Bayesian Model for Multiple Change-points Detection in Multivariate Time Series

TL;DR

This paper introduces a Bayesian method for detecting multiple change-points in multivariate time series that makes minimal assumptions, performs well on Gaussian and non-normal data, and learns shared change-point probabilities.

Contribution

It proposes a novel Bayesian framework combining local robust tests with global optimization, handling non-simultaneous change-points and unknown distributions.

Findings

Performs comparably to classical methods on Gaussian data.

Outperforms models with outliers and non-normal data.

Effectively learns shared change-point probabilities in multivariate data.

Abstract

This paper addresses the issue of detecting change-points in multivariate time series. The proposed approach differs from existing counterparts by making only weak assumptions on both the change-points structure across series, and the statistical signal distributions. Specifically change-points are not assumed to occur at simultaneous time instants across series, and no specific distribution is assumed on the individual signals. It relies on the combination of a local robust statistical test acting on individual time segments, with a global Bayesian framework able to optimize configurations from multiple local statistics (from segments of a unique time series or multiple time series). Using an extensive experimental set-up, our algorithm is shown to perform well on Gaussian data, with the same results in term of recall and precision as classical approaches, such as the fused lasso and the Bernoulli Gaussian model. Furthermore, it outperforms the reference models in the case of non normal data with outliers. The control of the False Discovery Rate by an acceptance level is confirmed. In the case of multivariate data, the probabilities that simultaneous change-points are shared by some specific time series are learned. We finally illustrate our algorithm with real datasets from energy monitoring and genomic. Segmentations are compared to state-of-the-art approaches based on fused lasso and group fused lasso.