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 can lead to random results. To address these issues, first we measure the causal effect of a rule from observational data---adjusting for the effect of potential confounders. Importantly, we provide a graphical criteria 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. On synthetic data, the proposed estimator converges faster to the ground truth than the naive estimator and recovers relevant causal rules even at small sample sizes. Extensive experiments on a variety of real-world datasets show that the proposed algorithm is efficient and discovers meaningful rules.

Existing algorithms for subgroup discovery with numerical targets do not optimize the error or target variable dispersion of the groups they find. This often leads to unreliable or inconsistent statements about the data, rendering practical applications, especially in scientific domains, futile. Therefore, we here extend the optimistic estimator framework for optimal subgroup discovery to a new class of objective functions: we show how tight estimators can be computed efficiently for all functions that are determined by subgroup size (non-decreasing dependence), the subgroup median value, and a dispersion measure around the median (non-increasing dependence). In the important special case when dispersion is measured using the average absolute deviation from the median, this novel approach yields a linear time algorithm. Empirical evaluation on a wide range of datasets shows that, when used within branch-and-bound search, this approach is highly efficient and indeed discovers subgroups with much smaller errors.