Interaction Models and Generalized Score Matching for Compositional Data

Applications such as the analysis of microbiome data have led to renewed interest in statistical methods for compositional data, i.e., data in the form of relative proportions. In particular, there is considerable interest in modelling interactions among such proportions. To this end we propose a class of exponential family models that accommodate arbitrary patterns of pairwise interaction. Special cases include Dirichlet distributions as well as Aitchison’s additive logistic normal distributions. Generally, the distributions we consider have a density that features a difficult-to-compute normalizing constant. To circumvent this issue, we design effective estimation methods based on generalized versions of score matching.