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December 2018 Nonparametric Bayesian Negative Binomial Factor Analysis
Mingyuan Zhou
Bayesian Anal. 13(4): 1065-1093 (December 2018). DOI: 10.1214/17-BA1070

Abstract

A common approach to analyze a covariate-sample count matrix, an element of which represents how many times a covariate appears in a sample, is to factorize it under the Poisson likelihood. We show its limitation in capturing the tendency for a covariate present in a sample to both repeat itself and excite related ones. To address this limitation, we construct negative binomial factor analysis (NBFA) to factorize the matrix under the negative binomial likelihood, and relate it to a Dirichlet-multinomial distribution based mixed-membership model. To support countably infinite factors, we propose the hierarchical gamma-negative binomial process. By exploiting newly proved connections between discrete distributions, we construct two blocked and a collapsed Gibbs sampler that all adaptively truncate their number of factors, and demonstrate that the blocked Gibbs sampler developed under a compound Poisson representation converges fast and has low computational complexity. Example results show that NBFA has a distinct mechanism in adjusting its number of inferred factors according to the sample lengths, and provides clear advantages in parsimonious representation, predictive power, and computational complexity over previously proposed discrete latent variable models, which either completely ignore burstiness, or model only the burstiness of the covariates but not that of the factors.

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Mingyuan Zhou. "Nonparametric Bayesian Negative Binomial Factor Analysis." Bayesian Anal. 13 (4) 1065 - 1093, December 2018. https://doi.org/10.1214/17-BA1070

Information

Published: December 2018
First available in Project Euclid: 16 November 2017

zbMATH: 06989976
MathSciNet: MR3855363
Digital Object Identifier: 10.1214/17-BA1070

Keywords: burstiness , count matrix factorization , hierarchical gamma-negative binomial process , parsimonious representation , self- and cross-excitation

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Vol.13 • No. 4 • December 2018
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