Identifiability of Generalized Hypergeometric Distribution (GHD) Directed Acyclic Graphical Models
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, 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.
BibTeX
@InProceedings{pmlr-v89-park19a,
title = {Identifiability of Generalized Hypergeometric Distribution (GHD) Directed Acyclic Graphical Models},
author = {Park, Gunwoong and Park, Hyewon},
booktitle = {Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics},
pages = {158--166},
year = {2019},
editor = {Chaudhuri, Kamalika and Sugiyama, Masashi},
volume = {89},
series = {Proceedings of Machine Learning Research},
month = {16--18 Apr},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v89/park19a/park19a.pdf},
url = {https://proceedings.mlr.press/v89/park19a.html},
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, 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.}
}