Rao-Blackwellising Bayesian Causal Inference


arXiv:2402.14781v1 Announce Sort: cross
Summary: Bayesian causal inference, i.e., inferring a posterior over causal fashions for the use in downstream causal reasoning duties, poses a tough computational inference drawback that’s little explored in literature. On this work, we mix strategies from order-based MCMC construction studying with latest advances in gradient-based graph studying into an efficient Bayesian causal inference framework. Particularly, we decompose the issue of inferring the causal construction into (i) inferring a topological order over variables and (ii) inferring the mum or dad units for every variable. When limiting the variety of mother and father per variable, we are able to precisely marginalise over the mum or dad units in polynomial time. We additional use Gaussian processes to mannequin the unknown causal mechanisms, which additionally permits their actual marginalisation. This introduces a Rao-Blackwellization scheme, the place all elements are eradicated from the mannequin, aside from the causal order, for which we study a distribution by way of gradient-based optimisation. The mixture of Rao-Blackwellization with our sequential inference process for causal orders yields state-of-the-art on linear and non-linear additive noise benchmarks with scale-free and Erdos-Renyi graph constructions.

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