Shapley-PC: Constraint-based Causal Structure Learning with a Shapley Inspired Framework

Abstract: Causal Structure Learning (CSL), also referred to as causal discovery, amounts to extracting causal relations among variables in data. CSL enables the estimation of causal effects from observational data alone, avoiding the need to perform real life experiments. Constraint-based CSL leverages conditional independence tests to perform causal discovery. We propose Shapley-PC, a novel method to improve constraint-based CSL algorithms by using Shapley values over the possible conditioning sets, to decide which variables are responsible for the observed conditional (in)dependences. We prove soundness, completeness and asymptotic consistency of Shapley-PC and run a simulation study showing that our proposed algorithm is superior to existing versions of PC.