Bayesian Model Selection for Change Point Detection and Clustering

TL;DR

This paper introduces a Bayesian-inspired method for detecting change points and clustering levels in piecewise constant signals, combining model selection with efficient algorithms and statistical guarantees.

Contribution

It proposes a novel nonparametric penalized least squares model selection approach for change point detection and clustering, with theoretical analysis and practical validation.

Findings

Algorithm effectively detects change points and clusters.

Statistical guarantees including oracle inequality and consistency.

Validated on simulated data demonstrating performance.

Abstract

We address the new problem of estimating a piece-wise constant signal with the purpose of detecting its change points and the levels of clusters. Our approach is to model it as a nonparametric penalized least square model selection on a family of models indexed over the collection of partitions of the design points and propose a computationally efficient algorithm to approximately solve it. Statistically, minimizing such a penalized criterion yields an approximation to the maximum a posteriori probability (MAP) estimator. The criterion is then analyzed and an oracle inequality is derived using a Gaussian concentration inequality. The oracle inequality is used to derive on one hand conditions for consistency and on the other hand an adaptive upper bound on the expected square risk of the estimator, which statistically motivates our approximation. Finally, we apply our algorithm to simulated data to experimentally validate the statistical guarantees and illustrate its behavior.