Expectation Maximization and Complex Duration Distributions for
  Continuous Time Bayesian Networks
  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
representation of CTBNs to allow a much richer class of transition durations
distributions, known as phase distributions. This class is a highly expressive
semi-parametric representation, which can approximate any duration distribution
arbitrarily closely. This extension to 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 - structure and parameters - from partially observed data, and, with the
use of phase distributions, achieves better performance than DBNs.
