. For instance, systematic feature selection and model validation strategies can significantly enhance the reliability of ADMET predictions, moving beyond the conventional practice of indiscriminately concatenating different molecular representations [11]. Similarly, advanced ML-based three-dimensional QSAR (3D-QSAR) models have demonstrated superior performance over traditional two-dimensional approaches for predicting ERα binding affinity, highlighting the evolutionary trajectory of computational methodologies [44]. This guide provides a comparative analysis of these applications, detailing experimental protocols, benchmarking data, and essential computational toolkits to guide researchers in selecting and optimizing ML models for specific discovery contexts.

Case Study 1: ADMET Property Prediction

Experimental Protocols and Model Benchmarking

Predicting ADMET properties early in the drug discovery pipeline is vital for prioritizing viable lead compounds. A comprehensive benchmarking study [11] established a rigorous protocol for this task. The process begins with data curation and cleaning from public sources like the Therapeutics Data Commons (TDC), followed by the calculation of diverse molecular descriptors and fingerprints (e.g., RDKit descriptors, Morgan fingerprints) [11]. Subsequently, a structured approach to feature selection and combination is employed, moving beyond simple concatenation. Finally, models are evaluated using cross-validation with statistical hypothesis testing and assessed on external test sets to ensure robustness and generalizability [11].

Table 1: Benchmarking Performance of ML Models on Key ADMET Endpoints [11]

ADMET Endpoint	Best-Performing Model	Key Molecular Representation	Performance Metric
Human Plasma Protein Binding	LightGBM	RDKit Descriptors + Morgan Fingerprints	MAE: 0.28 (log unit)
Caco-2 Permeability	Random Forest	Morgan Fingerprints	BA: 0.81
Hepatic Clearance	Support Vector Machine (SVM)	RDKit Descriptors	MAE: 0.41 (log unit)
hERG Cardiotoxicity	SVM	Molecular Embeddings	BA: 0.76
Solubility (Kinetic)	LightGBM	Constitutional Descriptors	MAE: 0.52 (log unit)

The data reveals that no single algorithm dominates all ADMET endpoints. While tree-based models like LightGBM and Random Forest often excel, Support Vector Machines (SVM) can be optimal for specific tasks like hERG cardiotoxicity prediction [11]. The choice of molecular representation is equally critical; simpler fingerprints and descriptors frequently match or surpass the performance of more complex, deep-learned embeddings for these ligand-based prediction tasks [11].

Impact of Data Diversity and Federated Learning

A significant challenge in ADMET prediction is the degradation of model performance when applied to novel chemical scaffolds. Recent initiatives demonstrate that data diversity and representativeness are more impactful for predictive accuracy and generalization than model architecture alone [46]. Federated learning has emerged as a powerful technique to overcome data limitations by enabling collaborative model training across distributed, proprietary datasets from multiple pharmaceutical companies without centralizing sensitive data [46]. This approach systematically extends the model's effective domain, leading to more robust predictors and a reported 40–60% reduction in prediction error for endpoints like human liver microsomal clearance and solubility [46].

Case Study 2: Estrogen Receptor Alpha (ERα) Binding Affinity

Machine Learning-based 3D-QSAR Models

The binding of endocrine-disrupting chemicals (EDCs) to Estrogen Receptor Alpha (ERα) is a major mechanism of toxicity and a key target for therapeutic intervention. A recent study [44] developed advanced machine learning-based 3D-QSAR models to predict the relative binding affinity (RBA) of small molecules to ERα. The methodology involved building models using a dataset from the VEGA IRFMN-RBA model and employing algorithms such as Multilayer Perceptron (MLP), Random Forest (RF), and Support Vector Machine (SVM). These 3D-QSAR models were validated against an external dataset and benchmarked against conventional VEGA models [44].

Table 2: Performance Comparison of ML-based 3D-QSAR Models for ERα Binding [44]

Prediction Model	Accuracy	Sensitivity	Specificity	Notes
MLP 3D-QSAR	0.89	0.91	0.87	Emerged as the most robust model
Random Forest 3D-QSAR	0.86	0.88	0.84	Good performance with built-in feature importance
SVM 3D-QSAR	0.85	0.87	0.83	Effective in high-dimensional space
Conventional VEGA 2D-QSAR	0.81	0.79	0.83	Baseline model for performance comparison

The results demonstrate that all ML-based 3D-QSAR models outperformed the conventional VEGA model, with the MLP model showing the highest accuracy and sensitivity [44]. This underscores the advantage of integrating three-dimensional structural information with powerful non-linear machine learning algorithms for predicting specific molecular interactions like ERα binding.

Counter-Propagation Artificial Neural Networks (CPANN)

An alternative, highly accurate approach for predicting receptor binding utilizes Counter-Propagation Artificial Neural Networks (CPANN). Researchers developed six CPANN models to predict compound binding to androgen and estrogen receptors (ERα and ERβ) as agonists or antagonists [48]. The models were trained on data from the EPA's CompTox Chemicals Dashboard, using DRAGON-derived structural descriptors. Validation via leave-one-out (LOO) tests showed exceptional performance, with prediction accuracy ranging from 94% to 100% for the various receptor models [48]. This highlights CPANN as a powerful tool for the safety prioritization of chemicals regarding endocrine disruption.

Case Study 3: NF-κB Inhibition Prediction

The NfκBin Model and Workflow

The transcription factor NF-κB is a central therapeutic target for chronic inflammatory diseases and cancers. The "NfκBin" tool was developed to specifically predict inhibitors of the TNF-α-induced NF-κB signaling pathway [45] [49]. The experimental workflow initiated with dataset collection from a PubChem high-throughput screen (AID 1852), comprising 1,149 inhibitors and 1,332 non-inhibitors [45] [49]. Subsequently, molecular descriptor calculation was performed using the PaDEL software, generating 17,967 initial descriptors and fingerprints. A critical feature selection step followed, applying univariate analysis and SVC-L1 regularization to identify the most relevant features. Finally, multiple machine learning models were trained and validated on an independent hold-out set [45] [49].

Diagram 1: NfκBin model workflow

Model Performance and Drug Repurposing

Initial models built on raw 2D, 3D, and fingerprint descriptors showed limited predictive power (AUC ≤ 0.66). However, after sophisticated feature selection, the final Support Vector Classifier (SVC) model achieved an AUC of 0.75 on the validation dataset, demonstrating the critical importance of feature engineering [45] [49]. The best-performing model was deployed to screen an FDA-approved drug library from DrugBank, successfully identifying several known NF-κB inhibitors, which validated its utility for drug repurposing [45]. This case study illustrates a complete pipeline from data curation to predictive application, showcasing the practical impact of ML in accelerating inhibitor discovery.

Diagram 2: TNF-α induced NF-κB pathway inhibition

The Scientist's Toolkit: Essential Research Reagents & Software

Table 3: Key Computational Tools for ML-Driven Drug Discovery

Tool/Software	Type	Primary Function	Application in Case Studies
PaDEL-Descriptor [45] [49]	Software	Calculates molecular descriptors and fingerprints	Feature generation for NF-κB inhibitor prediction
RDKit [11]	Cheminformatics Toolkit	Calculates molecular descriptors and handles cheminformatics tasks	Generation of RDKit descriptors and Morgan fingerprints for ADMET models
DRAGON [48]	Software	Calculates a wide range of molecular descriptors	Generation of structural descriptors for CPANN models of ER/AR binding
Scikit-learn [45] [11]	ML Library	Provides implementations of ML algorithms (SVM, RF, etc.)	Model building, feature selection, and data preprocessing
CPANN [48]	Algorithm	Counter-Propagation Artificial Neural Network	Predicting compound binding to estrogen and androgen receptors
Therapeutics Data Commons (TDC) [11]	Data Resource	Curated benchmarks for ADMET properties	Source of training and benchmarking data for ADMET models
CompTox Chemicals Dashboard [48]	Data Resource	EPA database with chemistry, toxicity, and exposure data	Source of activity data for ER/AR binding models
PubChem Bioassay [45] [49]	Data Resource	Repository of biological activity data	Source of NF-κB inhibitor and non-inhibitor data (AID 1852)
DrugBank [45] [49]	Data Resource	Database of FDA-approved drugs and drug-like molecules	Source for drug repurposing screening of NF-κB inhibitors

The benchmark comparisons across these case studies consistently demonstrate that success in ML-driven QSAR does not stem from a single "best" algorithm. Instead, it hinges on a multi-faceted approach that includes judicious feature selection, rigorous model validation, and access to diverse, high-quality data. The performance gains from systematic feature engineering, as seen in the NfκBin and ADMET studies, and the revolutionary potential of federated learning to expand chemical space coverage, underscore a fundamental shift in the field. As machine learning continues to be embedded in the drug discovery workflow, the methodologies and benchmarks detailed in this guide provide a roadmap for researchers to develop more predictive, reliable, and impactful models, ultimately accelerating the delivery of new therapeutics.

In the field of quantitative structure-activity relationship (QSAR) research and computational drug discovery, the ability to objectively evaluate machine learning models is paramount. High-quality, well-curated benchmarks provide the foundation for comparing algorithmic performance, tracking progress in the field, and ensuring that computational predictions translate to real-world drug discovery applications. Without standardized evaluation frameworks, researchers cannot reliably determine whether improvements in model architecture or training strategies genuinely enhance predictive capability for biologically relevant tasks.

The emergence of large-scale public chemogenomic resources like ChEMBL has fundamentally transformed QSAR research by providing massive amounts of experimental bioactivity data. However, raw data alone is insufficient for rigorous model evaluation. This has spurred the development of specialized benchmarking platforms that provide curated datasets, meaningful data splits, standardized evaluation metrics, and leaderboards for fair model comparison. Among these, the Therapeutics Data Commons (TDC) and the Compound Activity benchmark for Real-world Applications (CARA) have emerged as influential frameworks, each with distinct design philosophies and applications. This guide provides a comprehensive comparison of these resources, enabling researchers to select the most appropriate benchmark for their specific QSAR research objectives.

The following table summarizes the core characteristics of the three primary resources discussed in this comparison guide:

Table 1: Core Characteristics of Public QSAR Resources and Benchmarks

Resource	Primary Function	Data Sources	Key Strengths	Primary Use Cases
ChEMBL	Primary data repository	Manual curation from literature & patents	Massive scale (>2M compounds), broad target coverage	Data mining, feature generation, preliminary model training
TDC	Multi-level benchmarking ecosystem	ChEMBL, DrugBank, PubChem, BindingDB, & others	Extensive data functions, leaderboards, broad therapeutic scope	End-to-end model development & evaluation across diverse tasks
CARA	Specialized activity prediction benchmark	ChEMBL	Real-world task distinction (VS/LO), rigorous splitting schemes	Evaluating compound activity prediction models for drug discovery

ChEMBL serves as a foundational data source rather than a benchmark itself—a manually curated database of bioactive molecules with drug-like properties containing over 2 million compound records and 15 million activity measurements extracted from scientific literature [5] [50]. While indispensable for data mining and feature generation, its raw form lacks the structured tasks and evaluation frameworks needed for standardized benchmarking.

The Therapeutics Data Commons (TDC) addresses this gap by providing a coordinated ecosystem for accessing and evaluating AI capabilities across therapeutic modalities and discovery stages [51] [52]. TDC implements a unique three-tiered hierarchical structure (problem → task → dataset) that organizes machine learning challenges across single-instance prediction, multi-instance prediction, and generation problems. Its extensive data functions, standardized splits, and leaderboards support robust model development and comparison.

The CARA benchmark offers a specialized focus on compound activity prediction, specifically designed to reflect real-world drug discovery scenarios [5] [53] [50]. CARA's distinctive contribution lies in its careful distinction between virtual screening (VS) and lead optimization (LO) tasks, which correspond to different stages of the drug discovery pipeline and present different machine learning challenges.

Quantitative Comparison of Benchmark Capabilities

The following tables provide detailed quantitative comparisons of the TDC and CARA benchmarks across multiple dimensions:

Table 2: Benchmark Structure and Task Formulation Comparison

Characteristic	TDC	CARA
Task Scope	Broad (ADMET, target discovery, efficacy, safety, manufacturing)	Narrow (compound activity prediction)
Task Types	Single-instance prediction, multi-instance prediction, generation	Virtual screening (VS), lead optimization (LO)
Data Splitting	Multiple methods (random, scaffold, time, group)	New-protein (VS), new-assay (LO)
Learning Scenarios	Standard, few-shot, zero-shot	Zero-shot, few-shot
Evaluation Level	Dataset-level, benchmark group-level	Assay-level

Table 3: Dataset Composition and Scale

Metric	TDC (ADMET Group Examples)	CARA
Number of Datasets	20+ in ADMET_Group alone	6 primary tasks (VS/LO × All/Kinase/GPCR)
Typical Dataset Size	Hundreds to thousands of compounds	1,558 assays (1,078 VS + 480 LO)
Data Points	Varies by dataset (e.g., Caco2_Wang: 906 compounds)	297,050 activity measurements
Target Coverage	Diverse proteins, ADMET endpoints	Multiple protein classes with representative targets

Table 4: Evaluation Metrics and Model Assessment

Aspect	TDC	CARA
Primary Metrics	Varies by task (MAE, RMSE, ROC-AUC, etc.)	EF@1%, EF@5% (VS); Pearson, Spearman (LO)
Success Metrics	Leaderboard ranking	Success rates (SR@1%, SR@5%)
Evaluation Protocol	Minimum 5 independent runs with different seeds	Assay-level evaluation with multiple splitting
Performance Reporting	Mean ± standard deviation	Success rates per assay type

Experimental Design and Methodologies

CARA Benchmark Construction and Experimental Protocol

The CARA benchmark was constructed through meticulous curation of ChEMBL data with special attention to real-world applicability [5] [50]. The key methodological steps include:

Data Curation and Assay Classification:

• Activity data was grouped by ChEMBL Assay ID, with each assay representing a set of compound activities against a target protein under specific experimental conditions
• Assays were classified as Virtual Screening (VS) or Lead Optimization (LO) types based on compound similarity patterns
• VS assays contain compounds with diffuse distribution patterns (mean pairwise Tanimoto similarity: 0.26)
• LO assays contain congeneric compounds with high structural similarity (mean pairwise Tanimoto similarity: 0.65)

Data Splitting Strategies:

• For VS tasks: New-protein splitting ensures protein targets in test assays are unseen during training
• For LO tasks: New-assay splitting ensures congeneric compounds in test assays are unseen during training
• This rigorous splitting prevents data leakage and reflects real-world generalization requirements

Evaluation Methodologies:

• VS tasks use enrichment factors (EF@1%, EF@5%) and success rates (SR@1%, SR@5%) that prioritize identification of top-ranking active compounds
• LO tasks use correlation coefficients (Pearson, Spearman) that prioritize accurate ranking of congeneric series
• All evaluations are performed at the assay level with multiple runs to ensure statistical reliability

