  Recent years have seen many advances in methods for causal structure learning
from data. The empirical assessment of such methods, however, is much less
developed. Motivated by this gap, we pose the following question: how can one
assess, in a given problem setting, the practical efficacy of one or more
causal structure learning methods? We formalize the problem in a
decision-theoretic framework, via a notion of expected loss or risk for the
causal setting. We introduce a theoretical notion of causal risk as well as
sample quantities that can be computed from data, and study the relationship
between the two, both theoretically and through an extensive simulation study.
Our results provide an assumptions-light framework for assessing causal
structure learning methods that can be applied in a range of practical
use-cases.
