Score matching for compositional distributions

TL;DR

This paper introduces novel score matching estimators for compositional data, effectively handling zeros and high-dimensionality, with applications to microbiome data demonstrating good model fit.

Contribution

The paper develops a new score matching approach for compositional distributions on manifolds, addressing zero-inflation and computational challenges.

Findings

Estimators are scalable and have closed-form solutions.

Method performs well in simulations for truncation and Dirichlet models.

Model fits real microbiome data effectively.

Abstract

Compositional data and multivariate count data with known totals are challenging to analyse due to the non-negativity and sum-to-one constraints on the sample space. It is often the case that many of the compositional components are highly right-skewed, with large numbers of zeros. A major limitation of currently available estimators for compositional models is that they either cannot handle many zeros in the data or are not computationally feasible in moderate to high dimensions. We derive a new set of novel score matching estimators applicable to distributions on a Riemannian manifold with boundary, of which the standard simplex is a special case. The score matching method is applied to estimate the parameters in a new flexible truncation model for compositional data and we show that the estimators are scalable and available in closed form. Through extensive simulation studies, the scoring methodology is demonstrated to work well for estimating the parameters in the new truncation model and also for the Dirichlet distribution. We apply the new model and estimators to real microbiome compositional data and show that the model provides a good fit to the data.