Exact Bayesian inference for off-line change-point detection in tree-structured graphical models

TL;DR

This paper presents an exact Bayesian method for off-line change-point detection in multivariate time-series modeled by graphical models, specifically using spanning trees to enable efficient inference.

Contribution

It introduces a novel approach combining dynamic programming and algebraic spanning tree properties to perform exact Bayesian inference in change-point detection.

Findings

Efficient computation of posterior distributions for change-points.

Accurate detection results demonstrated on biological and neuroscience data.

Method handles graph and segmentation spaces simultaneously.

Abstract

We consider the problem of change-point detection in multivariate time-series. The multivariate distribution of the observations is supposed to follow a graphical model, whose graph and parameters are affected by abrupt changes throughout time. We demonstrate that it is possible to perform exact Bayesian inference whenever one considers a simple class of undirected graphs called spanning trees as possible structures. We are then able to integrate on the graph and segmentation spaces at the same time by combining classical dynamic programming with algebraic results pertaining to spanning trees. In particular, we show that quantities such as posterior distributions for change-points or posterior edge probabilities over time can efficiently be obtained. We illustrate our results on both synthetic and experimental data arising from biology and neuroscience.