Targeted Random Projection for Prediction From High-Dimensional Features

• 成果类型: Article
• 署名作者: Mukhopadhyay, Minerva; Dunson, David B.
• 署名单位: Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Kanpur; Duke University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2019.1677240
• 发表日期: 2020
• 页码: 1998-2010
• 关键词: bayesian variable selection; generalized linear-models; regression; regularization; CONVERGENCE; johnson

摘要

We consider the problem of computationally efficient prediction with high dimensional and highly correlated predictors when accurate variable selection is effectively impossible. Direct application of penalization or Bayesian methods implemented with Markov chain Monte Carlo can be computationally daunting and unstable. A common solution is first stage dimension reduction through screening or projecting the design matrix to a lower dimensional hyper-plane. Screening is highly sensitive to threshold choice, while projections often have poor performance in very high-dimensions. We propose targeted random projection (TARP) to combine positive aspects of both strategies. TARP uses screening to order the inclusion probabilities of the features in the projection matrix used for dimension reduction, leading to data-informed sparsity. We provide theoretical support for a Bayesian predictive algorithm based on TARP, including statistical and computational complexity guarantees. Examples for simulated and real data applications illustrate gains relative to a variety of competitors. for this article are available online.