Misspecified nonconvex statistical optimization for sparse phase retrieval

• 成果类型: Article; Proceedings Paper
• 署名作者: Yang, Zhuoran; Yang, Lin F.; Fang, Ethan X.; Zhao, Tuo; Wang, Zhaoran; Neykov, Matey
• 署名单位: Princeton University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; University System of Georgia; Georgia Institute of Technology; University System of Georgia; Georgia Institute of Technology; Northwestern University; Carnegie Mellon University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-019-01364-5
• 发表日期: 2019
• 页码: 545-571
• 关键词: crystallography

摘要

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.