Expectation Propagation for Continuous Time Bayesian Networks

TL;DR

This paper introduces an expectation propagation method for approximate inference in continuous time Bayesian networks, enabling flexible reasoning over variable trajectories and different time granularities.

Contribution

It develops a novel message passing scheme using expectation propagation tailored for CTBNs, allowing for efficient approximate inference over continuous trajectories.

Findings

Enables approximate inference conditioned on continuous time evidence

Allows variable time granularity in reasoning processes

Provides a scalable message passing framework for CTBNs

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. As shown previously, exact inference in CTBNs is intractable. We address the problem of approximate inference, allowing for general queries conditioned on evidence over continuous time intervals and at discrete time points. We show how CTBNs can be parameterized within the exponential family, and use that insight to develop a message passing scheme in cluster graphs and allows us to apply expectation propagation to CTBNs. The clusters in our cluster graph do not contain distributions over the cluster variables at individual time points, but distributions over trajectories of the variables throughout a duration. Thus, unlike discrete time temporal models such as dynamic Bayesian networks, we can adapt the time granularity at which we reason for different variables and in different conditions.