Bayesian Conditional Auto-Regressive LASSO Models to Learn Sparse Networks with Predictors
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Microbiome data generated by next generation sequencing continue to flourish. There is a need for statistical models that can decode microbes' reaction to the environment and interactions among microbes simultaneously. The model should have the ability to correctly incorporate prior knowledge from controlled experiments that are oftentimes conditioned on other responses. We introduce a novel Bayesian conditional auto-regressive (CAR) LASSO model to infer a sparse network structure with nodes for responses and for predictors and whose edges all represent conditional dependence, not conditional among responses and marginal between responses and predictors. We also propose an adaptive extension of the CAR LASSO model so that different shrinkage can be applied to different edges which allows the incorporation of edge-specific prior knowledge. Indeed, the conditional representation of our model coefficients and adaptivity allow us to adequately encode prior knowledge obtained by specific experimental interventions and agrees with the experimenter's intuition on average behavior of nodes under experiments. In addition, our model is able to equally handle small and big data and is computationally inexpensive through an efficient Gibbs sampling algorithm. With hierarchical structure, we extend the model to binary, counting and compositional responses by adding an appropriate sampling distribution to the core Normal model. Finally, we apply our model to two real-life microbial composition datasets: one related to human gut and one related to soil.
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