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A Review of Multivariate Distributions for Count Data Derived from the Poisson Distribution | | David I. Inouye
; Eunho Yang
; Genevera I. Allen
; Pradeep Ravikumar
; | | Date: |
1 Sep 2016 | | Abstract: | The Poisson distribution has been widely studied and used for modeling
univariate count-valued data. Multivariate generalizations of the Poisson
distribution that permit dependencies, however, 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 Poissons, and 3) where the node-conditional distributions are
derived from the Poisson. We discuss the development of multiple instances of
these classes. Then, we extensively compare multiple models from each class on
five real-world datasets from traffic accident data, crime statistics,
biological next generation sequencing data and text corpora. 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. (See arXiv paper comments for access to
supplementary material.) | | Source: | arXiv, 1609.0066 | | Services: | Forum | Review | PDF | Favorites | |
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