Identifiability of Generalized Hypergeometric Distribution (GHD) Directed Acyclic Graphical Models

Gunwoong Park, Hyewon Park
Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, PMLR 89:158-166, 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, 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.

Cite this Paper

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.} }
Endnote
%0 Conference Paper %T Identifiability of Generalized Hypergeometric Distribution (GHD) Directed Acyclic Graphical Models %A Gunwoong Park %A Hyewon Park %B Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Masashi Sugiyama %F pmlr-v89-park19a %I PMLR %P 158--166 %U https://proceedings.mlr.press/v89/park19a.html %V 89 %X 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.
APA
Park, G. & Park, H.. (2019). Identifiability of Generalized Hypergeometric Distribution (GHD) Directed Acyclic Graphical Models. Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 89:158-166 Available from https://proceedings.mlr.press/v89/park19a.html.

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