Change-point detection in regression models for ordered data via the max-EM algorithm

TL;DR

This paper introduces the max-EM algorithm, a new method for detecting change-points in regression models for ordered data, combining HMM and CEM techniques with proven efficiency and accuracy.

Contribution

The paper presents a novel max-EM algorithm that efficiently detects breakpoints in regression models, with theoretical guarantees and practical initialization strategies.

Findings

The max-EM algorithm achieves accurate breakpoint detection and parameter estimation.

Simulation results show strong performance across various regression models.

The statistical test effectively controls false positives and detects true change-points.

Abstract

We consider the problem of breakpoint detection in a regression modeling framework. To that end, we introduce a novel method, the max-EM algorithm which combines a constrained Hidden Markov Model with the Classification-EM (CEM) algorithm. This algorithm has linear complexity and provides accurate breakpoints detection and parameter estimations. We derive a theoretical result that shows that the likelihood of the data as a function of the regression parameters and the breakpoints location is increased at each step of the algorithm. We also present two initialization methods for the location of the breakpoints in order to deal with local maxima issues. Finally, a statistical test in the one breakpoint situation is developed. Simulation experiments based on linear, logistic, Poisson and Accelerated Failure Time regression models show that the final method that includes the initialization procedure and the max-EM algorithm has a strong performance both in terms of parameters estimation and breakpoints detection. The statistical test is also evaluated and exhibits a correct rejection rate under the null hypothesis and a strong power under various alternatives. Two real dataset are analyzed, the UCI bike sharing and the health disease data, where the interest of the method to detect heterogeneity in the distribution of the data is illustrated.