Propagation for Dynamic Continuous Time Chain Event Graphs

TL;DR

This paper introduces a new inference scheme for continuous time dynamic Chain Event Graphs (CT-DCEGs), enabling efficient analysis of asymmetric, evolving processes and demonstrating advantages over traditional models like DBNs in certain contexts.

Contribution

It extends the CEG propagation algorithm and develops an exact inference method for CT-DCEGs, handling temporal evidence and simplifying the graph structure.

Findings

CT-DCEGs outperform DBNs in asymmetric, ordered processes

The proposed scheme enables tractable exact inference in CT-DCEGs

Graph simplification occurs upon observing compatible evidence

Abstract

Chain Event Graphs (CEGs) are a family of event-based graphical models that represent context-specific conditional independences typically exhibited by asymmetric state space problems. The class of continuous time dynamic CEGs (CT-DCEGs) provides a factored representation of longitudinally evolving trajectories of a process in continuous time. Temporal evidence in a CT-DCEG introduces dependence between its transition and holding time distributions. We present a tractable exact inferential scheme analogous to the scheme in Kj{\ae}rulff (1992) for discrete Dynamic Bayesian Networks (DBNs) which employs standard junction tree inference by "unrolling" the DBN. To enable this scheme, we present an extension of the standard CEG propagation algorithm (Thwaites et al., 2008). Interestingly, the CT-DCEG benefits from simplification of its graph on observing compatible evidence while preserving the still relevant symmetries within the asymmetric network. Our results indicate that the CT-DCEG is preferred to DBNs and continuous time BNs under contexts involving significant asymmetry and a natural total ordering of the process evolution.