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.

本文研究了基于连续时间贝叶斯网络（CTBNs）的参数学习和结构学习方法， 提出了一种基于相位分布的扩展方法，可以更好地逼近时长分布的实现， 经实验结果表明，该算法可以在部分观测数据中学习出合理的结构和参数，并在人们寿命的真实数据集上比 DBN 算法表现更好。