  We introduce a new class of identifiable DAG models where the conditional
distribution of each node given its parents belongs to a family of generalized
hypergeometric distributions (GHD). A family of generalized hypergeometric
distributions includes a lot of discrete distributions such as the binomial,
Beta-binomial, negative binomial, Poisson, hyper-Poisson, and many more. We
prove that if the data drawn from the new class of DAG models, one can fully
identify the graph structure. We further present a reliable and polynomial-time
algorithm that recovers the graph from finitely many data. We show through
theoretical results and numerical experiments that our algorithm is
statistically consistent in high-dimensional settings (p>n) if the indegree of
the graph is bounded, and out-performs state-of-the-art DAG learning
algorithms.
