Propagation for Dynamic Continuous Time Chain Event Graphs
This provides a method for probabilistic inference in continuous-time event-based models, which is incremental as it extends existing propagation algorithms to dynamic settings.
The paper tackles the problem of performing exact inference in continuous time dynamic Chain Event Graphs (CT-DCEGs) for asymmetric state space processes, resulting in a tractable scheme that simplifies the graph with evidence and shows preference over Dynamic Bayesian Networks in contexts with asymmetry and natural ordering.
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 Kjærulff (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.