Generalized Resubstitution for Regression Error Estimation

2025-12-31 · Source: JMLR · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics · Depth: Expert, quick

Summary

Diego Marcondes and Ulisses Braga-Neto propose generalized resubstitution error estimators for regression, detailed in their 2026 paper. This new class of estimators allows for superior bias and variance properties compared to the standard sum of squares estimator, which uses a standard empirical probability measure and quadratic loss. The proposed estimators are proven consistent under broad assumptions. The authors introduce procedures for selecting the empirical measure, specifically using the method of moments and maximum pseudo-likelihood. Experimental results, demonstrated through polynomial regression, empirically confirm the improved finite-sample bias and variance of these new estimators. R code for the experiments is publicly available.

Key takeaway

For Machine Learning Engineers evaluating regression models, if you seek more accurate and robust error estimates, consider moving beyond the standard sum of squares. Investigate generalized resubstitution estimators, particularly those employing method of moments or maximum pseudo-likelihood for empirical measure selection. This approach can significantly improve the bias and variance of your model evaluations, leading to more reliable performance assessments.

Key insights

Generalized resubstitution error estimators improve regression accuracy by optimizing empirical probability measures and loss functions.

Principles

• Error estimators are defined by empirical probability measures and loss functions.
• Non-standard empirical measures yield superior bias and variance properties.
• Consistency of these estimators is provable under broad assumptions.

Method

Procedures for choosing the empirical measure, such as the method of moments and maximum pseudo-likelihood, are proposed to enhance regression error estimation.

In practice

• Apply non-standard empirical measures for improved error estimates.
• Utilize method of moments for empirical measure selection.
• Explore maximum pseudo-likelihood for optimal measure choice.

Topics

• Regression Error Estimation
• Generalized Resubstitution
• Empirical Probability Measures
• Bias-Variance Tradeoff
• Method of Moments
• Pseudo-Likelihood

Code references

• dmarcondes/genree

Best for: Research Scientist, AI Scientist, Machine Learning Engineer, Data Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by JMLR.