Bayesian Analysis

Nonparametric Bayesian Negative Binomial Factor Analysis

Mingyuan Zhou

Advance publication

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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.

Article information

Source
Bayesian Anal. (2017), 29 pages.

Dates
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.ba/1510801993

Digital Object Identifier
doi:10.1214/17-BA1070

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

Rights
Creative Commons Attribution 4.0 International License.

Citation

Zhou, Mingyuan. Nonparametric Bayesian Negative Binomial Factor Analysis. Bayesian Anal., advance publication, 16 November 2017. doi:10.1214/17-BA1070. https://projecteuclid.org/euclid.ba/1510801993


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