Inferring Change Points in Regression via Sample Weighting

2026-04-13

AI Summary

This study addresses the problem of change-point detection in high-dimensional generalized linear models by proposing a sample-weighted empirical risk minimization (Weighted ERM) framework that incorporates prior information about potential change points. The method constructs weighted M-estimators and maximum likelihood estimators, uniquely integrating sample weighting with change-point priors. Under high-dimensional Gaussian designs, the authors establish sharp asymptotic theory for the resulting estimators, enabling efficient posterior inference on change-point locations. Empirical results demonstrate that the proposed weakly informative prior–guided weighting scheme substantially improves estimation accuracy over existing approaches. The accompanying software is publicly available as open-source Python and R packages under the name weightederm.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

We study the problem of identifying change points in high-dimensional generalized linear models, and propose an approach based on sample-weighted empirical risk minimization. Our method, Weighted ERM, encodes priors on the change points via weights assigned to each sample, to obtain weighted versions of standard estimators such as M-estimators and maximum-likelihood estimators. Under mild assumptions on the data, we obtain a precise asymptotic characterization of the performance of our method for general Gaussian designs, in the high-dimensional limit where the number of samples and covariate dimension grow proportionally. We show how this characterization can be used to efficiently construct a posterior distribution over change points. Numerical experiments on both simulated and real data illustrate the efficacy of Weighted ERM compared to existing approaches, demonstrating that sample weights constructed with weakly informative priors can yield accurate change point estimators. Our method is implemented as an open-source package, weightederm, available in Python and R.

Problem

• change points
• high-dimensional regression
• generalized linear models
• sample weighting
• empirical risk minimization

Innovation

• change point detection
• weighted empirical risk minimization
• high-dimensional statistics
• generalized linear models
• asymptotic analysis