TDC Experimental Framework and Model Assessment

TDC provides a comprehensive framework for model evaluation across diverse therapeutic tasks [51] [54] [52]:

Benchmark Group Implementation:

• TDC organizes related benchmarks into groups (e.g., ADMET_Group) centered around common themes
• The benchmark group structure enables coordinated evaluation across multiple related datasets
• Standardized data loaders ensure consistent access patterns across all benchmarks

Evaluation Workflow:

• Models are evaluated using training/validation/test splits provided by TDC
• A minimum of five independent runs with different random seeds is required for leaderboard submission
• Performance is reported as mean ± standard deviation across runs
• Scaffold splitting is commonly used to assess generalization to novel chemotypes

Multi-tiered Assessment:

• Single-instance prediction: Standard metrics (MAE, RMSE, ROC-AUC) for property prediction
• Multi-instance prediction: Specialized metrics for interaction and polypharmacology prediction
• Generation tasks: Diversity, novelty, and drug-likeness metrics for generated compounds

CARA Benchmark Workflow

Performance Comparison and Experimental Findings

Model Performance Across Benchmark Types

Comparative evaluations reveal distinct performance patterns across VS and LO tasks in the CARA benchmark [5] [50]:

Virtual Screening Performance:

• Meta-learning and multi-task training strategies significantly improve VS task performance
• Enrichment factors at 1% (EF@1%) range from 5.2 to 18.7 across different model architectures
• Success rates (SR@1%) vary substantially, with best-performing models achieving ~45% success across VS assays
• Models demonstrate better performance on kinase-specific VS tasks compared to general VS tasks

Lead Optimization Performance:

• Standard QSAR models trained on individual assays achieve competitive performance for LO tasks
• Correlation coefficients (Pearson) range from 0.3 to 0.65 across different congeneric series
• Activity cliff prediction remains challenging for all model architectures
• Model performance is more consistent across LO tasks compared to VS tasks

TDC Benchmark Group Performance

Evaluations across TDC benchmark groups reveal important patterns in model generalization [51] [54]:

ADMET Group Performance:

• Best-performing models achieve MAE of 0.234 on Caco2_Wang permeability prediction
• Performance variability is observed across different ADMET endpoints
• Graph neural networks generally outperform traditional machine learning on molecular properties
• Scaffold split performance typically drops 15-30% compared to random splits

Multi-task Learning Benefits:

• Multi-task training improves performance on data-rich endpoints but can hurt performance on data-scarce endpoints
• Transfer learning from large molecular datasets improves few-shot learning capability
• Model performance correlates with training set size and chemical space coverage

Research Reagent Solutions

The following table details essential computational tools and resources for conducting benchmarked QSAR research:

Table 5: Essential Research Reagents for Benchmark QSAR Studies

Resource Category	Specific Tools	Function	Access
Primary Data Sources	ChEMBL, PubChem, BindingDB	Experimental activity data provision	Public web access
Benchmark Platforms	TDC, CARA	Model evaluation & comparison	Python APIs, GitHub
Chemical Representation	RDKit, Mordred	Molecular featurization & fingerprinting	Open-source Python packages
Deep Learning Frameworks	PyTorch, TensorFlow, DGL, PyG	Model implementation & training	Open-source
Specialized Prediction Tools	OPERA, admetSAR, MolTarPred	Baseline model implementation	Various (web, standalone)
Visualization & Analysis	t-SNE, PCA, Matplotlib	Chemical space analysis & result visualization	Open-source Python packages

QSAR Benchmarking Ecosystem

Based on comprehensive comparison of these benchmarking resources, we provide the following recommendations for different research scenarios:

For Virtual Screening and Lead Optimization Studies: CARA provides the most realistic evaluation framework due to its careful distinction between VS and LO tasks, rigorous splitting schemes that prevent data leakage, and task-appropriate evaluation metrics. Researchers should prioritize CARA for evaluating compound activity prediction models destined for practical drug discovery applications.

For Broad ADMET Property Prediction: TDC offers unparalleled coverage of absorption, distribution, metabolism, excretion, and toxicity endpoints with standardized evaluation protocols. Its benchmark group structure enables coordinated model development across multiple related properties, while its leaderboard system facilitates objective model comparison.

For Methodological Development and Algorithm Comparison: Both TDC and CARA provide robust evaluation frameworks, though TDC's broader scope may be advantageous for assessing general-purpose molecular machine learning methods. The requirement for multiple independent runs in both platforms ensures statistically reliable performance assessment.

For Real-world Applicability Assessment: CARA's assay-level evaluation and success rate metrics provide more clinically relevant performance indicators than aggregate metrics alone. Its focus on ranking quality rather than absolute value prediction aligns with practical medicinal chemistry decision-making.

The complementary strengths of these benchmarks suggest that comprehensive model evaluation should ideally incorporate both resources—using TDC for broad capability assessment and CARA for specific activity prediction tasks. As the field advances, continued development of biologically realistic benchmarks with appropriate evaluation metrics will be essential for translating computational advances into improved therapeutic outcomes.

Overcoming Common Pitfalls: Data, Design, and Performance Optimization

In quantitative structure-activity relationship (QSAR) research, data quality serves as the foundational element determining the predictive accuracy and reliability of machine learning models. The presence of dirty data—characterized by duplicates, inconsistencies, and noise—directly undermines model performance and compromises scientific validity, potentially costing organizations millions annually and significantly delaying drug discovery pipelines [55] [56]. Within this context, assay data presents unique challenges, as noisy process data from experimental measurements can obscure genuine signals and lead to flawed interpretations.

This guide provides a systematic comparison of contemporary data quality techniques and tools, benchmarking their performance specifically for QSAR applications. We evaluate traditional statistical methods against emerging machine learning and quantum-inspired approaches, providing researchers with experimental protocols and quantitative comparisons to inform their data quality strategies. The focus extends beyond basic cleaning to address the sophisticated challenges of standardizing diverse chemical data and detecting meaningful signals within noisy assay environments.

Foundational Data Quality Techniques

Effective data quality management employs several core techniques that work synergistically to transform raw, inconsistent data into a reliable resource for QSAR modeling.

Data Cleansing Core Components

• Data Deduplication: This process identifies and consolidates duplicate records representing the same entity (e.g., the same chemical compound entered multiple times with slight variations). Sophisticated matching algorithms detect duplicates even with variations in spelling, formatting, or missing information. Implementation involves starting with exact matches, progressing to fuzzy matching, establishing confidence scores for potential duplicates, and thorough testing before full deployment [55].

• Missing Value Imputation: Instead of deleting incomplete records—which can introduce bias and reduce statistical power—imputation replaces null or empty values with estimated values using statistical methods or algorithms. Techniques range from simple mean/median replacement to advanced methods like K-Nearest Neighbors (KNN) or multiple imputation, which account for relationships between variables and uncertainty in predictions [55].

• Outlier Detection and Treatment: This technique identifies data points that significantly deviate from the dataset's expected pattern or range. Outliers may arise from data entry errors, measurement artifacts, or genuine rare events. Detection methods include visual approaches (box plots, scatter plots) and statistical measures (Z-score, Interquartile Range). Treatment requires domain expertise to determine whether to remove, cap, or transform outliers, as some may represent valuable scientific anomalies [55].

Data Standardization Framework

Data standardization creates a consistent, uniform format for all data elements, enabling reliable comparison and integration across diverse sources. For QSAR research, this is particularly crucial when combining data from multiple assays, laboratories, or literature sources.

The standardization process follows a structured framework:

• Define Data Standards: Establish clear rules for each data element's format (e.g., canonical SMILES for chemical structures, standardized units for biological activity measurements) [57] [58].
• Profile and Audit: Assess existing data to identify inconsistencies and variations from the defined standards [57].
• Clean and Prepare: Remove duplicates and correct obvious errors before transformation [57].
• Apply Standardization Rules: Transform data into the standardized format using automated tools or scripts [57].
• Validate and Govern: Verify transformation accuracy and implement ongoing monitoring to maintain standards [57] [58].

Key standardization methods particularly relevant to chemical and biological data include data type standardization (ensuring consistent formats for dates, numerical values, etc.), textual standardization (case conversion, punctuation removal, abbreviation expansion), and numeric standardization (unit conversion, precision control) [57].

Table 1: Core Data Cleansing Techniques and Their Applications in QSAR Research

Technique	Primary Function	QSAR Application Example	Key Considerations
Data Deduplication [55]	Identifies/merges duplicate records	Consolidating multiple entries for the same chemical compound from different literature sources	Fuzzy matching algorithms essential for handling naming variations and typographical errors
Missing Value Imputation [55]	Replaces null/missing values	Estimating missing IC₅₀ values using molecular similarity or other structural descriptors	Choice of method (mean, KNN, regression) depends on missingness pattern and data structure
Outlier Detection [55]	Flags anomalous data points	Identifying potentially erroneous activity measurements or structural outliers	Requires domain expertise to distinguish measurement error from genuinely novel activity
Data Validation [55]	Checks accuracy against rules/sources	Verifying chemical structure validity and adherence to structural rules	Automated validation rules can flag physically impossible structures or activity values
Data Standardization [57]	Enforces consistent formats	Converting diverse activity measurements (e.g., Ki, IC₅₀) to standardized units and formats	Essential for combining datasets from multiple sources for model training

Advanced Methods for Noisy Assay Data

Assay data inherently contains various types of noise originating from biological variability, measurement imperfections, and environmental fluctuations. Traditional statistical process control methods are increasingly being augmented with machine learning approaches to detect subtle but scientifically significant shifts in noisy processes.

Traditional Statistical Control Methods

• Cumulative Sum (CUSUM) Charts: These control charts plot the cumulative sum of deviations from a process target value, making them highly effective for detecting small, persistent shifts in process mean. CUSUM charts are particularly valuable for identifying gradual drifts in assay performance that might otherwise go unnoticed [59].

• Exponentially Weighted Moving Average (EWMA) Charts: EWMA charts apply weighting factors that decrease exponentially, giving more importance to recent observations while still retaining some influence from historical data. This "limited memory" approach makes EWMA effective for detecting smaller shifts than traditional Shewhart control charts, while remaining relatively robust to normality assumptions [59].

Both CUSUM and EWMA methods require parameter tuning (e.g., K and H values for CUSUM, lambda smoothing factor for EWMA) to optimize sensitivity for detecting meaningful changes while minimizing false alarms from random noise [59].

Machine Learning and Quantum-Inspired Approaches

• Fused Lasso for Change Point Detection: This machine learning method, implemented through generalized regression, automatically identifies points in a dataset where the statistical properties change. Unlike traditional control charts that require parameter tuning, Fused Lasso can detect multiple change points in noisy data with minimal user intervention, making it particularly valuable for analyzing complex assay data where shift patterns may not be well understood in advance [59].

• Quantum-Inspired Methods: Recent research has developed quantum-inspired approaches that use quantum mathematical structures to represent complex data more efficiently. These methods, which can run on classical computers, improve intrinsic dimension estimation—a key technique for understanding dataset complexity that is often compromised by noise. This approach demonstrates particular promise for managing large, noisy datasets in fields like healthcare and epigenetics [60].

• Quantum Machine Learning for QSAR: Emerging research explores quantum machine learning classifiers for QSAR prediction, with studies suggesting they may outperform classical classifiers when limited training data or features are available. This quantum advantage in generalization power could prove valuable for QSAR modeling where high-quality experimental data is scarce or expensive to obtain [38].

Table 2: Comparison of Methods for Handling Noisy Assay Data

Method	Primary Strength	Implementation Complexity	Parameter Sensitivity	Best Suited Noise Pattern
CUSUM Charts [59]	Detects small, persistent mean shifts	Moderate	High - requires tuning of K and H parameters	Slow drifts, persistent bias
EWMA Charts [59]	Detects small shifts with limited memory	Moderate	Medium - requires lambda smoothing factor selection	Moderate, sustained shifts
Fused Lasso [59]	Automatic change point detection	High (requires specialized implementation)	Low - minimal parameter tuning needed	Multiple abrupt mean changes
Partition Platform [59]	Intuitive breakpoint identification	Low	Medium - requires specifying split criteria	Simple, distinct mean shifts
Quantum-Inspired [60]	Robust intrinsic dimension estimation in noise	High (emerging methodology)	Research stage - still being characterized	High-dimensional, complex noise

Experimental Protocols for Method Validation

Benchmarking Methodology for Data Quality Techniques

To objectively compare the performance of various data quality methods, researchers should implement a standardized benchmarking protocol:

• Dataset Selection and Preparation: Utilize well-characterized QSAR datasets with known properties, such as the estrogen receptor-binding activity dataset used in developing 3D-QSAR models [44]. Artificially introduce controlled amounts of specific data quality issues (duplicates, missing values, noise) to create a ground truth for evaluation.

• Performance Metrics Definition: Establish quantitative metrics relevant to QSAR applications, including:

  • Accuracy/Sensitivity/Selectivity for classification-based quality checks [44]
  • Mean Squared Error for imputation methods
  • Change Point Detection Accuracy for noise handling methods (true positive rate, false discovery rate)
  • Computational Efficiency (processing time, memory requirements)

• Model Training and Validation: Apply identical machine learning algorithms (e.g., Random Forest, Support Vector Machine, Multilayer Perceptron) to datasets processed with different quality techniques. Use rigorous cross-validation and external validation sets to assess generalization performance [44].

• Statistical Significance Testing: Employ appropriate statistical tests to determine whether performance differences between methods are statistically significant, rather than resulting from random variation.

Workflow for Integrated Data Quality Management

The following workflow diagram illustrates a comprehensive approach to managing data quality throughout the QSAR research pipeline:

Experimental Protocol for Signal Detection in Noisy Assay Data

For researchers specifically investigating method performance on noisy assay data, the following protocol provides a structured approach:

• Data Simulation: Generate synthetic assay data with known underlying signals (e.g., periodic patterns, step changes, gradual drifts) superimposed on controlled noise structures (Gaussian, Poisson, or more complex noise models).

• Method Implementation:

  • Apply CUSUM and EWMA control charts with systematically varied parameters [59]
  • Implement Fused Lasso change point detection using generalized regression frameworks [59]
  • Apply partition methods for breakpoint identification
  • Test quantum-inspired dimension estimation techniques where available [60]

• Performance Evaluation: Quantify each method's ability to accurately detect known change points while minimizing false positives across varying signal-to-noise ratios.

• Real-World Validation: Apply top-performing methods to historical assay data with documented process changes or quality events to verify real-world applicability.

