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. In the first half of this talk, I 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. In the second half, I will discuss an extension to discrete data structures including sparse compositional data, routinely occurring in microbiomics. I will discuss the methodological challenges with the Dirichlet distribution as a shrinkage prior to 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. I will provide some theoretical support for the proposed methods and show improved performance in several simulation settings and applications to microbiome data.

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Topic: Colloquia: Department of Statistics and Actuarial Science, University of Iowa

Time: Sep 10, 2020 03:15 PM Central Time (US and Canada)

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Meeting ID: 910 5155 4022