Expectation Maximization and Complex Duration Distributions for Continuous Time Bayesian Networks
This work addresses a key limitation in modeling structured stochastic processes by allowing non-exponential duration distributions, which is incremental but important for domains like survival analysis.
The authors tackled the problem of learning parameters and structure of Continuous Time Bayesian Networks (CTBNs) from partially observed data, showing that expectation maximization algorithms enable the use of phase distributions to model complex durations, which improved performance over Dynamic Bayesian Networks on a real dataset of life spans.
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.