##
Expectation Propagation for Continuous Time Bayesian Networks

[PDF]

### 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.

### Full Citation

U. Nodelman, D. Koller, and C.R. Shelton (2005). "Expectation
Propagation for Continuous Time Bayesian Networks." Proceedings of the
Twenty-first Conference on Uncertainty in AI (UAI) (pp. 431-440).

### Bibtex

@inproceedings{Nodelman+al:UAI05EP,
title = {Expectation Propagation for Continuous Time Bayesian Networks},
author = {U. Nodelman and D. Koller and C.R. Shelton},
booktitle = {Proceedings of the Twenty-first Conference on Uncertainty in AI (UAI)},
address = {Edinburgh, Scottland, UK},
month = {July},
year = 2005,
pages = {431--440},
}