The microbiome, which is inherently dynamic, plays essential roles in human physiology and its disruption has been implicated in numerous human diseases. Linking dynamic changes in the microbiome to the status of the human host is an important problem, which is complicated by limitations and complexities of the data. Model interpretability is key in the microbiome field, as practitioners seek to derive testable biological hypotheses from data or develop diagnostic tests that can be understood by clinicians. Interpretable structure must take into account domainspecific information key to biologists and clinicians including evolutionary relationships (phylogeny) and dynamic behavior of the microbiome. A Bayesian model was previously developed in the field, which uses Markov Chain Monte Carlo inference to learn human interpretable rules for classifying the status of the human host based on microbiome time-series data, but that approach is not scalable to increasingly large microbiome datasets being produced. We present a new fully-differentiable model that also learns human-interpretable rules for the same classification task, but in an end-to-end gradient-descent based framework. We validate the performance of our model on human microbiome data sets and demonstrate our approach has similar predictive performance to the fully Bayesian method, while running orders-of-magnitude faster and moreover learning a larger set of rules, thus providing additional biological insight into the effects of diet and environment on the microbiome
