Statistics and Computing

, Volume 27, Issue 5, pp 1331–1345 | Cite as

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

  • L. SchwallerEmail author
  • S. Robin


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.


Change-point detection Exact Bayesian inference Graphical model Multivariate time-series Spanning tree 



The authors thank Ivor Cribben (Alberta School of Business, Canada) for kindly providing the fMRI data. They also thank Sarah Ouadah (AgroParisTech, INRA, Paris, France) for fruitful discussions.

Supplementary material

11222_2016_9689_MOESM1_ESM.pdf (723 kb)
Supplementary material 1 (pdf 722 KB)


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.UMR MIA-Paris, AgroParisTech, INRAUniversité Paris-SaclayParisFrance

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