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arXiv · 2602.11947

Change-Point Detection via Piecewise Linear Fitting Using MIP

Apoorva Narula·Santanu S. Dey·Yao Xie
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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 multi-dimensional PWL models with shared change-points. Extensive computational experiments on benchmark real-world datasets demonstrate that the proposed formulations achieve reductions in solution times in comparison to the state-of-the-art.

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Apoorva Narula, Santanu S. Dey, Yao Xie. 2026-02-12. Change-Point Detection via Piecewise Linear Fitting Using MIP. https://arxiv.org/abs/2602.11947

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