Essential Research Reagents and Computational Tools

The experimental comparison of data quality methods requires both computational tools and reference datasets. The following table catalogues key resources mentioned in the literature:

Table 3: Essential Research Reagents and Tools for Data Quality Experiments

Tool/Category	Specific Examples	Primary Function	QSAR Research Application
Data Cleansing Platforms [61]	Integrate.io, Tibco Clarity, DemandTools	Automated data validation, deduplication, standardization	Preparing large chemical datasets for analysis
Statistical Analysis Software [59]	JMP Pro with CUSUM, EWMA, Fused Lasso	Statistical process control, change point detection	Identifying shifts or drifts in assay data quality
Machine Learning Environments [44]	Python Scikit-learn, R MICE package	Advanced imputation, outlier detection, model validation	Implementing ML-based 3D-QSAR models and data quality checks
Quantum Machine Learning [38]	Quantum classifiers for QSAR	QSAR prediction with limited data	Exploring quantum advantages in data-efficient learning
Reference Datasets [44]	Estrogen receptor-binding activity data	Benchmarking and method validation	Testing data quality method performance on known biological endpoints
Data Standardization Tools [61]	Informatica Cloud Data Quality, Oracle EDQ	Enforcing data formats, rules, and governance	Maintaining consistent data structures across QSAR datasets

Comparative Performance Analysis

Quantitative Benchmarking Results

Based on experimental evaluations across multiple studies, we can summarize the comparative performance of different approaches:

• Machine Learning vs. Traditional QSAR Models: In direct comparisons, machine learning-based 3D-QSAR models employing algorithms like Multilayer Perceptron (MLP), Random Forest (RF), and Support Vector Machine (SVM) have demonstrated superior accuracy, sensitivity, and selectivity compared to traditional VEGA models for predicting estrogen receptor-binding activity [44].

• Quantum-Classical Hybrid Performance: Research on quantum machine learning for QSAR with incomplete data suggests that quantum classifiers can outperform classical counterparts when limited features are available and training data is scarce, highlighting a potential quantum advantage in data-efficient learning scenarios relevant to drug discovery [38].

• Change Point Detection Methods: In comparative studies of methods for detecting low-level shifts in noisy process data, Fused Lasso approaches have shown advantages in automatically identifying multiple change points without extensive parameter tuning, while traditional CUSUM and EWMA methods remain highly effective for detecting specific shift patterns when properly configured [59].

Practical Implementation Recommendations

Based on the aggregated experimental evidence:

• For Standard QSAR Data Quality: Implement a layered approach combining traditional deduplication and standardization [55] [57] with machine learning-based validation [44], particularly for high-value datasets where accuracy is critical.

• For Noisy Assay Data: Begin with traditional control charts (CUSUM/EWMA) for ongoing process monitoring [59], employing Fused Lasso or partition methods for retrospective analysis of historical data to identify undocumented process changes.

• For Data-Scarce Scenarios: Explore emerging quantum-inspired methods [60] and quantum machine learning approaches [38] when working with limited training data or features, particularly in early-stage discovery where experimental data is expensive to acquire.

• Tool Selection Strategy: Choose platforms that support automated validation and standardization at scale [61] [58], prioritizing those with specialized functionality for chemical and biological data types commonly encountered in QSAR research.

The optimal data quality strategy depends significantly on specific research contexts, including data volume, noise characteristics, and computational resources. A thoughtful, multi-method approach consistently outperforms reliance on any single technique, providing robust data quality assurance across the diverse challenges encountered in QSAR research.

Advanced Feature Selection and Hyperparameter Tuning for Enhanced Generalization

In modern Quantitative Structure-Activity Relationship (QSAR) research, the transition from simple linear models to sophisticated machine learning (ML) frameworks has introduced both unprecedented opportunities and significant challenges in predictive generalization. The core dilemma lies in balancing model complexity with interpretability while ensuring robust performance on unseen chemical data. As chemical space expands with billions of potential compounds, the selection of optimal feature representations and hyperparameters becomes increasingly critical for developing reliable predictive models in computational drug discovery and cheminformatics [1]. This comparative guide examines current methodologies, performance benchmarks, and practical protocols for enhancing generalization capabilities in QSAR research, providing researchers with evidence-based recommendations for model selection and optimization.

The evolution from classical statistical approaches to AI-integrated QSAR modeling has fundamentally transformed the field. Modern QSAR now incorporates advanced machine learning and deep learning approaches, including graph neural networks and SMILES-based transformers, which require sophisticated feature selection and tuning strategies to prevent overfitting and ensure generalizability [1]. This guide objectively evaluates the current landscape of feature selection techniques and hyperparameter optimization methods through systematic benchmarking, providing researchers with actionable insights for developing more robust and generalizable QSAR models.

Comparative Performance Benchmarking

Algorithm Performance Across QSAR Tasks

Table 1: Comparative performance of machine learning algorithms across different QSAR studies

Algorithm	Application Context	Performance Metrics	Key Strengths	Limitations
Ridge/Lasso Regression	Predicting physicochemical properties using topological indices [62] [63]	Test MSE: 3540.23-3617.74, R²: 0.9322-0.9374 [62] [63]	Effective multicollinearity handling, prevents overfitting [62] [63]	Limited nonlinear pattern capture
Gradient Boosting (XGBoost)	Pyrazole corrosion inhibition prediction [9]	Training R²: 0.96, Test R²: 0.75 (2D descriptors) [9]	Strong predictive ability, handles complex relationships [9]	Requires extensive hyperparameter tuning [62]
Random Forest	ADMET prediction benchmarks [11]	Varied performance across datasets [11]	Robust to noise, built-in feature importance [1]	Performance variability across chemical spaces [11]
Support Vector Machines (SVM)	BCRP inhibitor classification [64]	Effective for complex, small-medium datasets [64]	Effective in high-dimensional spaces [64] [1]	Sensitive to hyperparameter choices [64]
Quantum Machine Learning	QSAR with incomplete data [38]	Superior performance with limited features/Data [38]	Enhanced generalization with data scarcity [38]	Emerging technology, limited accessibility

Impact of Optimization on Model Performance

Table 2: Hyperparameter optimization impact on model performance

Model	Before Optimization	After Optimization	Optimization Method	Performance Gain
Gradient Boosting [62] [63]	MSE: 4488.04, R²: 0.5659 [62] [63]	MSE: 1494.74, R²: 0.9171 [62] [63]	Expanded hyperparameter grid via GridSearchCV [62] [63]	66.7% MSE reduction, 62.1% R² improvement
Deep Neural Network [64]	Dependent on initial configuration [64]	Optimized architecture and parameters [64]	Bayesian optimization with preliminary grid search [64]	Significant but unquantified improvement reported [64]
Multiple ML Algorithms [64]	Suboptimal hyperparameters [64]	Task-specific tuned parameters [64]	Bayesian optimization via mlrMBO package in R [64]	Enhanced cross-validation MCC values [64]

Experimental Protocols and Workflows

Standardized QSAR Modeling Pipeline

The following workflow represents a consensus methodology derived from multiple recent QSAR studies, integrating best practices for feature selection, model training, and validation:

Data Preparation and Cleaning: The initial phase involves rigorous data collection and preprocessing. Studies consistently emphasize the importance of data cleaning to address issues such as "inconsistent SMILES representations, duplicate measurements with varying values, and inconsistent binary labels" [11]. Standardization includes removing inorganic salts and organometallic compounds, extracting organic parent compounds from salt forms, adjusting tautomers for consistent functional group representation, canonicalizing SMILES strings, and de-duplication with consistency checks [11]. For instance, in pesticide toxicity modeling, a dataset of 311 pesticides was refined to 299 compounds after excluding outliers with high residuals to enhance model reliability [65].

Molecular Descriptor Calculation and Feature Selection: Diverse molecular descriptors are computed, ranging from 1D descriptors (e.g., molecular weight), 2D topological indices [62] [63], to 3D descriptors accounting for molecular shape and electrostatic properties [1]. Feature selection is critical for enhancing model interpretability and preventing overfitting. Commonly employed techniques include Select KBest approach [9], LASSO for automatic feature selection [1], principal component analysis (PCA) for dimensionality reduction [38] [1], and recursive feature elimination (RFE) [1]. In advanced workflows, similarity-based read-across descriptors (q-RASAR) are integrated with conventional molecular descriptors to further improve predictive performance [65].

Hyperparameter Optimization Framework

Optimization Protocols: Advanced QSAR studies employ sophisticated hyperparameter tuning strategies that move beyond basic grid search. The Bayesian optimization (model-based optimization) algorithm has emerged as a compelling global optimization method for black-box functions that "can obtain an ideal solution only after a few objective function evaluations by designing appropriate surrogate model and acquisition function" [64]. A common protocol involves an initial coarse hyperparameter tuning based on grid search within relatively wide ranges to determine smaller regions where models perform well, followed by Bayesian optimization to zoom into these regions and find optimal settings [64]. For the DNN model in BCRP inhibitor classification, fixed parameters included the ADADELTA optimizer and ReLU activation function, with all configurations trained for 300 epochs [64].

Validation and Significance Testing: To enhance reliability, modern benchmarking incorporates cross-validation with statistical hypothesis testing, adding a robust layer to model evaluation [11]. This approach is particularly valuable in noisy domains like ADMET prediction. Furthermore, practical scenario evaluation—where models trained on one data source are tested on another—provides critical insights into real-world generalization capabilities [11]. Studies also emphasize the importance of assessing applicability domains using tools like Williams and Insubria plots to identify when predictions fall outside reliable boundaries [65].

The QSAR Researcher's Toolkit

Essential Research Reagents and Computational Solutions

Table 3: Essential tools and resources for advanced QSAR modeling

Tool/Resource	Type	Primary Function	Application Examples
RDKit [11] [1]	Cheminformatics Library	Molecular descriptor calculation, fingerprint generation	RDKit descriptors, Morgan fingerprints [11]
Scikit-learn [1]	Machine Learning Library	ML algorithms implementation, feature selection	Linear models, SVM, RF, feature selection techniques [1]
Caret Package (R) [64]	Modeling Framework	Simplified model training, preprocessing	Traditional ML methods implementation [64]
H2O Package (R) [64]	Deep Learning Platform	DNN implementation and training	Deep neural network modeling [64]
Chemprop [11]	Deep Learning Library	Message Passing Neural Networks	Molecular property prediction [11]
Bayesian Optimization [64]	Optimization Algorithm	Hyperparameter tuning	mlrMBO package for R [64]
GridSearchCV [62] [63]	Hyperparameter Tuning	Exhaustive parameter search	Systematic hyperparameter optimization [62] [63]
SHAP Analysis [9]	Interpretability Framework	Model prediction interpretation	Identifying key influential descriptors [9]
Select KBest [9]	Feature Selection Method	Univariate feature selection	Selecting most relevant molecular descriptors [9]
PCA [38] [1]	Dimensionality Reduction	Feature space simplification	Reducing descriptor dimensionality [38] [1]

Discussion and Future Directions

Key Findings and Practical Implications

The benchmarking analysis reveals several critical insights for QSAR researchers. First, simpler models like Ridge and Lasso Regression frequently outperform more complex alternatives for datasets with inherent linear relationships, achieving superior test MSE (3617.74 and 3540.23, respectively) and R² scores (0.9322 and 0.9374, respectively) in predicting physicochemical properties [62] [63]. This demonstrates that model complexity doesn't automatically guarantee better performance and underscores the importance of matching algorithm selection to dataset characteristics.

Second, hyperparameter optimization consistently delivers substantial performance improvements across model types. The dramatic enhancement of Gradient Boosting Regression—from initial MSE of 4488.04 to 1494.74 after tuning [62] [63]—highlights the critical value of systematic parameter optimization. Similarly, Bayesian optimization has proven particularly valuable for efficiently navigating complex hyperparameter spaces [64].

Third, feature representation selection significantly impacts model performance, with different descriptor types showing varying suitability across prediction tasks. Recent research emphasizes moving beyond arbitrary feature concatenation toward systematic representation selection informed by dataset characteristics [11]. Emerging approaches like quantum machine learning show particular promise for scenarios with limited data availability, demonstrating superior generalization power when feature numbers and training samples are constrained [38].

Future Research Directions

The field is rapidly evolving toward more sophisticated integration of AI methodologies with traditional QSAR approaches. Graph neural networks and SMILES-based transformers represent promising directions for capturing complex structural relationships [1]. Additionally, quantitative Read-Across Structure-Activity Relationship (q-RASAR) models that integrate conventional molecular descriptors with similarity and error-based metrics offer enhanced predictive performance and mechanistic interpretability [65].

Future research must also address the critical challenge of model interpretability and regulatory acceptance. Techniques like SHAP (SHapley Additive exPlanations) analysis are increasingly important for identifying key descriptors influencing predictions and providing mechanistic insights into structure-activity relationships [9]. As the field progresses, developing standardized benchmarking protocols and validation frameworks will be essential for advancing reliable QSAR modeling in drug discovery and environmental toxicology applications.

Traditional metrics like balanced accuracy often fail to capture true model utility in virtual screening, where active compounds are exceptionally rare. This paradigm shift champions Precision (Positive Predictive Value, PPV) as the critical metric for imbalanced QSAR tasks. Evidence from benchmarking studies on ADMET properties and skin sensitization confirms that models optimized for precision significantly enhance the cost-effectiveness of drug discovery by prioritizing the reliable identification of true active compounds, thereby reducing wasted experimental resources on false positives [66] [11] [67].

The Imbalance Problem in Virtual Screening

Virtual screening represents a quintessential imbalanced classification problem. The fundamental challenge is that the number of potentially active compounds (the positive class) is drastically outnumbered by the number of inactive compounds (the negative class). In this context, standard evaluation metrics become misleading.

• The Failure of Accuracy: A model that simply predicts "inactive" for all compounds can achieve over 99% accuracy in a screen where only 1% of compounds are active, despite being practically useless [66] [68].
• The Limitations of Balanced Accuracy: While balanced accuracy mitigates this issue by averaging the accuracy per class, it still treats false positives and false positives as equally costly, which is rarely the case in resource-intensive experimental follow-up [67].

The following workflow illustrates the critical decision points in model evaluation for imbalanced virtual screening, highlighting the pivotal role of precision.

Evaluating Classifiers for Imbalanced Virtual Screening

Critical Evaluation Metrics for Imbalanced Data

Understanding the limitations of balanced accuracy requires a deeper look at the metrics that truly matter when positive examples are scarce.

The Precision (PPV) Imperative

Precision (or Positive Predictive Value) answers the critical question for a project lead: "When my model says a compound is active, how often is it correct?" [66] [69]. Mathematically, it is defined as:

[ \text{Precision} = \frac{TP}{TP + FP} ]

A high-precision model ensures that resources are not wasted on experimentally validating false positives. In a typical virtual screening workflow, this translates directly to higher productivity and lower costs [69].

The Supporting Cast of Metrics

While precision is paramount, it should not be evaluated in isolation.

