GENERALIZED MATRIX DECOMPOSITION REGRESSION: ESTIMATION AND INFERENCE FOR TWO-WAY STRUCTURED DATA

• 成果类型: Article
• 署名作者: Wang, By yue; Shojaie, Ali; Randolph, Timothy; Knight, Parker; Ma, Jing
• 署名单位: University of Colorado System; University of Colorado Anschutz Medical Campus; University of Washington; University of Washington Seattle; Fred Hutchinson Cancer Center; Harvard University; Fred Hutchinson Cancer Center
• 刊物名称: ANNALS OF APPLIED STATISTICS
• ISSN/ISSBN: 1932-6157
• DOI: 10.1214/23-AOAS1746
• 发表日期: 2023
• 页码: 2944-2969
• 关键词: human gut microbiome; confidence-intervals; selection; sparsity; regions; tests; MODEL

摘要

Motivated by emerging applications in ecology, microbiology, and neu-roscience, this paper studies high-dimensional regression with two-way struc-tured data. To estimate the high-dimensional coefficient vector, we pro-pose the generalized matrix decomposition regression (GMDR) to efficiently leverage auxiliary information on row and column structures. GMDR extends the principal component regression (PCR) to two-way structured data, but un-like PCR, GMDR selects the components that are most predictive of the out-come, leading to more accurate prediction. For inference on regression coef-ficients of individual variables, we propose the generalized matrix decompo-sition inference (GMDI), a general high-dimensional inferential framework for a large family of estimators that include the proposed GMDR estimator. GMDI provides more flexibility for incorporating relevant auxiliary row and column structures. As a result, GMDI does not require the true regression co-efficients to be sparse but constrains the coordinate system representing the regression coefficients according to the column structure. GMDI also allows dependent and heteroscedastic observations. We study the theoretical proper-ties of GMDI in terms of both the type-I error rate and power and demonstrate the effectiveness of GMDR and GMDI in simulation studies and an applica-tion to human microbiome data.