Agnostic estimation for misspecified phase retrieval models

Matey Neykov, Zhaoran Wang, Han Liu

Research output: Contribution to journalConference article

4 Citations (Scopus)

Abstract

The goal of noisy high-dimensional phase retrieval is to estimate an s-sparse parameter β ∈ ℝd from n realizations of the model Y = (XTβ)2 + ϵ. Based on this model, we propose a significant semi-parametric generalization called mis-specified phase retrieval (MPR), in which Y = f(XTβ,ϵ) with unknown f and Cov(Y, (XTβ)2) > 0. For example, MPR encompasses Y = h(|XTβ |) + ϵ with increasing h as a special case. Despite the generality of the MPR model, it eludes the reach of most existing semi-parametric estimators. In this paper, we propose an estimation procedure, which consists of solving a cascade of two convex programs and provably recovers the direction of β. Our theory is backed up by thorough numerical results.

Original languageEnglish (US)
Pages (from-to)4096-4104
Number of pages9
JournalAdvances in Neural Information Processing Systems
StatePublished - Jan 1 2016
Event30th Annual Conference on Neural Information Processing Systems, NIPS 2016 - Barcelona, Spain
Duration: Dec 5 2016Dec 10 2016

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

Cite this

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Agnostic estimation for misspecified phase retrieval models. / Neykov, Matey; Wang, Zhaoran; Liu, Han.

In: Advances in Neural Information Processing Systems, 01.01.2016, p. 4096-4104.

Research output: Contribution to journalConference article

TY - JOUR

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AU - Wang, Zhaoran

AU - Liu, Han

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AB - The goal of noisy high-dimensional phase retrieval is to estimate an s-sparse parameter β∗ ∈ ℝd from n realizations of the model Y = (XTβ∗)2 + ϵ. Based on this model, we propose a significant semi-parametric generalization called mis-specified phase retrieval (MPR), in which Y = f(XTβ∗,ϵ) with unknown f and Cov(Y, (XTβ∗)2) > 0. For example, MPR encompasses Y = h(|XTβ∗ |) + ϵ with increasing h as a special case. Despite the generality of the MPR model, it eludes the reach of most existing semi-parametric estimators. In this paper, we propose an estimation procedure, which consists of solving a cascade of two convex programs and provably recovers the direction of β∗. Our theory is backed up by thorough numerical results.

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