Targeted Random Projection for Prediction From High-Dimensional Features

Published

Journal Article

© 2019, © 2019 American Statistical Association. 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. Supplementary materials for this article are available online.

Full Text

Duke Authors

Cited Authors

  • Mukhopadhyay, M; Dunson, DB

Published Date

  • January 1, 2019

Published In

Electronic International Standard Serial Number (EISSN)

  • 1537-274X

International Standard Serial Number (ISSN)

  • 0162-1459

Digital Object Identifier (DOI)

  • 10.1080/01621459.2019.1677240

Citation Source

  • Scopus