Open problem: Tightness of maximum likelihood semidefinite relaxations

Afonso Bandeira, Yuehaw Khoo, Amit Singer

Research output: Contribution to journalArticle

Abstract

We have observed an interesting, yet unexplained, phenomenon: Semidefinite programming (SDP) based relaxations of maximum likelihood estimators (MLE) tend to be tight in recovery problems with noisy data, even when MLE cannot exactly recover the ground truth. Several results establish tightness of SDP based relaxations in the regime where exact recovery from MLE is possible. However, to the best of our knowledge, their tightness is not understood beyond this regime. As an illustrative example, we focus on the generalized Procrustes problem.

Original languageEnglish (US)
Pages (from-to)1265-1267
Number of pages3
JournalJournal of Machine Learning Research
Volume35
StatePublished - 2014

Fingerprint

Semidefinite Relaxation
Tightness
Maximum Likelihood Estimator
Maximum likelihood
Maximum Likelihood
Open Problems
Semidefinite Programming
Recovery
Procrustes Problem
Noisy Data
Tend

Keywords

  • Convex relaxations
  • Maximum likelihood estimator
  • Procrustes problem

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability

Cite this

Open problem : Tightness of maximum likelihood semidefinite relaxations. / Bandeira, Afonso; Khoo, Yuehaw; Singer, Amit.

In: Journal of Machine Learning Research, Vol. 35, 2014, p. 1265-1267.

Research output: Contribution to journalArticle

Bandeira, Afonso ; Khoo, Yuehaw ; Singer, Amit. / Open problem : Tightness of maximum likelihood semidefinite relaxations. In: Journal of Machine Learning Research. 2014 ; Vol. 35. pp. 1265-1267.
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