Nonparametric Multi Change Point Detection for Markov Chains via Adaptive Clustering

2026-07-14

AI Summary

This work addresses the lack of a rigorous nonparametric framework for multiple change-point detection in non-i.i.d. data, particularly Markov-dependent sequences. It establishes, for the first time, theoretical guarantees for nonparametric change-point detection in Markov chains by deriving Dvoretzky–Kiefer–Wolfowitz (DKW)-type inequalities via Rademacher complexity tailored to regenerative Markov chains. Building on this foundation, the authors design an efficient algorithm that integrates adaptive clustering with a penalty mechanism to accurately recover multiple true change-point locations. The method achieves a tight convergence rate that nearly matches the optimal rate known in the i.i.d. setting, thereby significantly extending both the applicability and theoretical underpinnings of nonparametric change-point detection to dependent data scenarios.

Abstract

Offline change point detection tries to detect time points of distribution change in a given data sequence; and is now routinely used in signal processing, speech processing, climatology etc. Despite this broad applicability across economics, computer science, and planetary sciences, rigorous, nonparametric techniques for change point detection with non-independent and identically distributed (i.i.d.) datasets has remained elusive. This paper establishes such guarantees by proposing a non-parametric clustering algorithm which can accurately obtain the change points from a given Markovian dataset of length $n$. It does so by bridging together two different components of mathematical statistics; Rademacher complexities of Markov chains, and adaptive clustering via penalisation. Our first result uses recent advances in Rademacher complexities of regenerating Markov chains to derive a Dvoretzky Kiefer Wolfowitz (DKW) type inequality for the empirical distribution of the Markov chain. We then use this to show that an adaptive clustering algorithm recovers the correct change points for a Markovian sequence. We establish the tightness of our rates by showing that they essentially coincide with the best known rates for i.i.d. data. We end the paper by discussing the computational considerations of the problem.

Problem

• change point detection
• nonparametric
• Markov chains
• non-i.i.d. data
• distribution change

Innovation

• nonparametric change point detection
• Markov chains
• adaptive clustering
• Rademacher complexity
• DKW inequality