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Abstract:
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Learning the causal structure from a partially observed dynamic system with feedback is largely unexplored. Markov properties for dynamical systems can be represented by local independence graphs (LIGs), which are directed but not necessarily acyclic, and they can thus represent feedback. We introduce mixed directed graphs (MDGs) as a generalization of LIGs with a corresponding separation criterion. The class of MDGs is closed under marginalization. Thus Markov properties for a partially observed system can be represented by MDGs, and MDGs can be learned via tests for local conditional independence. Directed edges that are shared by all Markov equivalent MDGs can be interpreted as learned causal relations. We demonstrate how this can be implemented in practice for multivariate point processes.
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