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Inference Complexity in Continuous Time Bayesian Networks

The continuous time Bayesian network (CTBN) enables temporal reasoning by representing a system as a factored, finite-state Markov process. The CTBN uses a traditional Bayesian network (BN) to specify the initial distribution. Thus, the complexity results of Bayesian networks also apply to CTBNs through this initial distribution. However, the question remains whether propagating the probabilities through time is, by itself, also a hard problem. We show that exact and approximate inference in continuous time Bayesian networks is NP-hard even when the initial states are given.