Randomized tests for high-dimensional regression: A more efficient and powerful solution

Yue Li, Ilmun Kim, Yuting Wei

Research output: Contribution to journalConference articlepeer-review

Abstract

We investigate the problem of testing the global null in the high-dimensional regression models when the feature dimension p grows proportionally to the number of observations n. Despite a number of prior work studying this problem, whether there exists a test that is model-agnostic, efficient to compute and enjoys a high power, still remains unsettled. In this paper, we answer this question in the affirmative by leveraging the random projection techniques, and propose a testing procedure that blends the classical F-test with a random projection step. When combined with a systematic choice of the projection dimension, the proposed procedure is proved to be minimax optimal and, meanwhile, reduces the computation and data storage requirements. We illustrate our results in various scenarios when the underlying feature matrix exhibits an intrinsic lower dimensional structure (such as approximate low-rank or has exponential/polynomial eigen-decay), and it turns out that the proposed test achieves sharp adaptive rates. Our theoretical findings are further validated by comparisons to other state-of-the-art tests on the synthetic data.

Original languageEnglish
JournalAdvances in Neural Information Processing Systems
Volume2020-December
Publication statusPublished - 2020
Event34th Conference on Neural Information Processing Systems, NeurIPS 2020 - Virtual, Online
Duration: 2020 Dec 62020 Dec 12

Bibliographical note

Funding Information:
∗Y. Wei is supported in part by the NSF grant CCF-2007911 and DMS-2015447.

Publisher Copyright:
© 2020 Neural information processing systems foundation. All rights reserved.

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

Fingerprint

Dive into the research topics of 'Randomized tests for high-dimensional regression: A more efficient and powerful solution'. Together they form a unique fingerprint.

Cite this