(Almost) Automating Causal Inference With Tractable Probabilistic Circuits

Approximate inference can lead to wrong conclusions when working with causal effects. For exact causal inference, the community has started using Probabilistic Circuits (PCs). However, these PCs have only been shown to work on discrete domains and only for backdoor adjustment, and as we show, existing previous methods fail to represent the dependencies present in the data under general vtree structures. We therefore develop a general-purpose causal inference engine for PCs that cover continuous and mixed domains, general vtree structures, and identifiable interventional queries. To this end, we pinpoint where existing circuits fall short: their conditioning operation is not exactly evaluable for a broad class of estimands, and their construction loses the capacity to model dependencies on general vtree structures. We develop the tools that overcome both: a diversity-preserving circuit construction, and disjoint continuous leaves that extend exact inference to mixed domains. We introduce T-ID, a tractability-aware extension of the ID algorithm, whose soundness and completeness we prove. T-ID takes as input a query, a causal graph, and a circuit, and outputs identifiability, tractability relative to the weak marginal determinisms available in the circuit, and a compositional query with a stated complexity bound. Reproducible experiments on synthetic continuous and mixed structural causal models corroborate our theoretical predictions.