Bayesian Compressed Regression

• 成果类型: Article
• 署名作者: Guhaniyogi, Rajarshi; Dunson, David B.
• 署名单位: University of California System; University of California Santa Cruz; Duke University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2014.969425
• 发表日期: 2015
• 页码: 1500-1514
• 关键词: CONVERGENCE-RATES; variable selection; Gaussian process; likelihood; johnson; models

摘要

As an alternative to variable selection or shrinkage in high-dimensional regression, we propose to randomly compress the predictors prior to analysis. This dramatically reduces storage and computational bottlenecks, performing well when the predictors can be projected to a low-dimensional linear subspace with minimal loss of information about the response. As opposed to existing Bayesian dimensionality reduction approaches, the exact posterior distribution conditional on the compressed data is available analytically, speeding up computation by many orders of magnitude while also bypassing robustness issues due to convergence and mixing problems with MCMC. Model averaging is used to reduce sensitivity to the random projectionmatrix, while accommodating uncertainty in the subspace dimension. Strong theoretical support is provided for the approach by showing near parametric convergence rates for the predictive density in the large p small n asymptotic paradigm. Practical performance relative to competitors is illustrated in simulations and real data applications.