# A Nonparametric Approach for Multiple Change Point Analysis of Multivariate Data

arXiv: https://arxiv.org/abs/1306.4933 · HTML: https://mlsanity.com/paper/1306.4933/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jun 2013.

## Built on by (most cited first, 28 of 28)

- [Random Forests for Change Point Detection](https://mlsanity.com/paper/2205.04997/) (2022)
- [WATCH: Wasserstein Change Point Detection for High-Dimensional Time Series Data](https://mlsanity.com/paper/2201.07125/) (2022)
- [Minder: Faulty Machine Detection for Large-scale Distributed Model Training](https://mlsanity.com/paper/2411.01791/) (2024)
- [A Log-Linear Non-Parametric Online Changepoint Detection Algorithm based on Functional Pruning](https://mlsanity.com/paper/2302.02718/) (2023)
- [Kernel Two-Sample Tests in High Dimension: Interplay Between Moment Discrepancy and Dimension-and-Sample Orders](https://mlsanity.com/paper/2201.00073/) (2021)
- [Memory-free Online Change-point Detection: A Novel Neural Network Approach](https://mlsanity.com/paper/2207.03932/) (2022)
- [Detecting Change Intervals with Isolation Distributional Kernel](https://mlsanity.com/paper/2212.14630/) (2022)
- [Adaptive Bernstein Change Detector for High-Dimensional Data Streams](https://mlsanity.com/paper/2306.12974/) (2023)
- [Segmenting Watermarked Texts From Language Models](https://mlsanity.com/paper/2410.20670/) (2024)
- [A computationally efficient framework for vector representation of persistence diagrams](https://mlsanity.com/paper/2109.08239/) (2021)
- [On Rank Energy Statistics via Optimal Transport: Continuity, Convergence, and Change Point Detection](https://mlsanity.com/paper/2302.07964/) (2023)
- [Non-parametric online market regime detection and regime clustering for multidimensional and path-dependent data structures](https://mlsanity.com/paper/2306.15835/) (2023)
- [Post Hoc Inference for Component Attribution in Multivariate Change-Point Detection](https://mlsanity.com/paper/2607.14814/) (2026)
- [Subspace Change-Point Detection via Low-Rank Matrix Factorisation](https://mlsanity.com/paper/2110.04044/) (2021)
- [Self-Supervised Transformer Architecture for Change Detection in Radio Access Networks](https://mlsanity.com/paper/2302.02025/) (2023)
- [A fast topological approach for predicting anomalies in time-varying graphs](https://mlsanity.com/paper/2305.06523/) (2023)
- [Dynamics, behaviours, and anomaly persistence in cryptocurrencies and equities surrounding COVID-19](https://mlsanity.com/paper/2101.00576/) (2021)
- [Population based change-point detection for the identification of homozygosity islands](https://mlsanity.com/paper/2111.10187/) (2021)
- [Noise-contrastive Online Change Point Detection](https://mlsanity.com/paper/2206.10143/) (2022)
- [Dynamic Interpretable Change Point Detection](https://mlsanity.com/paper/2211.03991/) (2022)
- [Change Point Detection with Conceptors](https://mlsanity.com/paper/2308.06213/) (2023)
- [Anomalous Change Point Detection Using Probabilistic Predictive Coding](https://mlsanity.com/paper/2405.15727/) (2024)
- [Score-based change point detection via tracking the best of infinitely many experts](https://mlsanity.com/paper/2408.14073/) (2024)
- [Active Learning for Multiple Change Point Detection in Non-stationary Time Series with Deep Gaussian Processes](https://mlsanity.com/paper/2505.20452/) (2025)
- [Detecting Changes in Causal Dependence with Kernels and Copulas](https://mlsanity.com/paper/2605.05809/) (2026)
- [SPACE: Sample-cloud Predictive Adaptive Conformal Ellipsoids for Multivariate Time-Series Forecasting](https://mlsanity.com/paper/2608.17333/) (2026)
- [Deciding When to Decide: Testing Operational Suboptimality Under Distributional Shift](https://mlsanity.com/paper/2608.29465/) (2026)
- [High-Dimensional Online Change Point Detection with Adaptive Thresholding and Interpretability](https://mlsanity.com/paper/2609.24278/) (2026)

## Abstract (arXiv)

Change point analysis has applications in a wide variety of fields. The general problem concerns the inference of a change in distribution for a set of time-ordered observations. Sequential detection is an online version in which new data is continually arriving and is analyzed adaptively. We are concerned with the related, but distinct, offline version, in which retrospective analysis of an entire sequence is performed. For a set of multivariate observations of arbitrary dimension, we consider nonparametric estimation of both the number of change points and the positions at which they occur. We do not make any assumptions regarding the nature of the change in distribution or any distribution assumptions beyond the existence of the alpha-th absolute moment, for some alpha in (0,2). Estimation is based on hierarchical clustering and we propose both divisive and agglomerative algorithms. The divisive method is shown to provide consistent estimates of both the number and location of change points under standard regularity assumptions. We compare the proposed approach with competing methods in a simulation study. Methods from cluster analysis are applied to assess performance and to allow simple comparisons of location estimates, even when the estimated number differs. We conclude with applications in genetics, finance and spatio-temporal analysis.