# Localizing Changes in High-Dimensional Regression Models

arXiv: https://arxiv.org/abs/2010.10410 · HTML: https://mlsanity.com/paper/2010.10410/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Oct 2020.

## Built on by (most cited first, 8 of 8)

- [Online Kernel CUSUM for Change-Point Detection](https://mlsanity.com/paper/2211.15070/) (2022)
- [Inference for Change Points in High Dimensional Mean Shift Models](https://mlsanity.com/paper/2107.09150/) (2021)
- [Denoising and change point localisation in piecewise-constant high-dimensional regression coefficients](https://mlsanity.com/paper/2110.14298/) (2021)
- [Noise-contrastive Online Change Point Detection](https://mlsanity.com/paper/2206.10143/) (2022)
- [Quick Adaptive Ternary Segmentation: An Efficient Decoding Procedure For Hidden Markov Models](https://mlsanity.com/paper/2305.18578/) (2023)
- [Inferring Change Points in High-Dimensional Regression via Approximate Message Passing](https://mlsanity.com/paper/2404.07864/) (2024)
- [Score-based change point detection via tracking the best of infinitely many experts](https://mlsanity.com/paper/2408.14073/) (2024)
- [High-Dimensional Nonparametric Change-Point Detection via Low-Rank Degree-Three Density Projection](https://mlsanity.com/paper/2608.15466/) (2026)

## Abstract (arXiv)

This paper addresses the problem of localizing change points in high-dimensional linear regression models with piecewise constant regression coefficients. We develop a dynamic programming approach to estimate the locations of the change points whose performance improves upon the current state-of-the-art, even as the dimensionality, the sparsity of the regression coefficients, the temporal spacing between two consecutive change points, and the magnitude of the difference of two consecutive regression coefficient vectors are allowed to vary with the sample size. Furthermore, we devise a computationally-efficient refinement procedure that provably reduces the localization error of preliminary estimates of the change points. We demonstrate minimax lower bounds on the localization error that nearly match the upper bound on the localization error of our methodology and show that the signal-to-noise condition we impose is essentially the weakest possible based on information-theoretic arguments. Extensive numerical results support our theoretical findings, and experiments on real air quality data reveal change points supported by historical information not used by the algorithm.