Analyzing Error Sources in Global Feature Effect Estimation

2026-03-16

AI Summary

This study addresses the lack of systematic understanding of error mechanisms and data selection strategies in estimating global feature effects, such as partial dependence (PD) and accumulated local effects (ALE). It proposes a novel mean squared error decomposition framework that disentangles model bias, estimation bias, model variance, and estimation variance at the estimator level. Through an integrated approach combining bias–variance analysis, probabilistic modeling, and multi-model simulation experiments, the work reveals how these error components interact with model characteristics, sample size, and the choice between training and hold-out data. The findings show that while using training data introduces slight bias, its larger sample size substantially reduces variance; ALE is more sensitive to sample size than PD; and cross-validation–based estimation effectively mitigates variance from overfitted models, offering both theoretical grounding and practical guidance.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Natural Language Processing: Interpretability, Analysis, and Evaluation of NLP Models

Application Category

• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Global feature effects such as PD and ALE plots are widely used to interpret black-box models. However, they are only estimates of true underlying effects, and their reliability depends on multiple sources of error. Despite the popularity of global feature effects, these error sources are largely unexplored. In particular, the practically relevant question of whether to use training or holdout data to estimate feature effects remains unanswered. We address this gap by providing a systematic, estimator-level analysis that disentangles sources of bias and variance for PD and ALE. To this end, we derive a mean-squared-error decomposition that separates model bias, estimation bias, model variance, and estimation variance, and analyze their dependence on model characteristics, data selection, and sample size. We validate our theoretical findings through an extensive simulation study across multiple data-generating processes, learners, estimation strategies (training data, validation data, and cross-validation), and sample sizes. Our results reveal that, while using holdout data is theoretically the cleanest, potential biases arising from the training data are empirically negligible and dominated by the impact of the usually higher sample size. The estimation variance depends on both the presence of interactions and the sample size, with ALE being particularly sensitive to the latter. Cross-validation-based estimation is a promising approach that reduces the model variance component, particularly for overfitting models. Our analysis provides a principled explanation of the sources of error in feature effect estimates and offers concrete guidance on choosing estimation strategies when interpreting machine learning models.

Problem

• global feature effects
• error sources
• partial dependence
• accumulated local effects
• model interpretation

Innovation

• feature effect estimation
• bias-variance decomposition
• partial dependence
• accumulated local effects
• cross-validation