A review of multivariate distributions for count data derived from the Poisson distribution

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The Poisson distribution has been widely studied and used for modeling univariate count-valued data. However, multivariate generalizations of the Poisson distribution that permit dependencies have been far less popular. Yet, real-world, high-dimensional, count-valued data found in word counts, genomics, and crime statistics, for example, exhibit rich dependencies and motivate the need for multivariate distributions that can appropriately model this data. We review multivariate distributions derived from the univariate Poisson, categorizing these models into three main classes: (1) where the marginal distributions are Poisson, (2) where the joint distribution is a mixture of independent multivariate Poisson distributions, and (3) where the node-conditional distributions are derived from the Poisson. We discuss the development of multiple instances of these classes and compare the models in terms of interpretability and theory. Then, we empirically compare multiple models from each class on three real-world datasets that have varying data characteristics from different domains, namely traffic accident data, biological next generation sequencing data, and text data. These empirical experiments develop intuition about the comparative advantages and disadvantages of each class of multivariate distribution that was derived from the Poisson. Finally, we suggest new research directions as explored in the subsequent Discussion section. (C) 2017 Wiley Periodicals, Inc.
Publisher
WILEY
Issue Date
2017-05
Language
English
Article Type
Review
Citation

WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL STATISTICS, v.9, no.3

ISSN
1939-0068
DOI
10.1002/wics.1398
URI
http://hdl.handle.net/10203/223769
Appears in Collection
AI-Journal Papers(저널논문)
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