• Recall (Sensitivity/TPR): Measures the model's ability to find all the active compounds (\text{Recall} = \frac{TP}{TP + FN}). A high recall is important when missing a true active (a false negative) is very costly [66].
• F1 Score: The harmonic mean of precision and recall (\text{F1} = 2 \times \frac{\text{Precision} \times \text{Recall}}{\text{Precision} + \Recall}). It provides a single score to balance both concerns, but may not emphasize precision sufficiently for all virtual screening contexts [66] [70].
• PR AUC (Area Under the Precision-Recall Curve): More informative than the ROC AUC for imbalanced data, as it focuses directly on the performance of the positive class (actives) without being influenced by the large number of negatives [70].
• Specificity (TNR): Measures the model's ability to correctly identify inactive compounds (\text{Specificity} = \frac{TN}{TN + FP}). While relevant, its impact is often overshadowed by the class imbalance [68].

Table 1: Key Metrics for Imbalanced Classification in Virtual Screening

Metric	Definition	Interpretation in Virtual Screening	When to Prioritize
Precision (PPV)	(\frac{TP}{TP + FP})	Proportion of predicted actives that are true actives.	Always critical when experimental follow-up is expensive.
Recall (Sensitivity)	(\frac{TP}{TP + FN})	Proportion of all true actives that are found.	When the cost of missing an active compound is prohibitively high.
F1 Score	(2 \times \frac{\text{Precision} \times \text{Recall}}{\text{Precision} + \text{Recall}})	Balance between precision and recall.	For a single metric that balances both FP and FN.
PR AUC	Area under Precision-Recall curve	Overall model performance across thresholds, focused on the positive class.	Superior to ROC AUC for imbalanced data; evaluates ranking of actives.
Balanced Accuracy	(\frac{Sensitivity + Specificity}{2})	Average of per-class accuracy.	Can be misleading as it weights FPs and FNs equally, which is often unrealistic.

Benchmarking Evidence: Precision-Driven Performance

Recent benchmarking studies in cheminformatics provide compelling data for this paradigm shift, demonstrating that model and metric selection drastically impacts practical outcomes.

ADMET Feature Representation Benchmark

A 2025 benchmarking study of machine learning for ADMET predictions highlighted the impact of feature representation and model selection. The study, which performed rigorous cross-validation and statistical testing, provides a template for robust evaluation. While the study compared multiple metrics, its structured approach to identifying optimal model configurations directly supports the goal of improving predictive reliability, which is the foundation of high precision [11].

Table 2: Performance Snippet from ADMET Benchmarking Study (Best Performing Models Shown)

Dataset	Best Model	Key Feature Representation	Noteworthy Metric Performance
Clearance (Microsomal)	LightGBM	Combined Descriptors & Fingerprints	High precision in identifying low-clearance compounds.
Solubility	Random Forest	RDKit Descriptors	Strong regression performance (R²), enabling reliable ranking.
PPBR	SVM	Molecular Fragments	Effective classification impacting plasma binding predictions.

Experimental Protocol: The benchmark involved [11]:

• Data Curation: Public ADMET datasets from TDC and others were cleaned (standardizing SMILES, removing salts, deduplication).
• Feature Selection: A structured evaluation of molecular representations (fingerprints, descriptors, deep-learned features) and their combinations.
• Model Training: Multiple algorithms (SVM, Random Forest, LightGBM, MPNN) were trained.
• Robust Evaluation: Combined cross-validation with statistical hypothesis testing to validate performance differences.
• Performance Assessment: Models were evaluated on hold-out test sets and in a practical cross-source scenario (model trained on one data source, tested on another).

Skin Sensitization QSAR Model

A QSAR study for skin sensitization based on the BMDC assay developed a predictive model using Support Vector Machines (SVM) and molecular fragment descriptors. The model's performance was evaluated using balanced accuracy. However, the context of the assay's application—prioritizing chemicals for further testing—means that precision is a critical, albeit less highlighted, metric. A model with high precision ensures that resources are focused on compounds most likely to be true sensitizers [67].

Table 3: Performance of BMDC Assay and QSAR Model in Skin Sensitization Prediction

Method	Sensitivity (Recall)	Specificity	Balanced Accuracy	Implied Practical Focus
BMDC Assay (Experimental)	High	High	0.82 (vs. LLNA)	Reliability in detecting true sensitizers (Recall) & non-sensitizers.
QSAR Model (SVM)	--	--	0.82 (5-CV)	Cost-effective, rapid prioritization of potential sensitizers (Precision).

Experimental Protocol: The study involved [67]:

• Data Collection: Experimentally generated BMDC assay data for 123 substances.
• Descriptor Calculation: ISIDA software was used to compute molecular fragment descriptors.
• Model Training: An SVM was trained to classify chemicals as sensitizers or non-sensitizers based on the BMDC data.
• Validation: Model performance was assessed via 5-fold cross-validation, reporting balanced accuracy.

The Scientist's Toolkit: Essential Research Reagents

Implementing a precision-focused virtual screening pipeline requires a suite of computational tools and data resources.

Table 4: Essential "Research Reagents" for Precision-Focused QSAR

Tool / Resource	Type	Function in the Workflow
RDKit	Cheminformatics Library	Calculates molecular descriptors (rdkit_desc) and fingerprints (e.g., Morgan), which are crucial features for classical ML models [11].
Therapeutics Data Commons (TDC)	Data Repository	Provides curated, public benchmarks for ADMET and other molecular properties, enabling robust and standardized model evaluation [11].
Scikit-learn	ML Library	Provides implementations of SVM, Random Forest, and functions for calculating metrics (precisionscore, averageprecision_score) and cross-validation [70].
LightGBM / CatBoost	Gradient Boosting Library	High-performance tree-based algorithms that often achieve top results in benchmarking studies and handle class imbalance well [11] [71].
CycPeptMPDB	Specialized Database	Curated database of cyclic peptide membrane permeability; an example of a high-quality, application-specific dataset for training reliable models [4].

The evidence from contemporary benchmarking studies is clear: clinging to balanced accuracy as a primary metric for virtual screening is a suboptimal strategy. The field must undergo a paradigm shift towards a precision-first mindset. By consciously selecting models and thresholds that maximize PPV, and validating them using metrics like PR AUC, researchers can deliver QSAR models that directly enhance the efficiency and success rate of drug discovery campaigns. This approach ensures that computational predictions translate into tangible, cost-effective experimental gains.

Expanding Chemical Space Coverage with Federated Learning and Multi-Task Architectures

The accelerating growth of make-on-demand chemical libraries, which currently contain over 70 billion readily available molecules, presents unprecedented opportunities for drug discovery [40]. However, this vastness also represents a fundamental challenge: the experimental data used to train predictive quantitative structure-activity relationship (QSAR) models captures only limited sections of this immense chemical space [46]. When models encounter novel molecular scaffolds or compounds outside their training distribution, predictive performance degrades significantly, contributing to the high failure rates in drug development, where approximately 40–45% of clinical attrition is still attributed to unfavorable absorption, distribution, metabolism, excretion, and toxicity (ADMET) properties [46].

To address this limitation, two innovative machine learning paradigms have emerged: federated learning and multi-task architectures. Federated learning enables collaborative model training across distributed proprietary datasets without centralizing sensitive data, thereby systematically expanding the chemical space a model can learn from [46]. Multi-task learning leverages shared information across related prediction tasks to improve generalization and data efficiency [72]. This guide provides a comparative analysis of these approaches, examining their performance, experimental protocols, and applicability for expanding chemical space coverage in drug discovery.

Federated Learning for Chemical Space Expansion

Core Concept and Workflow

Federated learning provides a methodological framework for training machine learning models across multiple decentralized data sources without exchanging or centralizing the underlying data. In the context of drug discovery, this allows pharmaceutical companies, research institutions, and other stakeholders to collaboratively improve model performance while maintaining complete governance and ownership of their proprietary datasets [46] [73]. The fundamental premise is that each organization's experimental assays describe only a small fraction of relevant chemical space, making isolated modeling efforts inherently limited.

The typical federated learning workflow involves these key steps:

• Initialization: A central server initializes a global model architecture and shares it with all participating partners.
• Local Training: Each partner trains the model on their local, private dataset.
• Parameter Aggregation: Partners send only the model parameter updates (not the data) to the central server.
• Model Averaging: The server aggregates these updates to create an improved global model.
• Iteration: Steps 2-4 are repeated for multiple rounds to refine the model.

Experimental Evidence and Performance Metrics

Large-scale cross-pharma collaborations have consistently demonstrated the advantages of federated learning for expanding chemical space coverage. The MELLODDY project, which involved collaboration across multiple pharmaceutical companies, demonstrated that federated learning systematically outperforms local baselines, with performance improvements scaling with the number and diversity of participants [46].

Table 1: Performance Benefits of Federated Learning in ADMET Prediction

Metric	Performance Improvement	Study Reference
Prediction Error Reduction	40-60% reduction across endpoints including human and mouse liver microsomal clearance, solubility (KSOL), and permeability (MDR1-MDCKII)	Polaris ADMET Challenge [46]
Applicability Domain	Expanded model robustness when predicting across unseen scaffolds and assay modalities	Heyndrickx et al., JCIM 2023 [46]
Data Heterogeneity Handling	Superior models for all contributors even when assay protocols, compound libraries, or endpoint coverage differed substantially	Heyndrickx et al., 2023; Zhu et al., Nat. Commun. 2022 [46]
Multi-task Settings	Largest gains for pharmacokinetic and safety endpoints where overlapping signals amplify one another	Heyndrickx et al., 2023; Wenzel et al., JCIM 2019 [46]

A novel approach called FLuID (Federated Learning Using Information Distillation) further enhances this framework by employing a data-centric approach that leverages knowledge distillation to federate information effectively across multiple organizations [73]. This method ensures original private labels remain anonymous and untraceable, addressing data protection and governance requirements while being model-agnostic to support various machine learning techniques [73].

Experimental Protocol for Federated Learning Implementation

For researchers seeking to implement federated learning, the following experimental protocol, based on best practices from the Apheris Federated ADMET Network, ensures rigorous and reproducible results [46]:

• Data Validation and Preparation

  • Perform sanity checks and assay consistency checks with normalization
  • Slice data by scaffold, assay, and activity cliffs to assess modelability
  • Apply rigorous data curation standards to ensure quality

• Model Training and Evaluation

  • Implement scaffold-based cross-validation runs across multiple seeds and folds
  • Evaluate a full distribution of results rather than a single score
  • Apply appropriate statistical tests to distinguish real gains from random noise

• Benchmarking

  • Compare against various null models and noise ceilings
  • Assess how performance improvement translates to improved molecule prioritization

The following diagram illustrates the logical workflow and relationships in a federated learning system for drug discovery:

Multi-Task Architectures for Chemical Space Exploration

Core Concept and Methodological Innovations

Multi-task learning (MTL) represents a different approach to expanding chemical space coverage by leveraging shared information across related prediction tasks. Rather than training separate models for each molecular property, MTL jointly trains a single model on multiple tasks, allowing it to discover underlying patterns and relationships that improve generalization [72]. This is particularly valuable for ADMET prediction, where different properties often share common structural determinants.

The QW-MTL (Quantum-enhanced and task-Weighted Multi-Task Learning) framework exemplifies recent advancements in this area [72]. This innovative approach addresses two key challenges in MTL for drug discovery:

• Representation Enhancement: Incorporation of quantum chemical (QC) descriptors to enrich molecular representations with electronic structure and interaction information that is crucial for accurately predicting pharmacokinetic and toxicity properties.
• Dynamic Task Balancing: Introduction of a novel exponential task weighting scheme that combines dataset-scale priors with learnable parameters to dynamically balance losses across tasks during training.

Experimental Evidence and Performance Metrics

QW-MTL has demonstrated superior performance across standardized benchmarks, significantly outperforming single-task baselines on 12 out of 13 ADMET classification tasks from the Therapeutics Data Commons (TDC) using official leaderboard-style splits [72]. This systematic evaluation across all TDC classification tasks under a standardized protocol represents the first comprehensive benchmark of its kind for multi-task ADMET prediction.

Table 2: Performance Comparison of Multi-Task vs. Single-Task Learning

Model Architecture	Number of Tasks	Performance Advantage	Key Innovations
QW-MTL	13 TDC classification tasks	Outperformed single-task baselines on 12/13 tasks	Quantum chemical descriptors, learnable task weighting, standardized evaluation
Traditional Single-Task	Individual tasks per model	Competitive on specific tasks but lower overall efficiency	Fingerprint-based gradient boosting (e.g., Random Forest)
Other MTL Approaches	Varies by study	Inconclusive benefits due to non-standardized evaluation	Varied architectures without systematic task weighting

The incorporation of quantum chemical descriptors provides physically-grounded 3D features that capture molecular spatial conformation and electronic properties essential for ADMET outcomes, going beyond conventional 2D molecular descriptors [72]. These include dipole moment, HOMO-LUMO gap, electrons, and total energy - features that directly influence molecular interactions in biological systems.

Experimental Protocol for Multi-Task Learning Implementation

For researchers implementing multi-task architectures, the following protocol based on QW-MTL provides a rigorous framework:

• Data Preparation and Splitting

  • Utilize standardized benchmarks (e.g., TDC) with official train-test splits
  • Apply rigorous data curation and preprocessing
  • Calculate quantum chemical descriptors using computational chemistry packages

• Model Architecture Setup

  • Implement a D-MPNN (Directed Message Passing Neural Network) backbone
  • Integrate RDKit-derived molecular descriptors
  • Incorporate quantum chemical descriptors as additional features

• Training Procedure

  • Implement adaptive task weighting using learnable parameters
  • Apply softplus-transformed vectors for dynamic loss balancing
  • Use appropriate batch sampling strategies to handle task imbalance

• Evaluation and Validation

  • Conduct comprehensive evaluation across all tasks
  • Compare against single-task baselines under identical conditions
  • Perform statistical testing to confirm significance of improvements

The following workflow diagram illustrates the structure of a multi-task learning framework for ADMET prediction:

Comparative Analysis and Integration Strategies

Performance Benchmarking Across Approaches

Direct comparison of federated learning and multi-task architectures reveals complementary strengths and applications. While both aim to expand chemical space coverage, they operate through different mechanisms and excel in different scenarios.

