Exact Bayesian inference for off-line change-point detection in tree-structured graphical models
This provides a method for researchers in fields like biology and neuroscience to analyze time-series data with structural changes, though it is incremental as it builds on existing dynamic programming and algebraic techniques.
The paper tackles the problem of detecting change-points in multivariate time-series where the underlying graphical model's structure and parameters change abruptly, and demonstrates that exact Bayesian inference is possible when using spanning trees as graph structures, enabling efficient computation of posterior distributions for change-points and edge probabilities.
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.