Identifiability of Generalized Hypergeometric Distribution (GHD) Directed Acyclic Graphical Models
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Proceedings of Machine Learning Research, PMLR 89:158166, 2019.
Abstract
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, Betabinomial, negative binomial, Poisson, hyperPoisson, 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 polynomialtime algorithm that recovers the graph from finitely many data. We show through theoretical results and numerical experiments that our algorithm is statistically consistent in highdimensional settings (p >n) if the indegree of the graph is bounded, and outperforms stateoftheart DAG learning algorithms.
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