Bayesian Multinomial Logistic Normal Models through Marginally Latent Matrix-T Processes

TL;DR

This paper introduces a new class of Bayesian models called marginally latent matrix-t processes for analyzing multivariate count data, offering faster and more accurate inference than traditional MCMC methods.

Contribution

It develops inference schemes for MLN models using marginally latent matrix-t processes, significantly improving speed and accuracy over existing methods.

Findings

Inference schemes are 4-5 orders of magnitude faster than MCMC.

Models effectively handle complex covariance structures in count data.

Demonstrated high accuracy in practical applications.

Abstract

Bayesian multinomial logistic-normal (MLN) models are popular for the analysis of sequence count data (e.g., microbiome or gene expression data) due to their ability to model multivariate count data with complex covariance structure. However, existing implementations of MLN models are limited to handling small data sets due to the non-conjugacy of the multinomial and logistic-normal distributions. We introduce MLN models which can be written as marginally latent matrix-t process (LTP) models. Marginally LTP models describe a flexible class of generalized linear regression, non-linear regression, and time series models. We develop inference schemes for Marginally LTP models and, through application to MLN models, demonstrate that our inference schemes are both highly accurate and often 4-5 orders of magnitude faster than MCMC.