Latent Factor Analysis and Regression of Multivariate Poisson

De, Ananyapam (2023) Latent Factor Analysis and Regression of Multivariate Poisson. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS dissertation of Ananyapam De (18MS075)) Thesis_18MS075.pdf - Submitted Version Restricted to Repository staff only Download (2MB)

Abstract

Correlated count variables are ubiquitous and are typically modelled using normal distributions to analyze their correlations or to conduct regression. However, the normal approximation is not very accurate when many of these counts are less than 10. The Poisson lognormal describes D correlated counts yi (i subscript) ϵ {0, 1, 2 . . .} as a mixture of Poissons with rates μy (superscript) i(subscript) = ezi (zi superscript)) with a persample latent variables z ~ N(μ,Σ). This distribution is a natural alternative to the normal distribution for count vectors since it models overdispersed and correlated distributions. In this work we present a variational inference method to train models based on this distribution, that allows us to perform regression and latent factor analysis for overdispersed correlated counts. We use amortization allowing us to perform accurate inference by learning only a small number of parameters. We begin by employing Laplace approximations and later move on to using neural networks. Based on the results of our study, we assert that our model outperforms PLNmodels, the highly e↵ective approach developed by Chiquet et al. for learning correlated count data and present evidence to support this claim which highlight the distinctive features of our model that contribute to its performance. Further we extend this approach to other distributions like the Bernoulli, Gamma, Gumbel etc.

Actions (login required)

View Item