The Maximum Entropy Principle For Compositional Data

Abstract

In this work, we provide a general method for inferring the stochastic behavior of compositional systems. Our approach is guided by the principle of maximum entropy, a data-driven modeling technique. In particular, we show that our method can accurately capture stochastic, inter-species relationships with minimal model parameters. We provide two proofs of principle. First, we measure the relative abundances of different bacteria and infer how they interact. Second, we show that our method outperforms a common alternative for the extraction of gene-gene interactions in triple-negative breast cancer. Author summaryCompositional systems, represented as proportions of some whole, are ubiquitous. They encompass the abundances of proteins in a cell, the distribution of organisms in nature, and the stoichiometry of the most basic chemical reactions. Thus, a central goal is to understand how such processes emerge from the behaviors of their components and their pairwise interactions. Such a study, however, is challenging for two key reasons. Firstly, such systems are complex and depend, often stochastically, on their constituent parts. Secondly, the data lie on a simplex which influences their correlations. We provide a general and data-driven modeling tool for compositional systems to resolve both of these issues. We achieve this through the principle of maximum entropy, which requires only minimal assumptions and limited experimental data in contrast to current alternatives. We show that our approach provides novel and biologically-intuitive insights and is promising as a comprehensive quantitative framework for compositional data.