Continuous-Time Bayesian Networks with Clocks

TL;DR

This paper extends Continuous Time Bayesian Networks (CTBNs) by allowing arbitrary survival time distributions using node-wise clocks, enabling more flexible modeling of continuous-time stochastic processes without sacrificing tractability.

Contribution

It introduces a novel approach with node-wise clocks to model semi-Markov processes in CTBNs, avoiding auxiliary states and maintaining computational efficiency.

Findings

Effective algorithms for parameter and structure inference.

Successful experiments on synthetic and gene regulatory network data.

Advantages over existing CTBN extensions demonstrated.

Abstract

Structured stochastic processes evolving in continuous time present a widely adopted framework to model phenomena occurring in nature and engineering. However, such models are often chosen to satisfy the Markov property to maintain tractability. One of the more popular of such memoryless models are Continuous Time Bayesian Networks (CTBNs). In this work, we lift its restriction to exponential survival times to arbitrary distributions. Current extensions achieve this via auxiliary states, which hinder tractability. To avoid that, we introduce a set of node-wise clocks to construct a collection of graph-coupled semi-Markov chains. We provide algorithms for parameter and structure inference, which make use of local dependencies and conduct experiments on synthetic data and a data-set generated through a benchmark tool for gene regulatory networks. In doing so, we point out advantages compared to current CTBN extensions.