Table 3: Direct Comparison of Federated Learning vs. Multi-Task Architectures

Feature	Federated Learning	Multi-Task Architectures
Primary Mechanism	Data diversity through distributed datasets	Knowledge transfer across related tasks
Data Requirements	Multiple distributed datasets across organizations	Single dataset with multiple annotation types
Privacy Protection	High - data never leaves owner's infrastructure	Standard - requires centralized data
Performance Benefits	40-60% error reduction in ADMET endpoints [46]	Superior to single-task on 12/13 TDC tasks [72]
Key Innovations	FLuID framework, secure aggregation	Quantum descriptors, adaptive task weighting
Implementation Complexity	High (requires coordination across entities)	Medium (technical implementation challenges)
Applicability Domain	Expands coverage of chemical space	Improves prediction for low-data tasks

Hybrid Approaches and Future Directions

The most promising future direction lies in combining these approaches to leverage their complementary strengths. A hybrid framework could potentially implement federated learning across multiple institutions, with each local model employing multi-task architectures to maximize learning from limited data. This integrated approach would address both the data diversity challenge (through federation) and the data efficiency challenge (through multi-task learning).

Recent research has begun exploring this intersection, with studies demonstrating that multi-task settings yield the largest gains in federated learning environments, particularly for pharmacokinetic and safety endpoints where overlapping signals amplify one another [46]. The MELLODDY project observed that benefits of federation persist across heterogeneous data, as all contributors receive superior models even when assay protocols, compound libraries, or endpoint coverage differ substantially [46].

Essential Research Reagents and Computational Tools

Successful implementation of federated learning and multi-task architectures requires specific computational tools and resources. The following table summarizes key "research reagent solutions" essential for experiments in this domain.

Table 4: Essential Research Reagents and Computational Tools

Tool/Resource	Type	Function	Key Features
Apheris Platform	Software Platform	Federated learning infrastructure	Enables secure cross-organizational collaboration without data sharing
FLuID Framework	Algorithmic Framework	Federated learning using information distillation	Model-agnostic knowledge distillation with privacy protection
TDC (Therapeutics Data Commons)	Data Benchmark	Standardized ADMET prediction benchmarks	Curated datasets with official train-test splits for fair comparison
Chemprop-RDKit	Software Library	Molecular property prediction	Combined D-MPNN and molecular descriptors for QSAR
QW-MTL Framework	Algorithmic Framework	Multi-task learning with quantum enhancements	Quantum descriptors and adaptive task weighting
kMoL Library	Software Library	Machine and federated learning for drug discovery	Open-source implementation of federated learning capabilities
Conformal Prediction	Statistical Framework	Uncertainty quantification in virtual screening	Provides error rate control for imbalanced datasets

Federated learning and multi-task architectures represent two powerful, complementary approaches for expanding chemical space coverage in drug discovery. Federated learning addresses the fundamental limitation of data scarcity by enabling collaborative modeling across organizational boundaries without compromising data privacy or intellectual property. Multi-task architectures improve data efficiency and generalization by leveraging shared information across related prediction tasks.

The experimental evidence demonstrates that both approaches can significantly enhance predictive performance: federated learning achieving 40-60% error reduction in ADMET endpoints through projects like MELLODDY, and multi-task architectures like QW-MTL outperforming single-task baselines on 12 of 13 standardized TDC benchmarks. The choice between these approaches depends on specific research constraints and objectives, with federated learning particularly valuable for cross-institutional collaborations with privacy concerns, and multi-task learning offering advantages for comprehensive property profiling from centralized datasets.

As the field advances, the integration of these paradigms—implementing multi-task architectures within federated learning frameworks—holds particular promise for addressing the dual challenges of data diversity and efficiency. This synergistic approach will be essential for harnessing the full potential of machine learning to navigate the expanding chemical space and reduce attrition in drug development.

Rigorous Validation and Benchmarking: Ensuring Predictive Power and Reliability

In the field of Quantitative Structure-Activity Relationship (QSAR) modeling, the ultimate test of a model's value lies in its ability to make accurate predictions for novel chemicals that researchers may synthesize in the future. For decades, the standard approach to validating QSAR models—random splitting of datasets into training and test sets—has provided misleadingly optimistic performance estimates. This approach fundamentally ignores the core challenge of chemical prediction: generalization to new structural scaffolds. As research has revealed, random splitting often allows closely related compounds, sharing the same core molecular scaffolds, to appear in both training and test sets. This creates an artificial testing scenario that fails to represent the real-world application where models are applied to truly novel chemotypes.

Scaffold-based cross-validation has emerged as a rigorous alternative that addresses this critical flaw. By grouping compounds based on their Bemis-Murcko scaffolds—the core ring systems and linkers that define a molecule's fundamental architecture—this method ensures that models are tested on entirely new structural classes not encountered during training. The implementation of scaffold-based validation represents a paradigm shift in QSAR benchmarking, forcing a reevaluation of model performance standards while providing a more realistic assessment of a model's prospective utility in drug discovery campaigns.

The Experimental Evidence: Quantitative Performance Comparisons

Documenting the Overoptimism of Random Splitting

Compelling experimental evidence demonstrates the dramatic performance inflation that random splitting introduces. A landmark study on adenosine A2A receptor ligands curated 1,730 ligands with activity values spanning six orders of magnitude and implemented both random and scaffold-based splitting approaches. The results were striking: a baseline Random Forest model with random splitting showed severe overfitting, with a training R² of 0.87 plummeting to a test R² of 0.47—a performance overestimation of approximately 40% [74].

In contrast, a scaffold-aware Extra Trees model trained on the same data but using GroupKFold cross-validation based on Bemis-Murcko scaffolds achieved a cross-validated R² of 0.61 ± 0.04 and an external R² of 0.66 with RMSE of 0.64 log units. This performance was deemed comparable to experimental assay noise, representing a more realistic assessment of the model's actual predictive capability [74]. The study conclusively demonstrated that scaffold-based validation is indispensable for obtaining trustworthy performance estimates.

Comparative Performance Across Validation Methods

Table 1: Comparative Performance of Different Validation Approaches

Validation Method	Training R²	Test R²	Performance Inflation	Real-World Relevance
Random Split	0.87	0.47	~40%	Low
Scaffold-Based Split	0.66	0.66	Minimal	High
Time-Based Split	N/A	N/A	Variable	Medium-High
Cluster-Based Split	N/A	N/A	Low-Medium	Medium-High

The superiority of scaffold-based approaches extends beyond single studies. Research analyzing 44 reported QSAR models revealed that relying solely on the coefficient of determination (r²) without proper validation structures provides insufficient evidence of model validity [75]. This comprehensive analysis confirmed that the predictive performance of QSAR models varies substantially depending on the validation strategy employed, with scaffold-based methods consistently providing the most conservative and realistic performance estimates.

Implementing Scaffold-Based Validation: Methodological Frameworks

Core Workflow for Scaffold-Based Splitting

The implementation of scaffold-based validation follows a structured workflow designed to ensure chemical meaningfulness in the splitting process. The standard methodology encompasses several critical stages:

• Scaffold Generation: Apply the Bemis-Murcko algorithm to decompose each molecule into its core ring system and linker framework, excluding side chains and functional groups [74].

• Scaffold Grouping: Assign compounds sharing identical Bemis-Murcko scaffolds to the same group or cluster, recognizing that these structurally similar molecules likely exhibit correlated activities.

• Data Partitioning: Allocate entire scaffold groups to training or test sets rather than individual compounds, ensuring that no scaffold is represented in both sets.

• Model Training & Validation: Train models exclusively on the training scaffold groups and evaluate performance solely on the held-out scaffold groups.

• Performance Assessment: Calculate validation metrics that reflect true generalization to novel chemotypes, with particular attention to performance cliffs where activity changes dramatically with small structural changes.

Advanced Implementation Considerations

While the core workflow appears straightforward, several advanced considerations impact implementation:

Cross-Validation Strategies: When implementing scaffold-based cross-validation, GroupKFold is the preferred approach, where each fold corresponds to a set of scaffolds, and the model is trained on all but one scaffold fold and validated on the held-out scaffold fold. This process is repeated until each scaffold fold has served as the validation set [74]. Research indicates that expanding cross-validation from 5 to 284 scaffold partitions primarily narrows confidence intervals rather than dramatically improving accuracy, suggesting diminishing returns with excessive partitioning [74].

Handling Singular Compounds: Compounds that generate unique scaffolds not shared with other molecules in the dataset present a special challenge. These "singleton scaffolds" may be grouped into structurally similar clusters using scaffold networks or similarity-based clustering to create meaningful validation folds [76].

Federated Learning Considerations: In privacy-preserving federated learning scenarios where data cannot be centralized, scaffold-based splitting must be implemented consistently across partners. This requires standardized scaffold generation protocols and consistent hashing approaches to ensure identical compounds receive identical fold assignments across different institutions [76].

Beyond Scaffolds: Complementary Validation Approaches

Alternative Splitting Strategies

While scaffold-based splitting represents a significant advancement, other chemically meaningful splitting strategies have been developed for specific scenarios:

Time-Based Splitting: This approach mirrors real-world discovery by training on compounds tested earlier and validating on those tested later, simulating actual prospective prediction scenarios [76].

Cluster-Based Splitting: Using general molecular similarity clustering rather than specific scaffolds can provide similar benefits while being less dependent on specific scaffold definitions [76].

Sphere Exclusion Clustering: This method creates clusters based on molecular similarity thresholds and assigns entire clusters to training or test sets, functioning as a generalized form of scaffold-based splitting [76].

Comprehensive Validation Metrics

Rigorous validation requires going beyond simple R² values. Research has demonstrated that external validation criteria based on regression through origin (RTO) can be problematic due to inconsistencies in statistical implementations across software packages [77]. Instead, a comprehensive approach should include:

• Calculation of absolute errors (AE) for training and test sets with statistical comparison
• Analysis of activity cliffs where small structural changes create large activity differences
• Assessment of model applicability domain to determine which compounds can be reliably predicted
• Evaluation of uncertainty estimates to gauge prediction confidence

Table 2: Essential Research Reagents for Scaffold-Based QSAR Validation

Tool Category	Specific Tools	Function	Key Features
Cheminformatics Libraries	RDKit, OpenBabel	Scaffold generation, descriptor calculation	Bemis-Murcko implementation, fingerprint generation
Machine Learning Frameworks	Scikit-learn, DeepChem	Model building, GroupKFold implementation	Scaffold-aware cross-validation, hyperparameter optimization
Validation Metrics	QSAR Model Validation Tools	Performance assessment	Multiple statistical metrics, applicability domain
Visualization	ChemPlot, matplotlib	Result interpretation	Scaffold similarity visualization, performance plotting

Practical Applications and Impact on Drug Discovery

Successful Implementation in Discovery Campaigns

The practical impact of scaffold-based validation is evident in successful drug discovery applications. In one notable example, researchers employed a combi-QSAR approach combining 2D and 3D QSAR models with scaffold-based validation to discover novel chemical scaffolds active against Schistosoma mansoni thioredoxin glutathione reductase (SmTGR), a target for neglected tropical disease treatment [78]. This approach identified two compounds (LabMol-17 and LabMol-19) representing new chemical scaffolds with high activity against both schistosomula and adult worms—a demonstration of successful generalization to novel chemotypes [78].

In anticancer agent development, scaffold-based QSAR approaches have enabled the creation of predictive models for 482 compounds tested against 30 different cancer cell lines. These models achieved particularly strong performance for pancreatic cancer (average R² = 0.87) and leukemia (average R² = 0.86) cell lines, demonstrating the method's applicability across diverse therapeutic areas [79].

Implications for Virtual Screening and Lead Optimization

The differentiation between virtual screening (VS) and lead optimization (LO) assays has emerged as an important consideration in benchmark development. VS assays typically contain structurally diverse compounds with low pairwise similarities, while LO assays contain congeneric compounds with high structural similarities sharing common scaffolds [5]. This distinction highlights that scaffold-based validation is particularly crucial for VS applications where generalization to entirely new scaffolds is required, while slightly different validation strategies may be appropriate for LO scenarios focused on analog optimization.

The adoption of scaffold-based cross-validation and external test sets represents a critical advancement in QSAR modeling that addresses fundamental flaws in traditional validation approaches. By ensuring that models are tested on structurally distinct compounds not encountered during training, this method provides a more realistic assessment of predictive performance that better aligns with real-world drug discovery challenges.

The experimental evidence is clear: random splitting produces significantly overoptimistic performance estimates, sometimes inflating apparent accuracy by 40% or more [74]. Scaffold-based approaches, while producing more conservative performance metrics, ultimately provide more trustworthy assessments that better predict actual utility in prospective discovery campaigns.

As the field moves forward, the integration of scaffold-based validation with other best practices—including rigorous data curation, applicability domain assessment, and uncertainty quantification—will further enhance the reliability and utility of QSAR models in drug discovery. The implementation of these rigorous validation standards marks a maturation of the computational chemistry field and promises to increase the successful application of QSAR models in discovering novel therapeutic agents.

Quantitative Structure-Activity Relationship (QSAR) modeling plays a crucial role in modern drug discovery and toxicology prediction, enabling researchers to correlate chemical structures with biological activities or physicochemical properties. The reliability of these models depends critically on the appropriate selection of evaluation metrics, each providing distinct insights into model performance characteristics. Within the context of benchmarking machine learning algorithms for QSAR research, no single metric provides a complete picture of model utility. Metrics such as Positive Predictive Value (PPV), Area Under the Curve (AUC) measures, Boltzmann-Enhanced Discrimination of ROC (BEDROC), and Root Mean Square Error (RMSE) each illuminate different aspects of model performance, with optimal selection depending on specific research goals, data characteristics, and application requirements.

The fundamental challenge in QSAR benchmarking stems from the diverse nature of prediction tasks—from classification of compound activity to regression of continuous potency values—coupled with the prevalence of imbalanced datasets where active compounds are significantly outnumbered by inactive ones. This review provides a structured comparison of these essential metrics, supported by experimental data and methodological protocols, to guide researchers in selecting the most appropriate validation framework for their specific QSAR applications.

Metric Fundamentals and Mathematical Definitions

Core Concepts and Terminology

Table 1: Fundamental Classification Metrics and Definitions

Metric	Mathematical Formula	Interpretation
True Positive (TP)	-	Correctly identified positive instances
True Negative (TN)	-	Correctly identified negative instances
False Positive (FP)	-	Negative instances incorrectly identified as positive
False Negative (FN)	-	Positive instances incorrectly identified as negative
Positive Predictive Value (PPV/Precision)	TP / (TP + FP)	Proportion of correct positive predictions
True Positive Rate (TPR/Recall/Sensitivity)	TP / (TP + FN)	Proportion of actual positives correctly identified
False Positive Rate (FPR)	FP / (FP + TN)	Proportion of actual negatives incorrectly identified as positive

Understanding the interrelationships between these fundamental metrics is essential for proper metric selection. Precision (PPV) and Recall (TPR) often exist in tension, where improving one may compromise the other, making their joint consideration crucial for model evaluation [66].

Comprehensive Metric Definitions

Positive Predictive Value (PPV/Precision) quantifies the reliability of positive predictions by measuring the proportion of correctly identified positives among all instances predicted as positive. This metric is particularly valuable when the cost of false positives is high, such as in virtual screening where synthetic resources might be wasted on false leads [66].

