Abstract:  Analysis of two-way structured data, i.e., data with structures among both variables and samples, is becoming increasingly common in ecology, biology and neuroscience. For example, a sample-by-taxon abundance data matrix in a microbiome study may have columns structured by the phylogeny of taxa and rows structured by an ecologically defined distance between samples. Classical dimension-reduction tools, such as the singular value decomposition (SVD), may perform poorly for two-way structured data. The generalized matrix decomposition (GMD, Allen et al., 2014) extends the SVD to two-way structured data and thus constructs singular vectors that account for both structures. In the first part of the talk, I will present a graphical visualization tool for two-way structured data, called the GMD-biplot, that can simultaneously display sample clustering and important variables that contribute to the observed sample clustering. In the second part of the talk, I propose the GMD regression (GMDR) as an estimation/prediction tool that seamlessly incorporates two-way structures into high-dimensional linear models. The proposed GMDR directly regresses the outcome on a set of GMD components, selected by a novel procedure that guarantees the best prediction performance. We then propose the GMD inference (GMDI) framework to identify variables that are associated with the outcome for any model in a large family of regression models that includes GMDR. As opposed to most existing tools for high-dimensional inference, GMDI efficiently accounts for pre-specified two-way structures and can provide asymptotically valid inference even for non-sparse coefficient vectors. 

Dr. Wang is an assistant professor of Statistics in the School of Mathematical and Natural Sciences at Arizona State University. Prior to joining ASU, he worked as a senior fellow in the Department of Biostatistics, University of Washington. Dr. Wang obtained his PhD degree in Biostatistics at UNC-Chapel Hill in 2018.