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Change-Point Detection via Piecewise Linear Fitting Using...
[Submitted on 12 Feb 2026 (v1), last revised 9 Aug 2026 (this ve · 2026-02-12 · via stat updates on arXiv.org

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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.

Submission history

From: Apoorva Narula [view email]
[v1] Thu, 12 Feb 2026 13:43:56 UTC (102 KB)
[v2] Sun, 9 Aug 2026 18:47:17 UTC (73 KB)