  There has been a growing interest in causal learning in recent years.
Commonly used representations of causal structures, including Bayesian networks
and structural equation models (SEM), take the form of directed acyclic graphs
(DAGs). We provide a novel mixed-integer quadratic programming formulation and
associated algorithm that identifies DAGs on up to 50 vertices, where these are
identifiable. We call this method ExDAG, which stands for Exact learning of
DAGs. Although there is a superexponential number of constraints that prevent
the formation of cycles, the algorithm adds constraints violated by solutions
found, rather than imposing all constraints in each continuous-valued
relaxation. Our empirical results show that ExDAG outperforms local
state-of-the-art solvers in terms of precision and outperforms state-of-the-art
global solvers with respect to scaling, when considering Gaussian noise. We
also provide validation with respect to other noise distributions.
