Mattia Billa | Searcharxiv

arXiv2026

A Comparative Study of Model Selection Criteria for Symbolic Regression

Effective model selection is critical in symbolic regression (SR) to identify mathematical expressions that balance accuracy and complexity, and have low expected error on unseen data. Many modern implementations of genetic programming (GP) for SR generate a set of Pareto optimal candidate solutions, but reliable automatic selection of solutions that generalize well remains an open issue. Current literature offers various information-theoretic and Bayesian approaches, yet comprehensive comparisons of their performance across different data regimes are limited. This study presents a systematic empirical comparison of widely used selection criteria: the Akaike information criterion (AIC), the corrected AIC (AICc), the Bayesian information criterion (BIC), minimum description length (MDL), as well as Efron's bootstrap estimate for the in-sample prediction error on seven synthetic datasets with Gaussian noise. We rank candidate expressions generated by perturbing ground-truth functions to assess generalization error and selection probability of the ground-truth expression. Our findings reveal that MDL consistently identifies models with the lowest test error and the shortest length across most datasets. While no single criterion dominates all results, MDL and BIC produced the highest probability of selecting the ground-truth expressions.

cs.LG↗

arXiv2026

Interpretable ML Under the Microscope: Performance, Meta-Features, and the Regression-Classification Predictability Gap

As machine learning models are increasingly deployed in high-stakes domains, the need for interpretability has grown to meet strict regulatory and accountability constraints. Despite this interest, systematic evaluations of inherently interpretable models for tabular data remain scarce and often focus solely on aggregated performance. To address this gap, we evaluate sixteen interpretable methods, including Explainable Boosting Machines (EBMs), Symbolic Regression (SR), and Generalized Optimal Sparse Decision Trees, across 216 real-world tabular datasets. We assess predictive accuracy, computational efficiency, and generalization under distributional shifts. Moving beyond aggregate performance rankings, we further analyze how model behavior varies with dataset meta-features and operationalize these descriptors to study algorithm selection. Our analyses reveal a clear dichotomy: in regression tasks, models exhibit a predictable performance hierarchy dominated by EBMs and SR that can be inferred from dataset characteristics. In contrast, classification performance remains highly dataset-dependent with no stable hierarchy, showing that standard complexity measures fail to provide actionable guidance. Furthermore, we identify an "interpretability tax", showing that models explicitly optimizing for structural sparsity incur significantly longer training times. Overall, these findings provide practical guidance for practitioners seeking a balance between interpretability and predictive performance, and contribute to a deeper empirical understanding of interpretable modeling for tabular data.

cs.LG↗