Discovering reliable causal rules

We study the problem of deriving policies, or rules, that when enacted on a complex system, cause a desired outcome. Absent the ability to perform controlled experiments, such rules have to be inferred from past observations of the system's behaviour. This is a challenging problem for two reasons: First, observational effects are often unrepresentative of the underlying causal effect because they are skewed by the presence of confounding factors. Second, naive empirical estimations of a rule's effect have a high variance, and, hence, their maximisation typically leads to spurious results. To address these issues, we first identify conditions on the underlying causal system that—by correcting for the effect of potential confounders—allow estimating the causal effect from observational data. Importantly, we provide a criterion under which causal rule discovery is possible. Moreover, to discover reliable causal rules from a sample, we propose a conservative and consistent estimator of the causal effect, and derive an efficient and exact algorithm that maximises the estimator. Extensive experiments on a variety of real-world and synthetic datasets show that the proposed estimator converges faster to the ground truth than the naive estimator, recovers causal rules even at small sample sizes, and the proposed algorithm efficiently discovers meaningful rules.