2016/08/31 by David I. Inouye, Eunho Yang, Inouye, David I. +5 · 1 citation
Decision Sciences · Computer Science · #Data Quality and Management #Bayesian Methods and Mixture Models #Bayesian Modeling and Causal Inference
paper · pdf · doi:10.48550/arxiv.1609.00066
The Poisson distribution has been widely studied and used for modeling\nunivariate count-valued data. Multivariate generalizations of the Poisson\ndistribution that permit dependencies, however, have been far less popular.\nYet, real-world high-dimensional count-valued data found in word counts,\ngenomics, and crime statistics, for example, exhibit rich dependencies, and\nmotivate the need for multivariate distributions that can appropriately model\nthis data. We review multivariate distributions derived from the univariate\nPoisson, categorizing these models into three main classes: 1) where the\nmarginal distributions are Poisson, 2) where the joint distribution is a\nmixture of independent multivariate Poisson distributions, and 3) where the\nnode-conditional distributions are derived from the Poisson. We discuss the\ndevelopment of multiple instances of these classes and compare the models in\nterms of interpretability and theory. Then, we empirically compare multiple\nmodels from each class on three real-world datasets that have varying data\ncharacteristics from different domains, namely traffic accident data,\nbiological next generation sequencing data, and text data. These empirical\nexperiments develop intuition about the comparative advantages and\ndisadvantages of each class of multivariate distribution that was derived from\nthe Poisson. Finally, we suggest new research directions as explored in the\nsubsequent discussion section.\n