Learning Generalized Hypergeometric Distribution (GHD) DAG models
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We introduce a new class of identifiable DAG models, where each node has a conditional distribution given its parents belongs to a family of generalized hypergeometric distributions (GHD). a family of generalized hypergeometric distributions (GHD) includes a lot of discrete distributions such as Binomial, Beta-binomial, Poisson, Poisson type, displaced Poisson, hyper-Poisson, logarithmic, and many more. We prove that if the data drawn from the new class of DAG models, one can fully identify the graph. We further provide a reliable and tractable algorithm that recovers the directed graph from finitely many data. We show through theoretical results and simulations that our algorithm is statistically consistent even in high-dimensional settings (n >p) if the degree of the graph is bounded, and performs well compared to state-of-the-art DAG-learning algorithms.
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