Publications

A complete and up-to-date list of my publications is available on Google Scholar .

1) Change-Point Detection via Piecewise Linear Fitting Using MIP

February 2026

Apoorva Narula, Santanu S. Dey, and Yao Xie

View 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 multidimensional PWL models with shared change-points. Extensive computational experiments on benchmark real-world datasets demonstrate that the proposed formulations reduce solution times under both ℓ1 and ℓ2 loss functions compared with the state of the art.

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Sparse change-point detection results Univariate change-point detection with continuity

2) Teaching Case

When Linear Regression Isn’t Enough: Building Optimization Models for Change-Point Detection and Trend Analysis

About the Teaching Case

This teaching case introduces piecewise-linear fitting as a framework for identifying changes in trends in time-series data. It guides students from classical linear regression to dynamic programming and mixed-integer optimization.

The case compares alternative optimization formulations based on their computational efficiency, scalability, and modeling properties, and illustrates the framework using applications in financial time series and hurricane-induced power outages.

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