A regularization-based adaptive test for high-dimensional generalized linear models

Chong Wu, Gongjun Xu, Xiaotong Shen, Wei Pan

Research output: Contribution to journalArticlepeer-review

Abstract

In spite of its urgent importance in the era of big data, testing high-dimensional parameters in generalized linear models (GLMs) in the presence of high-dimensional nuisance parameters has been largely under-studied, especially with regard to constructing powerful tests for general (and unknown) alternatives. Most existing tests are powerful only against certain alternatives and may yield incorrect Type I error rates under high-dimensional nuisance parameter situations. In this paper, we propose the adaptive interaction sum of powered score (aiSPU) test in the framework of penalized regression with a non-convex penalty, called truncated Lasso penalty (TLP), which can maintain correct Type I error rates while yielding high statistical power across a wide range of alternatives. To calculate its p-values analytically, we derive its asymptotic null distribution. Via simulations, its superior finite-sample performance is demonstrated over several representative existing methods. In addition, we apply it and other representative tests to an Alzheimer's Disease Neuroimaging Initiative (ADNI) data set, detecting possible gene-gender interactions for Alzheimer's disease. We also put R package \aispu"implementing the proposed test on GitHub.

Original languageEnglish (US)
JournalJournal of Machine Learning Research
Volume21
StatePublished - Jun 2020
Externally publishedYes

Bibliographical note

Funding Information:
We thank reviewers and the action editor for helpful comments. The authors thank Xi-anyang Zhang for sharing the R code implementing three-step procedures. This research was supported by the National Institutes of Health (NIH) grants R01GM113250, R01GM126002, R01HL105397, R01AG065636 and R01HL116720, by NSF grants DMS 1711226, DMS 1712717, DMS 1952539, SES 1659328 and SES 1846747, and by the Minnesota Supercomputing Institute. The investigators within the ADNI contributed to the design and implementation of ADNI and provided data, but did not participate in analysis or writing of this report. A complete listing of ADNI investigators can be found at http://adni. loni.usc.edu/wp-content/uploads/how_to_apply/ADNI_Acknowledgement_List.pdf.

Funding Information:
We thank reviewers and the action editor for helpful comments. The authors thank Xianyang Zhang for sharing the R code implementing three-step procedures. This research was supported by the National Institutes of Health (NIH) grants R01GM113250, R01GM126002, R01HL105397, R01AG065636 and R01HL116720, by NSF grants DMS 1711226, DMS 1712717, DMS 1952539, SES 1659328 and SES 1846747, and by the Minnesota Supercomputing Institute. The investigators within the ADNI contributed to the design and implementation of ADNI and provided data, but did not participate in analysis or writing of this report. A complete listing of ADNI investigators can be found at http://adni. loni.usc.edu/wp-content/uploads/how_to_apply/ADNI_Acknowledgement_List.pdf.

Keywords

  • Adaptive Test
  • Gene-Environmental Interaction
  • Truncated Lasso Penalty

Fingerprint Dive into the research topics of 'A regularization-based adaptive test for high-dimensional generalized linear models'. Together they form a unique fingerprint.

Cite this