Expectation Maximization and Complex Duration Distributions for Continuous Time Bayesian Networks

TL;DR

This paper extends continuous time Bayesian networks (CTBNs) to include phase distributions for more flexible duration modeling, introduces EM-based learning algorithms, and demonstrates improved performance on real-world lifespan data.

Contribution

It introduces a method to learn CTBNs with complex duration distributions using EM and SEM, overcoming previous limitations to exponential durations.

Findings

The extended CTBNs can model arbitrary duration distributions.

The EM algorithm enables learning from partially observed data.

Phase distributions improve model performance on lifespan data.

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 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.