Tractable Bounding of Counterfactual Queries by Knowledge Compilation

David Huber, Yizuo Chen, Alessandro Antonucci, Adnan Darwiche, Marco Zaffalon

Keywords: Causal inference, partially identifiable queries, counterfactuals, tractable arithmetic circuits, knowledge compilation.

TL;DR: We discuss the advantages of a symbolic knowledge compilation based on tractable arithmetic circuits in speeding up the computation of bounds to counterfactual queries in structural causal models.

Abstract: We discuss the problem of bounding partially identifiable queries, such as counterfactuals, in Pearlian structural causal models. A recently proposed iterated EM scheme yields an inner approximation of those bounds by sampling the initialisation parameters. Such a method requires multiple (Bayesian network) queries over models sharing the same structural equations and topology, but different exogenous probabilities. This setup makes a compilation of the underlying model to an arithmetic circuit advantageous, thus inducing a sizeable inferential speed-up. We show how a single symbolic knowledge compilation allows us to obtain the circuit structure with symbolic parameters to be replaced by their actual values when computing the different queries. We also discuss parallelisation techniques to further speed up the bound computation. Experiments against standard Bayesian network inference show clear computational advantages with up to an order of magnitude of speed-up.

Submission Number: 16