A tensor decomposition model for longitudinal microbiome studies

Abstract

Longitudinal microbiome studies can help delineate true biological signals from the high interindividual variability that is common in microbiome data. However, there are few methods available for unsupervised dimension reduction of time course microbial abundance observations. Existing methods do not fully observe the distribution characteristics of such data types, namely, zero-inflation, compositionality, and overdispersion. We present a tensor decomposition model and a semiparametric quasi-likelihood estimation method for the decomposition of longitudinal microbiome data, by gen-eralizing existing approaches in tensor decomposition of Gaussian data. Optimization is performed through projected gradient descent additionally allowing interpretability constraints. We show through simulation studies our method is able to recover low rank structures from microbiome time course data, better than existing approaches. Lastly, we apply our method to two existing longitudinal microbiome studies, to detect global microbial changes associated with dietary and pharmaceutical effects, as well as infant birth modes.