# Change-Point Detection via Piecewise Linear Fitting Using MIP

arXiv: https://arxiv.org/abs/2602.11947 · HTML: https://mlsanity.com/paper/2602.11947/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 25 references that are in the map.
- First posted on arXiv 12 Feb 2026.

## Builds on (most cited first, 5 of 5)

- [High-dimensional changepoint estimation via sparse projection](https://mlsanity.com/paper/1606.06246/) (2016)
- [Composite Difference-Max Programs for Modern Statistical Estimation Problems](https://mlsanity.com/paper/1803.00205/) (2018)
- [Sample-Based Piecewise Linear Power Flow Approximations Using Second-Order Sensitivities](https://mlsanity.com/paper/2501.13825/) (2025)
- [Multi-Sensor Slope Change Detection](https://mlsanity.com/paper/1509.00114/) (2015)
- [Non-Monotonicity of Branching Rules with respect to Linear Relaxations](https://mlsanity.com/paper/2402.05213/) (2024)

## Abstract (arXiv)

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.