Open problem: Tightness of maximum likelihood semidefinite relaxations

Afonso S. Bandeira, Yuehaw Khoo, Amit Singer

Research output: Contribution to journalConference article

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 - Jan 1 2014
Event27th Conference on Learning Theory, COLT 2014 - Barcelona, Spain
Duration: Jun 13 2014Jun 15 2014

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Keywords

  • Convex relaxations
  • Maximum likelihood estimator
  • Procrustes problem

ASJC Scopus subject areas

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

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