Bayesian Model Selection for Identifying Markov Equivalent Causal Graphs
Many approaches to causal discovery are limited by their inability to discriminate between Markov equivalent graphs given only observational data. We formulate causal discovery as a marginal likelihood based Bayesian model selection problem. We adopt a parameterization based on the notion of the independence of causal mechanisms which renders Markov equivalent graphs distinguishable. We complement this with an empirical Bayesian approach to setting priors so that the actual underlying causal graph is assigned a higher marginal likelihood than its alternatives. Adopting a Bayesian approach also allows for straightforward modeling of unobserved confounding variables, for which we provide a variational algorithm to approximate the marginal likelihood, since this desirable feat renders the computation of the marginal likelihood intractable. We believe that the Bayesian approach to causal discovery both allows the rich methodology of Bayesian inference to be used in various difficult aspects of this problem and provides a unifying framework to causal discovery research. We demonstrate promising results in experiments conducted on real data, supporting our modeling approach and our inference methodology.
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