Expectation Maximization and Complex Duration Distributions for Continuous Time Bayesian Networks (2005)

by Uri Nodelman, Christian R. Shelton, and Daphne Koller

Abstract: Continuous time Bayesian networks (CTBNs) describe structured stochastic processes with finitely many states that evolve over continuous time. A CTBN is a directed (possibly cyclic) dependency graph over a set of variables, each of which represents a finite state continuous time Markov process whose transition model is a function of its parents. We address the problem of learning the parameters and structure of a CTBN from partially observed data. We show how to apply expectation maximization (EM) and structural expectation maximization (SEM) to CTBNs. The availability of the EM algorithm allows us to extend the representaiton of CTBNs to allow a much richer class of transition duration distributions, known as phase distributions. This class is a highly expressive semi-parametric representation, which can approximate any duration distribution arbitrarily closely. This extension of the CTBN framework addresses one of the main limitations of both CTBNs and DBNs - the restriction to exponentially / geometrically distributed duration. We present experimental results on a real data set of people's life spans, showing that our algorithm learns reasonable models - structures and parameters - from partially observed data, and, with the use of phase distributions, achieves better performance than DBNs.

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Uri Nodelman, Christian R. Shelton, and Daphne Koller (2005). "Expectation Maximization and Complex Duration Distributions for Continuous Time Bayesian Networks." Proceedings of the Twenty-First International Conference on Uncertainty in Artificial Intelligence (pp. 421-430).

Bibtex citation

@inproceedings{NodSheKol05,
   author = "Uri Nodelman and Christian R. Shelton and Daphne Koller",
   title = "Expectation Maximization and Complex Duration Distributions for Continuous Time {B}ayesian Networks",
   booktitle = "Proceedings of the Twenty-First International Conference on Uncertainty in Artificial Intelligence",
   booktitleabbr = "{UAI}",
   year = 2005,
   pages = "421--430",
}