A0869
Title: Generalized matrix decomposition regression and inference for two-way structured data
Authors: Yue Wang - Arizona State University (United States)
Ali Shojaie - University of Washington (United States)
Parker Knight - University of Florida (United States)
Timothy Randolph - Fred Hutchinson Cancer Research Center (United States) [presenting]
Jing Ma - Fred Hutchinson Cancer Center (United States)
Abstract: Two-way structured data arise naturally in many applications, including microbiome studies. Characteristics of these data are (i) structured relationships among the variables, which may be informed by extrinsic information, and/or (ii) non-independent and non-Euclidean relationships among observations. For modelling data of this type, a penalized regression framework is proposed that exploits the Generalized Matrix Decomposition (GMD), a natural extension of classical dimension reduction methods such as principal component analysis (PCA) and generalized PCA. The GMD of a matrix accounts for the prescribed structure among its columns (variables) and rows (observations). The GMD regression approach includes efficient estimation, valid inference, and exploratory graphics in a GMD biplot.
