Inferring Change Points in Regression via Sample Weighting

arXiv stat.ML / 4/14/2026

💬 OpinionIdeas & Deep AnalysisTools & Practical UsageModels & Research

共有:

Key Points

The paper addresses detecting change points in high-dimensional generalized linear models using a sample-weighted empirical risk minimization (Weighted ERM) framework.
It encodes prior beliefs about where change points occur by assigning weights to individual samples, producing weighted versions of standard M-estimators and maximum-likelihood estimators.
The authors provide an asymptotic performance characterization in the high-dimensional regime (samples and covariate dimensions growing proportionally) under mild assumptions, focusing on Gaussian designs.
They show how the asymptotic characterization can be used to efficiently construct a posterior distribution over change points.
Experiments on simulated and real datasets indicate Weighted ERM can outperform existing methods, and the authors release an open-source Python/R implementation (weightederm).

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.