Mixed-Integer Programming for Change-point Detection

2026-02-12

AI Summary

This study addresses the offline multiple changepoint detection problem, aiming to accurately identify structural change locations in time series. The authors propose a globally optimal piecewise linear fitting method based on mixed-integer programming (MIP) and extend it to handle both multidimensional shared changepoints and sparse changepoint scenarios. The key innovation lies in constructing a family of strengthened MIP formulations whose linear programming relaxations possess the integer projection property with respect to segment assignment variables, yielding tighter relaxation bounds than existing approaches. Experimental results demonstrate that the proposed method significantly outperforms state-of-the-art algorithms on multiple real-world datasets, achieving substantially improved computational efficiency.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

We present a new mixed-integer programming (MIP) approach for offline multiple change-point detection by casting the problem as a globally optimal piecewise linear (PWL) fitting problem. Our main contribution is a family of strengthened MIP formulations whose linear programming (LP) relaxations admit integral projections onto the segment assignment variables, which encode the segment membership of each data point. This property yields provably tighter relaxations than existing formulations for offline multiple change-point detection. We further extend the framework to two settings of active research interest: (i) multidimensional PWL models with shared change-points, and (ii) sparse change-point detection, where only a subset of dimensions undergo structural change. Extensive computational experiments on benchmark real-world datasets demonstrate that the proposed formulations achieve reductions in solution times under both $\ell_1$ and $\ell_2$ loss functions in comparison to the state-of-the-art.

Problem

• change-point detection
• mixed-integer programming
• piecewise linear fitting
• multidimensional time series
• sparse change-points

Innovation

• mixed-integer programming
• change-point detection
• piecewise linear fitting
• LP relaxation
• sparse change-point