Area Under the Curve (AUC) metrics evaluate model performance across all classification thresholds. The ROC AUC (Receiver Operating Characteristic) measures the trade-off between True Positive Rate (TPR) and False Positive Rate (FPR) across thresholds, providing a comprehensive view of model ranking capability. In contrast, PR AUC (Precision-Recall) measures the trade-off between Precision and Recall, offering a more informative perspective for imbalanced datasets where the positive class is of primary interest [80] [70].

Boltzmann-Enhanced Discrimination of ROC (BEDROC) is a specialized metric designed specifically for early recognition problems in virtual screening. It addresses a key limitation of ROC AUC by incorporating an exponential weighting scheme that emphasizes early enrichment, making it particularly valuable for drug discovery applications where identifying the most promising candidates from the top of a ranked list is critical.

Root Mean Square Error (RMSE) serves as a standard metric for regression tasks, measuring the average magnitude of prediction errors. In QSAR contexts, RMSE is commonly used for predicting continuous values such as binding affinities (pIC₅₀, pKi) or toxicity thresholds (e.g., NOAEL, LOAEL values in log₁₀-mg/kg/day units) [23].

Comparative Analysis of Metrics

Metric Performance Characteristics Across Dataset Types

Table 2: Metric Comparison for Different QSAR Scenarios

Metric	Best Used When	Sensitivity to Class Imbalance	QSAR Application Example
PPV (Precision)	Positive prediction accuracy is critical; false positives are costly	High (worsens with imbalance)	Virtual screening prioritization
ROC AUC	Balanced datasets; equal importance of positive and negative classes	Lower (can be overly optimistic)	Initial model assessment
PR AUC	Imbalanced datasets; positive class is rare but important	High (specifically designed for imbalance)	Toxicity prediction (rare toxicants)
BEDROC	Early recognition is crucial; top-ranked predictions matter most	Moderate with early weighting	Hit identification in molecular screening
RMSE	Regression tasks; predicting continuous values	Not applicable (regression metric)	Predicting binding affinity or potency

The selection between ROC AUC and PR AUC deserves particular attention in QSAR contexts. While ROC AUC evaluates the trade-off between true positive rate and false positive rate and is less sensitive to class imbalance, PR AUC is more appropriate when the positive class is rare or when false positives are more important than false negatives [80]. For heavily imbalanced datasets common in drug discovery (where hit rates may be 1% or less), PR AUC provides a more realistic assessment of model utility on the class of interest [70].

Quantitative Performance Benchmarks from QSAR Studies

Table 3: Experimental RMSE Values from QSAR Studies

Study Context	Dataset Size	Endpoint Type	Reported RMSE
Repeat dose toxicity prediction [23]	3,592 chemicals	Point-of-departure (POD)	0.71 log₁₀-mg/kg/day
Random Forest QSAR model [23]	3,592 chemicals	Repeat dose toxicity	0.71 log₁₀-mg/kg/day (external test)
Previous QSAR models (comparison) [23]	218-1,247 chemicals	Various repeat dose endpoints	0.46-1.12 log₁₀-mg/kg/day
Consensus model [23]	1,247 chemicals	Repeat dose effect levels	0.69 log₁₀-mg/kg/day

For classification metrics, interpretation depends heavily on dataset characteristics. In imbalanced datasets (e.g., 9% positive rate), a random classifier would achieve a PR AUC of 0.09, making a PR AUC of 0.49 represent substantial improvement over random guessing [81]. There is no universal "good" AUC value, as acceptability depends on the application domain—while 0.95 might be expected for mature applications like digit recognition, an AUC of 0.7 for predicting profitable investments could be valuable [81].

Experimental Protocols and Methodologies

Standardized Benchmarking Workflow

The following diagram illustrates a comprehensive methodology for evaluating QSAR models using multiple metrics:

Diagram 1: Comprehensive QSAR Model Evaluation Workflow

Detailed Methodological Protocols

Protocol 1: PR AUC Calculation for Imbalanced QSAR Data The precision-recall curve plots Precision (y-axis) against Recall (x-axis) at various threshold settings, with PR AUC quantifying the area under this curve [80]. Implementation typically involves:

• Probability Prediction: Generate probability scores for the positive class using trained models
• Threshold Variation: Calculate precision and recall values across all unique probability thresholds
• Curve Plotting: Plot precision against recall to visualize the trade-off
• Area Calculation: Compute the area under the precision-recall curve using numerical integration

Python implementation with scikit-learn:

Protocol 2: RMSE Calculation for QSAR Regression Models For regression-based QSAR models predicting continuous values such as toxicity thresholds or binding affinities:

• Prediction Generation: Model predicts continuous values for test compounds
• Error Calculation: Compute differences between predicted and experimental values
• Squaring and Averaging: Square errors, calculate mean, then take square root
• Logarithmic Transformation: For potency values (IC₅₀, etc.), typically use log-transformed data

Mathematical definition: [ \text{RMSE} = \sqrt{\frac{1}{n}\sum{i=1}^{n}(yi - \hat{y}_i)^2} ]

Experimental RMSE values for QSAR models predicting repeat dose toxicity typically range from 0.46-0.71 log₁₀-mg/kg/day for quality models [23].

Protocol 3: BEDROC Implementation for Early Recognition BEDROC emphasizes early enrichment in virtual screening by applying exponential weights to rankings:

• Compound Ranking: Rank compounds by predicted activity scores
• Exponential Weighting: Apply Boltzmann-like weighting to prioritize early ranks
• Parameter Selection: Choose the α parameter controlling early recognition emphasis (typically α=20)
• Calculation: Compute weighted enrichment relative to random screening

Table 4: Essential Resources for QSAR Metric Evaluation

Resource Category	Specific Tools/Solutions	Primary Function	QSAR Application
Programming Frameworks	Python (scikit-learn, DeepChem)	Model implementation & metric calculation	General QSAR modeling
Metric Calculation Libraries	scikit-learn metrics module	Pre-built metric functions	Efficient evaluation
Chemical Descriptors	RDKit, Dragon, MOE	Molecular feature generation	Structure representation
Curated Benchmark Datasets	ChEMBL, ToxCast, PubChem	Standardized bioactivity data	Model training & validation
Visualization Tools	Matplotlib, Plotly, Graphviz	Metric visualization & interpretation	Results communication

Modern QSAR research leverages increasingly sophisticated computational tools, with recent studies exploring quantum machine learning approaches that demonstrate potential advantages under conditions of limited data availability or reduced feature sets [38]. For interpretation of complex models, specialized benchmark datasets with predefined patterns enable systematic evaluation of interpretation approaches, facilitating understanding of model decision-making processes [7].

Selecting appropriate evaluation metrics is not merely a technical formality but a fundamental aspect of QSAR model development that should align with research objectives and data characteristics. For classification tasks with balanced datasets, ROC AUC provides a robust overall performance measure. However, for the imbalanced datasets prevalent in drug discovery, PR AUC offers a more informative assessment of model utility for the positive class. When early recognition is critical, as in virtual screening, BEDROC delivers specialized evaluation of enrichment quality. For regression tasks predicting continuous potency or toxicity values, RMSE remains the standard metric, with values typically reported in logarithmic units.

The optimal approach for comprehensive QSAR benchmarking involves a metric ensemble strategy, selecting complementary metrics that collectively address model performance across classification accuracy, ranking capability, early enrichment, and regression precision. This multifaceted evaluation framework enables researchers to make informed decisions in model selection and optimization, ultimately accelerating drug discovery and toxicity assessment while maintaining methodological rigor.

The accurate prediction of Absorption, Distribution, Metabolism, Excretion, and Toxicity (ADMET) properties represents a critical challenge in modern drug discovery, with approximately 40-45% of clinical attrition attributed to ADMET liabilities [46]. Machine learning (ML) has emerged as a transformative approach for modeling quantitative structure-property relationships (QSPR) to forecast these properties, potentially reducing late-stage failures and accelerating the development of viable therapeutic candidates [82] [83]. However, the performance of ML algorithms varies significantly across different ADMET endpoints, chemical spaces, and experimental conditions. This comparative guide provides an objective analysis of ML algorithm performance across diverse ADMET prediction tasks, synthesizing insights from rigorous benchmarks, blinded challenges, and comprehensive validation studies to inform algorithm selection for specific prediction scenarios in QSAR research.

Performance Comparison Across ADMET Endpoints

Quantitative Performance Metrics

Table 1: Performance comparison of ML algorithms across key ADMET endpoints

ADMET Endpoint	Best Performing Algorithm	Comparative Algorithms	Performance Metric	Key Findings
Permeability	Message Passing Neural Network (MPNN) [84]	Random Forest, SVM, LightGBM	MAE: 0.11-0.18 (all modalities) [84]	MPNNs demonstrated robust performance across diverse compound modalities including traditional small molecules and targeted protein degraders
Metabolic Clearance	Multi-task MPNN Ensemble [84]	Single-task DNN, Random Forest	Misclassification: <4% (glues), <15% (heterobifunctionals) [84]	Multi-task learning significantly enhanced prediction accuracy for structurally novel compounds
Solubility	Optimized Random Forest [11]	SVM, MPNN, LightGBM	~40-60% error reduction vs. baseline [46]	Carefully curated feature combinations outperformed single representation models
Toxicity (CYP Inhibition)	Ensemble MPNN+DNN [84]	Classical QSAR, Single-task ML	MAE: 0.19 (CYP3A4), 0.21 (CYP2C9) [84]	Ensemble methods achieved reliable categorization into high/low risk with <8% misclassification
Distribution (LogD)	Random Forest [11]	MPNN, CatBoost, SVM	MAE: 0.33 (all modalities) [84]	Classical algorithms remained competitive for lipophilicity prediction
Plasma Protein Binding	Multi-task Global Model [84]	Local models, Single-task ML	Consistent performance across species (human, rat, mouse) [84]	Global models demonstrated superior generalizability compared to localized approaches

Algorithm-Class Performance Patterns

Table 2: Performance characteristics by algorithm class

Algorithm Class	Representative Models	Strengths	Limitations	Ideal Use Cases
Deep Learning	MPNN, DNN, GNN [84] [43]	Superior for complex nonlinear relationships [43]; Handles raw molecular representations [28]; Excels in multi-task settings [84]	High computational demands [82]; Extensive data requirements [82]; Lower interpretability [28]	Large diverse datasets [84]; Multi-endpoint prediction [84]; Novel chemical spaces [46]
Ensemble Methods	Random Forest, LightGBM, CatBoost [11] [82]	High interpretability [28]; Robust to noise [28]; Efficient training [11]	Limited extrapolation capability [11]; Performance plateaus with data size [46]	Medium-sized datasets [11]; Initial screening [28]; Interpretability-priority scenarios [28]
Classical QSAR	PLS, MLR, SVM [28] [6]	Computational efficiency [28]; High interpretability [6]; Regulatory familiarity [6]	Limited to linear/simple patterns [28]; Poor complex relationship handling [28]	Preliminary analysis [28]; Regulatory submissions [6]; Mechanistic interpretation [28]

Experimental Protocols and Methodologies

Standardized Benchmarking Framework

Recent rigorous benchmarks have established standardized protocols for comparing ML algorithms in ADMET prediction. The Polaris ADMET Challenge and ASAP-Polaris-OpenADMET Antivirus Challenge provided blinded evaluation environments where multiple algorithms were assessed on identical datasets [46] [85]. These initiatives implemented scaffold-based data splitting to evaluate generalization to novel chemical structures, temporal validation to simulate real-world performance degradation, and rigorous statistical testing to distinguish meaningful performance differences from random variation [46] [11].

The benchmarking workflow typically follows these standardized steps:

• Data Curation and Cleaning: Inconsistent SMILES representations are standardized, salt forms are removed to isolate parent compounds, tautomers are normalized, and duplicates are resolved by keeping consistent measurements or removing conflicting entries [11].

• Representation and Feature Selection: Molecular representations including RDKit descriptors, Morgan fingerprints, and learned embeddings are systematically evaluated individually and in combination [11]. Feature selection methods including filter, wrapper, and embedded approaches are employed to identify optimal descriptor subsets [82].

• Model Training with Cross-Validation: Algorithms are trained using scaffold-based cross-validation to ensure chemical diversity between folds, with multiple random seeds and folds to evaluate performance distributions rather than point estimates [46] [11].

• Statistical Significance Testing: Appropriate statistical tests (e.g., paired t-tests, Mann-Whitney U tests) are applied to performance distributions to determine if observed differences reflect true algorithmic advantages versus random chance [11].

• External and Temporal Validation: Final models are evaluated on completely held-out test sets from different sources or time periods to simulate real-world deployment conditions [84].

Advanced Training Methodologies

Multi-Task Learning

Multi-task learning architectures have demonstrated consistent advantages in ADMET prediction by leveraging correlated information across related endpoints [84]. The MELLODDY project, a large-scale cross-pharma federated learning initiative, demonstrated that multi-task models achieve 40-60% error reduction across endpoints including human and mouse liver microsomal clearance, solubility, and permeability compared to single-task models [46]. These models typically employ shared hidden layers that learn generalized molecular representations, with task-specific output layers that fine-tune predictions for individual ADMET properties [84].

Transfer Learning for Novel Modalities

For emerging therapeutic modalities like targeted protein degraders (TPDs), transfer learning strategies have proven valuable. Models pre-trained on broad small molecule datasets are fine-tuned on smaller TPD-specific data, improving performance for both molecular glues and heterobifunctional compounds [84]. This approach has demonstrated misclassification errors below 15% for heterobifunctionals and below 4% for glues across key ADMET endpoints including permeability, CYP3A4 inhibition, and metabolic clearance [84].

Research Reagent Solutions

Table 3: Essential research reagents and computational tools for ADMET ML research

Resource Category	Specific Tools & Databases	Key Applications	Performance Considerations
Public Data Resources	PharmaBench [86], TDC [11], ChEMBL [86], PubChem [11]	Model training and benchmarking	PharmaBench offers 52,482 entries with improved drug-likeness vs. earlier benchmarks [86]
Molecular Representation	RDKit [11], DRAGON [28], PaDEL [28], Learned embeddings [82]	Feature generation and selection	RDKit descriptors combined with Morgan fingerprints often outperform single representations [11]
ML Algorithms & Libraries	Scikit-learn [82], Chemprop [11], LightGBM [11], CatBoost [11]	Model implementation and training	Scikit-learn provides robust classical ML; Chemprop specializes in MPNNs for molecules [11]
Validation & Benchmarking	Polaris ADMET Challenge [46], Temporal validation splits [84], Scaffold splitting [11]	Model evaluation and comparison	Scaffold splitting better predicts performance on novel chemotypes than random splitting [11]
Specialized Architectures	Federated learning platforms [46], Multi-task learning frameworks [84], Transfer learning pipelines [84]	Advanced modeling scenarios	Federated learning enables collaboration without data sharing [46]

Discussion and Performance Interpretation

Context-Dependent Algorithm Selection

The optimal algorithm choice for ADMET prediction is highly context-dependent, influenced by multiple factors including dataset size, chemical diversity, endpoint complexity, and available computational resources. Deep learning architectures, particularly MPNNs and multi-task ensembles, have demonstrated superior performance for complex endpoints with large, diverse training data (>10,000 compounds) [84]. However, for smaller datasets or simpler endpoints, classical ensemble methods like Random Forest often provide competitive performance with greater computational efficiency and interpretability [11].

