  A key question in causal inference analyses is how to find subgroups with
elevated treatment effects. This paper takes a machine learning approach and
introduces a generative model, Causal Rule Sets (CRS), for interpretable
subgroup discovery. A CRS model uses a small set of short decision rules to
capture a subgroup where the average treatment effect is elevated. We present a
Bayesian framework for learning a causal rule set. The Bayesian model consists
of a prior that favors simple models for better interpretability as well as
avoiding overfitting, and a Bayesian logistic regression that captures the
likelihood of data, characterizing the relation between outcomes, attributes,
and subgroup membership. The Bayesian model has tunable parameters that can
characterize subgroups with various sizes, providing users with more flexible
choices of models from the \emph{treatment efficient frontier}. We find maximum
a posteriori models using iterative discrete Monte Carlo steps in the joint
solution space of rules sets and parameters. To improve search efficiency, we
provide theoretically grounded heuristics and bounding strategies to prune and
confine the search space. Experiments show that the search algorithm can
efficiently recover true underlying subgroups. We apply CRS on public and
real-world datasets from domains where interpretability is indispensable. We
compare CRS with state-of-the-art rule-based subgroup discovery models. Results
show that CRS achieved consistently competitive performance on datasets from
various domains, represented by high treatment efficient frontiers.
