B1304
Title: Shrinkage on simplex: Bayesian inference for sparse and structured compositional data
Authors: Jyotishka Datta - Virginia Polytechnic Institute and State University (United States) [presenting]
Abstract: Sparse signal recovery remains an important challenge in large scale data analysis and global-local (G-L) shrinkage priors have undergone an explosive development in the last decade in both theory and methodology. These developments have established the G-L priors as the state-of-the-art Bayesian tool for sparse signal recovery as well as default non-linear problems. While there is a huge literature proposing elaborate shrinkage and sparsity priors for high-dimensional real-valued parameters, there has been limited consideration of discrete data structures. We will survey the recent advances in G-L shrinkage priors, focusing on the optimality of these priors for both continuous as well as quasi-sparse count data. We will discuss an extension to discrete data structures including sparse compositional data, routinely observed in microbiomics. We will discuss the methodological challenges with the Dirichlet distribution as a shrinkage prior for high-dimensional probabilities for its inability to adapt to an arbitrary level of sparsity, and propose to address this gap by using a new prior distribution, specially designed to enable scaling to data with many categories. We will provide some theoretical support for the proposed methods and show improved performance in several simulation settings and application to microbiome data
