Exact Bayesian inference for off-line change-point detection in tree-structured graphical models
- 272 Downloads
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.
KeywordsChange-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.
- Arbeitman, M.N., Furlong, E.E.M., Imam, F., Johnson, E., Null, B.H., Baker, B.S., Krasnow, Ma., Scott, M.P., Davis, R.W., White, K.P.: Gene expression during the life cycle of Drosophila melanogaster. Science 297(5590), 2270–2275 (2002). doi: 10.1126/science.1072152. (ISSN: 1095-9203)CrossRefGoogle Scholar
- Barber, D., Cemgil, A.: Graphical models for time-series. IEEE Signal Process. Mag. (2010). doi: 10.1109/MSP.2010.938028 (ISSN: 1053-5888)
- Fox, E., Sudderth, E., Jordan, M., Willsky, A.: Nonparametric Bayesian learning of switching linear dynamical systems. Adv. Neural Inf. Process. Syst. 21, 457–464 (2009)Google Scholar
- Friedman, N., Murphy, K., Russell, S.: Learning the structure of dynamic probabilistic networks. In: Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence, pp. 139–147, (1998). doi: 10.1111/j.1469-7580.2008.00962.x
- Kolar, M., Song, L., Ahmed, A., Xing, E.P.: Estimating time-varying networks, 4. (2010). doi: 10.1214/09-AOAS308 (ISBN: 0001409107)
- Lauritzen, S.L.: Graphical Models. Oxford University Press, Oxford (1996). (ISBN: 0-19-852219-3)Google Scholar
- Murphy, K., Mian, S.: Modelling Gene Expression Data Using Dynamic Bayesian Networks. Technical report (1999)Google Scholar
- Schwaller, L., Robin, S., Stumpf, M.: Bayesian Inference of Graphical Model Structures Using Trees. http://arxiv.org/abs/1504.02723 (2015)
- Siracusa, M.R.: Tractable Bayesian inference of time-series dependence structure. In: Proceedings of the 23th International Conference on Artificial Intelligence and Statistics, vol. 5, pp. 528–535. (2009)Google Scholar
- Xuan, X., Murphy, K.: Modeling changing dependency structure in multivariate time series. In: Proceedings of the 24th International Conference on Machine Learning (2007), vol. 227, issue id m, pp. 1055–1062, (2007). doi: 10.1145/1273496.1273629 (ISSN: 1595937935)