Tree-based Generative Models with Applications to Microbiome Compositional Data

Abstract

In this work, we study conditional generative models of microbiome compositional data. Specifically, we propose three approaches for the conditional generation of such data: (1) a parametric model called the "logistic-tree normal" (LTN) model, (2) a conditional normalizing flow based on piecewise linear transforms defined with dyadic partition trees on the outcome space, and (3) learning the marginal distribution of the compositions and the conditional distribution of covariates given the compositions separately, followed by conditional sampling of the compositions using Langevin dynamics. We demonstrated through extensive experiments that the LTN model can incorporate complex design features, such as longitudinal sampling, and can be integrated into hierarchical models as a building block for inferential tasks, such as cross-group comparison. The non-parametric approaches better model the complex joint distributions of the compositions, and in practice, one can choose between these two depending on the covariates.