Tractable Bounding of Counterfactual Queries by Knowledge Compilation

TL;DR

This paper introduces a knowledge compilation approach to efficiently compute bounds on counterfactual queries in causal models, significantly speeding up inference compared to traditional Bayesian network methods.

Contribution

It proposes a symbolic knowledge compilation method that enables fast, repeated inference for counterfactual bounds in structural causal models, improving computational efficiency.

Findings

Up to tenfold speed-up in inference times

Effective parallelisation techniques demonstrated

Significant computational advantages over standard Bayesian inference

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.