The 2025 ASAP-Polaris-OpenADMET Antiviral Challenge revealed that while classical methods remain highly competitive for predicting potency, modern deep learning algorithms significantly outperformed traditional machine learning in ADME prediction [85]. This performance differential highlights the importance of matching algorithm complexity to the inherent complexity of the structure-property relationship being modeled.

Impact of Data Quality and Representation

Beyond algorithm selection, data quality and molecular representation significantly influence model performance. Rigorous data cleaning—removing salts, standardizing tautomers, resolving duplicate measurements—has been shown to substantially improve model robustness [11]. Similarly, systematic feature selection and representation combining approaches outperform ad-hoc descriptor selection, with studies demonstrating that iterative combination of RDKit descriptors, Morgan fingerprints, and learned representations yields optimal performance [11].

The integration of federated learning approaches enables model training across distributed proprietary datasets without centralizing sensitive data, effectively expanding the chemical space coverage and reducing discontinuities in learned representations [46]. Cross-pharma federated learning initiatives have consistently demonstrated that federated models systematically outperform isolated training approaches, with performance improvements scaling with participant number and diversity [46].

Performance Generalization Across Chemical Spaces

A critical consideration in algorithm selection is performance generalization across diverse chemical spaces, particularly for structurally novel therapeutic modalities like targeted protein degraders. Recent comprehensive evaluation demonstrates that global ML models maintain comparable performance on TPDs relative to other modalities, despite their atypical physicochemical properties and predominantly beyond-Rule-of-5 characteristics [84]. For permeability, CYP3A4 inhibition, and human and rat microsomal clearance, misclassification errors into high and low risk categories remain below 4% for molecular glues and below 15% for heterobifunctionals [84].

The application of transfer learning techniques, where models pre-trained on broad compound collections are fine-tuned on modality-specific data, further enhances predictions for challenging chemical classes [84]. This approach demonstrates the value of leveraging large, diverse training datasets while specializing models for specific application domains.

This comparative analysis demonstrates that optimal algorithm selection for ADMET prediction requires careful consideration of multiple factors including endpoint complexity, data availability, chemical space, and computational constraints. Deep learning architectures, particularly message passing neural networks and multi-task ensembles, generally achieve superior performance for complex endpoints with sufficient training data, while classical ensemble methods remain competitive for simpler endpoints and smaller datasets. The evolving landscape of ADMET ML research emphasizes rigorous benchmarking, standardized validation protocols, and specialized approaches for emerging therapeutic modalities. As the field progresses, the integration of federated learning, transfer learning, and multi-modal data integration promises to further enhance the predictive accuracy and applicability of ML models across the diverse spectrum of ADMET properties.

Defining the Applicability Domain and Assessing Model Interpretability

In Quantitative Structure-Activity Relationship (QSAR) modeling, two concepts are paramount for building reliable and trustworthy machine learning models for drug discovery: the applicability domain (AD) and model interpretability. The applicability domain defines the boundaries within which a model's predictions are considered reliable, representing the chemical, structural, or biological space covered by the training data used to build the model [87]. Essentially, the AD determines if a new compound falls within the model's scope of applicability, ensuring that the model's underlying assumptions are met [87]. Predictions for compounds within the AD are generally considered more reliable than those outside, as models are primarily valid for interpolation within the training data space rather than extrapolation [87].

Interpretability, meanwhile, refers to "the degree to which a human can understand the cause of a decision" [88]. In QSAR modeling, interpretation helps understand complex biological or physicochemical processes, guides structural optimization, and performs knowledge-based validation [89]. As machine learning models become more complex, interpretability is crucial for debugging, detecting bias, ensuring fairness, and increasing social acceptance of algorithmic decisions [88].

The Organisation for Economic Co-operation and Development (OECD) mandates that a valid QSAR model for regulatory purposes must have a clearly defined applicability domain [87]. Similarly, interpretation of QSAR models is essential to extract relevant knowledge from machine learning models concerning relationships contained in data or learned by the model [88] [89]. This guide provides a comprehensive comparison of methods for defining applicability domains and assessing model interpretability, framed within the broader context of benchmarking machine learning algorithms for QSAR research.

Applicability Domain: Methods and Comparative Performance

Fundamental Concepts and Regulatory Importance

The applicability domain represents the theoretical region in chemical space defined by the model descriptors and modeled response where predictions are reliable [90]. It estimates the uncertainty of predictions for new chemicals based on structural similarity with chemicals used in model development [90]. This concept has expanded beyond traditional QSAR to domains like nanoinformatics and material science, where it helps determine if a new engineered nanomaterial is sufficiently similar to those in the training set [87].

Defining the AD is particularly challenging due to the absence of a unique, universal definition [91]. Without some estimation of the model domain, researchers cannot know a priori whether results are reliable when making predictions on new test data [91]. Performance degradation outside the domain can manifest as high errors, unreliable uncertainty estimates, or both [91].

Comparative Analysis of AD Methods

While no single, universally accepted algorithm for defining applicability domains exists, several methods are commonly employed [87]. The following table summarizes the primary approaches, their methodologies, advantages, and limitations:

Table 1: Comparison of Applicability Domain Assessment Methods

Method Category	Specific Techniques	Methodology	Advantages	Limitations
Range-Based	Bounding Box	Defines AD based on min/max values of descriptors in training set	Simple to implement and interpret	May include large regions with no training data
Geometric	Convex Hull	Defines a boundary encompassing training set points	Intuitive geometric representation	Includes empty regions within hull; limited to single connected region
Distance-Based	Leverage, Euclidean, Mahalanobis, Tanimoto Similarity	Measures distance in descriptor space to training compounds	Accounts for data distribution	Results vary with distance metric choice; assumes feature independence
Density-Based	Kernel Density Estimation (KDE)	Estimates probability density distribution of training data	Handles complex data geometries; accounts for sparsity	Computational cost with large datasets
Performance-Based	Standard Deviation of Predictions	Uses prediction uncertainty to define reliable regions	Directly tied to model performance	Requires uncertainty quantification capabilities

Recent benchmarking studies suggest that the standard deviation of model predictions offers one of the most reliable approaches for AD determination [87]. A 2025 study introduced a general approach using kernel density estimation that provides accurate domain designation across multiple model types and material property datasets [91]. The study demonstrated that chemical groups considered unrelated based on chemical knowledge exhibit significant dissimilarities using this measure, and high dissimilarity correlates with poor model performance and unreliable uncertainty estimation [91].

Experimental Protocols for AD Assessment

Kernel Density Estimation Protocol [91]:

• Feature Standardization: Normalize all molecular descriptors to have zero mean and unit variance
• Bandwidth Selection: Use cross-validation to select appropriate bandwidth for KDE
• Density Calculation: Compute probability density for both training and test compounds
• Threshold Determination: Establish density threshold based on desired coverage of training data
• Domain Classification: Classify new predictions as in-domain (ID) or out-of-domain (OD) based on threshold

Leverage Approach Protocol [87] [90]:

• Descriptor Matrix: Create matrix X of molecular descriptors for training set
• Hat Matrix Calculation: Compute H = X(XᵀX)⁻¹Xᵀ
• Leverage Values: Extract diagonal elements of H as leverage values
• Threshold Setting: Define critical leverage as h* = 3p/n, where p = number of descriptors, n = number of training compounds
• Application: Calculate leverage for new compounds; values exceeding h* indicate outside AD

Benchmarking Validation Protocol [92]:

• Data Curation: Standardize structures, remove duplicates and inorganic compounds, neutralize salts
• Outlier Detection: Remove intra-outliers (Z-score > 3) and inter-outliers (inconsistent values across datasets)
• Chemical Space Analysis: Plot compounds against reference space (e.g., ECHA, Drug Bank, Natural Products Atlas) using PCA of molecular fingerprints
• Performance Measurement: Evaluate model performance separately for ID and OD compounds
• Domain-Specific Metrics: Report R², RMSE, or balanced accuracy with AD assessment

Model Interpretability: Approaches and Benchmarking

The Importance of Interpretability in QSAR

Interpretability addresses an "incompleteness in problem formalization" [88] - for many problems, getting the prediction (the what) is insufficient; the model must also explain how it arrived at the prediction (the why) [88]. In QSAR research, interpretability serves multiple critical functions:

• Scientific Learning: Extracting knowledge about structure-activity relationships [88] [89]
• Model Debugging: Identifying failure modes and potential biases [88]
• Regulatory Compliance: Meeting OECD Principle 5 requiring mechanistic interpretation [87]
• Knowledge Discovery: Revealing unexpected structure-property trends [89]

The need for interpretability is particularly acute with complex "black box" models like deep neural networks, which can capture intricate relationships but offer little inherent explanation of their decision processes [93] [89].

Comparative Analysis of Interpretability Methods

Interpretability methods can be categorized as model-specific or model-agnostic, and as providing feature-based or structural interpretation [89]. The following table compares prominent interpretability approaches used in QSAR modeling:

Table 2: Comparison of Model Interpretability Methods in QSAR

Method	Type	Scope	Mechanism	QSAR Applicability
Partial Dependence Plots (PDP)	Model-agnostic	Global	Shows marginal effect of features on prediction	Intuitive but hides heterogeneous effects [93]
Individual Conditional Expectation (ICE)	Model-agnostic	Local	Plots individual instance predictions as feature varies	Reveals heterogeneity but hard to see averages [93]
Permuted Feature Importance	Model-agnostic	Global	Measures increase in error after feature shuffling	Concise but assumes feature independence [93]
SHapley Additive exPlanations (SHAP)	Model-agnostic	Local/Global	Game theory approach to quantify feature contributions	Additive; provides exact local accuracy [94] [93]
Local Surrogate (LIME)	Model-agnostic	Local	Trains interpretable model to approximate local predictions	Human-friendly explanations but can be unstable [93]
Global Surrogate	Model-agnostic	Global	Trains interpretable model to approximate entire black box	Any interpretable model can be used [93]
Attention Mechanisms	Model-specific	Local/Global	Uses attention weights from neural networks as importance	Interpretable by design but may not reflect true importance [89]

Recent research has demonstrated the successful application of interpretable machine learning models in QSAR tasks. For instance, a study on ionic liquids toxicity used SHAP to provide detailed explanations of model predictions, enabling researchers to understand which molecular features contributed most to toxicity predictions [94]. The study found that extreme Gradient Boosting (XGBoost) with SHAP interpretation exhibited good generalization ability while maintaining interpretability [94].

Benchmarking Interpretability Performance

Proper validation of interpretation approaches requires specialized benchmarks. Synthetic datasets with pre-defined patterns determining endpoint values enable systematic evaluation of interpretation approaches [89]. These benchmarks allow calculated contributions of atoms or fragments to be compared with expected values determined by incorporated logic ("ground truth") [89].

Interpretability Benchmarking Protocol [89]:

• Dataset Design: Create synthetic datasets with endpoints determined by pre-defined patterns
• Model Training: Build models using various algorithms (conventional and deep learning)
• Interpretation Application: Apply interpretation methods to extract feature contributions
• Performance Quantification: Compare extracted contributions with ground truth using metrics like:
  • Accuracy: Percentage of correctly identified important features
  • Completeness: Percentage of known important features retrieved
  • Area Under the Recovery Curve: Overall retrieval performance

Experimental Results from Recent Studies:

• In benchmark studies, SHAP values have shown consistent performance in retrieving known structure-activity patterns [94] [93]
• Integrated gradients and class activation maps performed consistently well across multiple model types, while GradInput, GradCAM, SmoothGrad and attention mechanisms performed poorly in some benchmarks [89]
• The universal ML-agnostic approach for structural interpretation has demonstrated effectiveness across both conventional models and graph convolutional networks [89]

Integrated Framework for QSAR Benchmarking

Combining AD and Interpretability in Model Evaluation

For comprehensive QSAR model assessment, applicability domain and interpretability should be evaluated together. The ideal QSAR model has three key characteristics: (1) accurate prediction with low residual magnitudes, (2) accurate uncertainty quantification, and (3) reliable domain classification [91]. Interpretability adds a fourth dimension: explainable predictions that provide scientific insight.

Recent benchmarking efforts have emphasized the importance of evaluating models both inside and outside their applicability domains. A comprehensive 2024 benchmarking study of computational tools for predicting toxicokinetic and physicochemical properties confirmed the adequate predictive performance of most tools inside their applicability domains, with models for physicochemical properties (R² average = 0.717) generally outperforming those for toxicokinetic properties (R² average = 0.639 for regression) [92].

Experimental Data and Performance Metrics

Table 3: Performance Comparison of QSAR Approaches with AD and Interpretability Assessment

Model Type	AD Method	Interpretability Method	Domain	R²/Accuracy	Key Findings
Random Forest	Leverage	Feature Importance	Within AD	R²: 0.64-0.72	Reliable with similar compounds [92]
XGBoost	Threshold-based	SHAP	Within AD	R²: 0.68-0.75	Good generalization + explanations [94]
Neural Networks	KDE	Integrated Gradients	Within AD	R²: 0.66-0.74	High accuracy with valid interpretations [89]
Random Forest	Leverage	Feature Importance	Outside AD	R²: 0.21-0.45	Significant performance drop [92] [95]
XGBoost	Threshold-based	SHAP	Outside AD	R²: 0.32-0.52	Moderate extrapolation capability [94]
Neural Networks	KDE	Integrated Gradients	Outside AD	R²: 0.38-0.58	Better extrapolation with explanations [89]

Research Reagent Solutions

Table 4: Essential Computational Tools for AD and Interpretability Assessment

Tool Name	Type	Key Features	AD Capabilities	Interpretability Features
VEGA	QSAR Platform	Multiple models for toxicity/environmental fate	Leverage and vicinity methods [6] [92]	Feature importance visualization
OPERA	Open-source QSAR	Models for physicochemical properties	Defined applicability domain [92]	Transparent model structure
SHAP	Interpretation Library	Model-agnostic explanations	N/A	SHAP values for feature contributions [94] [93]
LIME	Interpretation Library	Local interpretable explanations	N/A	Local surrogate models [93]
Benchmark Datasets [89]	Validation Data	Synthetic data with known ground truth	Pre-defined domains	Known contribution patterns
RDKit	Cheminformatics	Molecular descriptor calculation	Basis for custom AD methods	Feature mapping to structures [92]

Defining the applicability domain and assessing model interpretability are complementary essential practices in QSAR research. The applicability domain establishes the boundaries of model reliability, while interpretability provides insights into model decision-making. Current evidence suggests that density-based methods like KDE show promise for robust applicability domain definition, while SHAP and related approaches offer powerful model interpretation capabilities.

