Misspecified nonconvex statistical optimization for sparse phase retrieval

Zhuoran Yang, Lin F. Yang, Ethan X. Fang*, Tuo Zhao, Zhaoran Wang, Matey Neykov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Existing nonconvex statistical optimization theory and methods crucially rely on the correct specification of the underlying “true” statistical models. To address this issue, we take a first step towards taming model misspecification by studying the high-dimensional sparse phase retrieval problem with misspecified link functions. In particular, we propose a simple variant of the thresholded Wirtinger flow algorithm that, given a proper initialization, linearly converges to an estimator with optimal statistical accuracy for a broad family of unknown link functions. We further provide extensive numerical experiments to support our theoretical findings.

Original languageEnglish (US)
Pages (from-to)545-571
Number of pages27
JournalMathematical Programming
Volume176
Issue number1-2
DOIs
StatePublished - Jul 1 2019

ASJC Scopus subject areas

  • Software
  • Mathematics(all)

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