Gibbs Sampling in Factorized Continuous-Time Markov Processes

TL;DR

This paper introduces a novel Gibbs sampling method for multi-component continuous-time processes, enabling efficient, unbiased approximate inference in complex models like continuous-time Bayesian networks.

Contribution

It develops the first asymptotically unbiased Gibbs sampling procedure tailored for factorized continuous-time Markov processes, exploiting network structure for efficiency.

Findings

Efficient sampling adapts to the process's natural time scale.

Reduces computational cost by exploiting network structure.

Provides asymptotically unbiased approximation in complex models.

Abstract

A central task in many applications is reasoning about processes that change over continuous time. Continuous-Time Bayesian Networks is a general compact representation language for multi-component continuous-time processes. However, exact inference in such processes is exponential in the number of components, and thus infeasible for most models of interest. Here we develop a novel Gibbs sampling procedure for multi-component processes. This procedure iteratively samples a trajectory for one of the components given the remaining ones. We show how to perform exact sampling that adapts to the natural time scale of the sampled process. Moreover, we show that this sampling procedure naturally exploits the structure of the network to reduce the computational cost of each step. This procedure is the first that can provide asymptotically unbiased approximation in such processes.