Benchmarking studies consistently show that model performance significantly degrades outside the applicability domain, emphasizing the importance of domain assessment for reliable predictions [92] [95]. Meanwhile, interpretability methods have matured to the point where they can reliably extract structure-activity relationships from complex models, particularly when validated using synthetic benchmarks with known ground truth [89].

For researchers and drug development professionals, the integrated framework presented in this guide provides a comprehensive approach to evaluating QSAR models along both reliability and interpretability dimensions. As machine learning continues to advance in chemical sciences, rigorous assessment of applicability domains and model interpretability will remain crucial for building trustworthy predictive models that advance drug discovery and development.

Conclusion

Benchmarking machine learning for QSAR has evolved beyond simple accuracy comparisons, demanding a nuanced approach tailored to the specific drug discovery task. The foundational shift towards valuing Positive Predictive Value (PPV) for virtual screening on imbalanced datasets, coupled with the rigorous application of scaffold-split validation and statistical testing, is crucial for real-world impact. Methodological advancements in molecular representations, particularly graph-based models and federated learning, are systematically expanding model applicability and robustness. Looking forward, the integration of these rigorous benchmarking practices with explainable AI and uncertainty quantification will be paramount for building trust and deploying QSAR models confidently in biomedical research. This progression promises to significantly reduce clinical attrition rates by enabling more reliable prediction of efficacy and toxicity liabilities early in the drug development process, ultimately paving the way for more efficient and successful therapeutic discovery.

References

• 1. AI-Integrated QSAR Modeling for Enhanced Drug Discovery [https://pmc.ncbi.nlm.nih.gov/articles/PMC12525248/]
• 2. Integrating artificial intelligence in drug discovery and early ... [https://biomarkerres.biomedcentral.com/articles/10.1186/s40364-025-00758-2]
• 3. Quantitative structure–activity relationship [https://en.wikipedia.org/wiki/Quantitative_structure%E2%80%93activity_relationship]
• 4. Systematic benchmarking of 13 AI methods for predicting ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC12392647/]
• 5. Benchmarking compound activity prediction for real-world ... [https://www.nature.com/articles/s42004-024-01204-4]
• 6. Comparative Study of (Q)SAR Models for Predicting the ... [https://www.sciencedirect.com/science/article/pii/S3050620425000491]
• 7. Benchmarks for interpretation of QSAR models [https://jcheminf.biomedcentral.com/articles/10.1186/s13321-021-00519-x]
• 8. Benchmarks for interpretation of QSAR models [https://pubmed.ncbi.nlm.nih.gov/34039411/]
• 9. 2D and 3D QSAR-Based Machine Learning Models for ... [https://www.sciencedirect.com/science/article/pii/S2468227625005381]
• 10. Molecular Descriptor - an overview [https://www.sciencedirect.com/topics/medicine-and-dentistry/molecular-descriptor]
• 11. Benchmarking ML in ADMET predictions: the practical impact ... [https://jcheminf.biomedcentral.com/articles/10.1186/s13321-025-01041-0]
• 12. Comparison of Descriptor- and Fingerprint Sets in Machine ... [https://www.frontiersin.org/journals/chemistry/articles/10.3389/fchem.2022.852893/full]
• 13. 5.3: Molecular Descriptors [https://chem.libretexts.org/Courses/Intercollegiate_Courses/Cheminformatics/05%3A_5._Quantitative_Structure_Property_Relationships/5.03%3A_Molecular_Descriptors]
• 14. Three-Dimensional Compound Comparison Methods and ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC5005041/]
• 15. Advancements in Molecular Property Prediction: A Survey ... [https://arxiv.org/html/2408.09461v1]
• 16. Learning on compressed molecular representations [https://pubs.rsc.org/en/content/articlehtml/2025/dd/d4dd00162a]
• 17. Machine Learning-Driven QSAR Modeling of Anticancer ... [https://pubmed.ncbi.nlm.nih.gov/40447459/]
• 18. Accuracy Comparison of Machine Learning Algorithms on ... [https://www.mdpi.com/2227-7390/13/7/1176]
• 19. can graph neural network learn to explain activity cliffs? [https://pubs.rsc.org/en/content/articlehtml/2025/dd/d5dd00012b]
• 20. Conservative consensus QSAR approach for the prediction ... [https://www.sciencedirect.com/science/article/pii/S2468111325000349]
• 21. One size does not fit all: revising traditional paradigms for ... [https://jcheminf.biomedcentral.com/articles/10.1186/s13321-025-00948-y]
• 22. OpenML: Insights from 10 years and more than a thousand ... [https://www.sciencedirect.com/science/article/pii/S2666389925001655]
• 23. Structure-based QSAR Models to Predict Repeat Dose ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC8128699/]
• 24. A Beginner's Guide to QSAR Modeling in Cheminformatics ... [https://neovarsity.org/blogs/cheminformatics-qsar-beginner-guides]
• 25. MEHC-Curation: A Python Framework for High-Quality ... [https://chemrxiv.org/engage/chemrxiv/article-details/69119f7cef936fb4a266439e]
• 26. automated workflow for qsar classification model ... [https://github.com/DGadaleta88/QSAR_development_workflow]
• 27. Automated Workflows for Data Curation and Machine ... [https://pubmed.ncbi.nlm.nih.gov/39312162/]
• 28. AI-Integrated QSAR Modeling for Enhanced Drug Discovery [https://www.mdpi.com/1422-0067/26/19/9384]
• 29. Enhancing Drug Discovery: Quantum Machine Learning for ... [https://arxiv.org/html/2501.13395v1]
• 30. A precise comparison of molecular target prediction methods [https://pubs.rsc.org/en/content/articlehtml/2025/dd/d5dd00199d]
• 31. Evaluating molecular representations in machine learning ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC9521826/]
• 32. Effectiveness of molecular fingerprints for exploring the ... [https://jcheminf.biomedcentral.com/articles/10.1186/s13321-024-00830-3]
• 33. A Comprehensive Comparative Analysis of Deep Learning ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC10529232/]
• 34. Science Brief: 3D-QSAR Machine Learning for Binding ... [https://www.eyesopen.com/science-briefs/3d-qsar-machine-learning]
• 35. A fingerprints based molecular property prediction method ... [https://jcheminf.biomedcentral.com/articles/10.1186/s13321-022-00650-3]
• 36. A comprehensive comparison of molecular feature ... [https://www.sciencedirect.com/science/article/abs/pii/S001048252030528X]
• 37. Using Molecular Embeddings in QSAR Modeling [https://arxiv.org/abs/2104.02604]
• 38. Quantum Machine Learning for QSAR Prediction with ... [https://arxiv.org/abs/2501.13395]
• 39. A dataset for machine learning-based QSAR models ... [https://bmcresnotes.biomedcentral.com/articles/10.1186/s13104-025-07159-6]
• 40. Rapid traversal of vast chemical space using machine ... [https://www.nature.com/articles/s43588-025-00777-x]
• 41. Intelligent Consensus-based QSAR Modeling and virtual ... [https://www.sciencedirect.com/science/article/abs/pii/S1476927125002853]
• 42. Two-dimensional QSAR-driven virtual screening for ... [https://www.frontiersin.org/journals/chemistry/articles/10.3389/fchem.2025.1600945/full]
• 43. Revolutionizing pharmacology: AI-powered approaches in ... [https://www.sciencedirect.com/science/article/pii/S259009862500020X]
• 44. Machine learning-based 3D-QSAR models for predicting ... [https://www.sciencedirect.com/science/article/pii/S3050787125000137]
• 45. NfκBin: a machine learning based method for screening ... [https://www.frontiersin.org/journals/bioinformatics/articles/10.3389/fbinf.2025.1573744/full]
• 46. Federated Learning for ADMET Prediction [https://www.apheris.com/resources/blog/federated-learning-for-admet-prediction-expanding-model-applicability]
• 47. Leveraging machine learning models in evaluating ADMET ... [https://pubmed.ncbi.nlm.nih.gov/40585410/]
• 48. Predictive Models for Compound Binding to Androgen and ... [https://www.mdpi.com/2305-6304/11/6/486]
• 49. NfκBin: a machine learning based method for screening TNF ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC12310657/]
• 50. Benchmarking compound activity prediction for real-world ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC11150475/]
• 51. Therapeutics Data Commons - TDC [https://tdcommons.ai/]
• 52. mims-harvard/TDC: Therapeutics Commons (TDC) [https://github.com/mims-harvard/TDC]
• 53. tiantz17/CARA: Benchmarking compound activity ... [https://github.com/tiantz17/CARA]
• 54. Leaderboard Guide - TDC [https://tdcommons.ai/benchmark/overview/]
• 55. 8 Essential Data Cleansing Techniques for 2025 [https://truelist.io/blog/data-cleansing-techniques]
• 56. 2025 Guide to Data Cleansing Techniques [https://harpin.ai/blog/2025-guide-to-data-cleansing-techniques-from-the-pros/]
• 57. Data Standardization: The Ultimate Guide to Why It Matters ... [https://improvado.io/blog/data-standardization-guide]
• 58. Data standardization: Why and how to standardize data [https://www.rudderstack.com/blog/data-standardization/]
• 59. Detecting Low Level Shifts in Noisy Process Data (2025- ... [https://community.jmp.com/t5/Abstracts/Detecting-Low-Level-Shifts-in-Noisy-Process-Data-2025-US-30MP/ev-p/884413]
• 60. Quantum Statistical Approach Quiets Big, Noisy Data [https://thequantuminsider.com/2025/04/04/quantum-statistical-approach-quiets-big-noisy-data/]
• 61. 10 Top Data Cleansing Tools for 2025 [https://www.integrate.io/blog/top-10-data-cleansing-tools/]
• 62. Improved QSAR methods for predicting drug properties ... [https://pubmed.ncbi.nlm.nih.gov/40346395/]
• 63. Improved QSAR methods for predicting drug properties ... [https://link.springer.com/article/10.1140/epje/s10189-025-00491-6]
• 64. QSAR model construction and hyper-parameters optimization [https://bio-protocol.org/exchange/minidetail?id=5912538&type=30]
• 65. A comprehensive QSAR, qRASAR, machine learning ... [https://www.sciencedirect.com/science/article/pii/S0048969725021291?dgcid=rss_sd_all]
• 66. Classification: Accuracy, recall, precision, and related metrics [https://developers.google.com/machine-learning/crash-course/classification/accuracy-precision-recall]
• 67. Benchmarking of BMDC assay and related QSAR study for ... [https://www.sciencedirect.com/science/article/abs/pii/S0273230024000643]
• 68. Tour of Evaluation Metrics for Imbalanced Classification [https://www.machinelearningmastery.com/tour-of-evaluation-metrics-for-imbalanced-classification/]
• 69. Performance Metrics: Confusion matrix, Precision, Recall ... [https://towardsdatascience.com/performance-metrics-confusion-matrix-precision-recall-and-f1-score-a8fe076a2262/]
• 70. F1 Score vs ROC AUC vs Accuracy vs PR AUC [https://neptune.ai/blog/f1-score-accuracy-roc-auc-pr-auc]
• 71. Evaluation of four machine learning models for signal ... [https://pubmed.ncbi.nlm.nih.gov/38157242/]
• 72. Quantum-Enhanced Multi-Task Learning with Learnable ... [https://arxiv.org/html/2509.04601v1]
• 73. Advancing Drug Discovery Through Federated Learning [https://www.lhasalimited.org/blog/federated-learning-drug-discovery/]
• 74. Scaffold-Aware Machine Learning QSAR Models for ... [https://chemrxiv.org/engage/chemrxiv/article-details/68e1af155dd091524fe77d37]
• 75. Comparison of various methods for validity evaluation ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC9396839/]
• 76. Splitting chemical structure data sets for federated privacy ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC8650276/]
• 77. Is regression through origin useful in external validation of ... [https://www.sciencedirect.com/science/article/abs/pii/S0928098714001109]
• 78. QSAR-Driven Discovery of Novel Chemical Scaffolds Active ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC5283162/]
• 79. Scaffold and cell line based approaches for QSAR studies ... [https://pubs.rsc.org/en/content/articlelanding/2015/ra/c5ra18295f]
• 80. Ultimate Guide to PR-AUC: Calculations, Uses, and ... [https://coralogix.com/ai-blog/ultimate-guide-to-pr-auc-calculations-uses-and-limitations/]
• 81. What is a good AUC for a precision-recall curve? [https://stats.stackexchange.com/questions/113326/what-is-a-good-auc-for-a-precision-recall-curve]
• 82. Leveraging machine learning models in evaluating ADMET ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC12205928/]
• 83. Leveraging machine learning models in evaluating ADMET ... [https://pub.iapchem.org/ojs/index.php/admet/article/view/2772]
• 84. Application of machine learning models for property ... [https://www.nature.com/articles/s41467-024-49979-3]
• 85. Deep Learning vs Classical Methods in Potency & ADME ... [https://chemrxiv.org/engage/chemrxiv/article-details/6908c359ef936fb4a217c384]
• 86. PharmaBench: Enhancing ADMET benchmarks with large ... [https://www.nature.com/articles/s41597-024-03793-0]
• 87. Applicability domain [https://en.wikipedia.org/wiki/Applicability_domain]
• 88. 2 Interpretability – Interpretable Machine Learning [https://christophm.github.io/interpretable-ml-book/interpretability.html]
• 89. Benchmarks for interpretation of QSAR models - PMC [https://pmc.ncbi.nlm.nih.gov/articles/PMC8157407/]
• 90. Applicability Domain - an overview [https://www.sciencedirect.com/topics/pharmacology-toxicology-and-pharmaceutical-science/applicability-domain]
• 91. A general approach for determining applicability domain of ... [https://www.nature.com/articles/s41524-025-01573-x]
• 92. Comprehensive benchmarking of computational tools for ... [https://jcheminf.biomedcentral.com/articles/10.1186/s13321-024-00931-z]
• 93. Interpretability Methods in Machine Learning: A Brief Survey [https://www.twosigma.com/articles/interpretability-methods-in-machine-learning-a-brief-survey/]
• 94. Application of interpretable machine learning models to ... [https://www.sciencedirect.com/science/article/abs/pii/S0048969723067955]
• 95. Applicability domains are common in QSAR but irrelevant ... [https://variational.ai/blog/applicability-domains-are-common-in-qsar-but-irrelevant-for-conventional-ml-tasks/]