Learning dynamic bayesian belief networks using conditional phase-type distributions

Abstract

In this paper, we introduce the Dynamic Bayesian Belief Network (DBBN) and show how it can be used in data mining. DBBNs generalise the concept of Bayesian Belief Networks (BBNs) to include a time dimension. We may thus represent a stochastic (or probabilistic) process along with causal information. The approach combines BBNs for modelling causal information with a latent Markov model for dealing with temporal (survival) events. It is assumed that the model includes both qualitative (causal) and quantitative (survival) variables. We introduce the idea of conditional phase-type (C-Ph) distributions to model such data. These models describe duration until an event occurs in terms of a process consisting of a sequence of phases-the states of a latent Markov model. Our approach is illustrated using data on hospital spells (the process) of geriatric patients along with personal details, admissions reasons, dependency levels and destination (the causal network).