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.