A review of multivariate distributions for count data derived from the Poisson distribution
Abstract
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. WIREs Comput Stat 2017, 9:e1398. doi: 10.1002/wics.1398
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Mar 28, 2017
- Source ID
- 10.1002/wics.1398
Entities
People
- David I. Inouye
- Eunho Yang
- Genevera I. Allen
- Pradeep Ravikumar
Organizations
- Army Research Office
- Baylor College of Medicine
- Carnegie Mellon University
- KAIST
- National Institutes of Health
- National Science Foundation
- Rice University
- University of Texas at Austin