# Optimal nonparametric multivariate change point detection and localization

arXiv: https://arxiv.org/abs/1910.13289 · HTML: https://mlsanity.com/paper/1910.13289/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Oct 2019.

## Built on by (most cited first, 11 of 11)

- [Random Forests for Change Point Detection](https://mlsanity.com/paper/2205.04997/) (2022)
- [Segmenting Human-LLM Co-authored Text via Change Point Detection](https://mlsanity.com/paper/2605.03723/) (2026)
- [Optimal Online Change Detection via Random Fourier Features](https://mlsanity.com/paper/2505.17789/) (2025)
- [Noise-contrastive Online Change Point Detection](https://mlsanity.com/paper/2206.10143/) (2022)
- [Online Heavy-tailed Change-point detection](https://mlsanity.com/paper/2306.09548/) (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)
- [Dynamic Elliptical Graph Factor Models via Riemannian Optimization with Geodesic Temporal Regularization](https://mlsanity.com/paper/2605.18316/) (2026)
- [High-dimensional nonparametric changepoint detection via low-rank degree-two density projection](https://mlsanity.com/paper/2608.13922/) (2026)
- [High-Dimensional Nonparametric Change-Point Detection via Low-Rank Degree-Three Density Projection](https://mlsanity.com/paper/2608.15466/) (2026)
- [Optimal detection of general moment changes: Simultaneous mean and covariance change detection and beyond](https://mlsanity.com/paper/2609.36594/) (2026)

## Abstract (arXiv)

We study the multivariate nonparametric change point detection problem, where the data are a sequence of independent p-dimensional random vectors whose distributions are piecewise-constant with Lipschitz densities changing at unknown times, called change points. We quantify the size of the distributional change at any change point with the supremum norm of the difference between the corresponding densities. We are concerned with the localization task of estimating the positions of the change points. In our analysis, we allow for the model parameters to vary with the total number of time points, including the minimal spacing between consecutive change points and the magnitude of the smallest distributional change. We provide information-theoretic lower bounds on both the localization rate and the minimal signal-to-noise ratio required to guarantee consistent localization. We formulate a novel algorithm based on kernel density estimation that nearly achieves the minimax lower bound, save possibly for logarithm factors. We have provided extensive numerical evidence to support our theoretical findings.