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Open problem: Tightness of maximum likelihood semidefinite relaxations

Author(s): Bandeira, Afonso S; Khoo, Yuehaw; Singer, Amit

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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.
Publication Date: 2014
Electronic Publication Date: 2014
Citation: Bandeira, A.S., Khoo, Y. & Singer, A.. (2014). Open Problem: Tightness of maximum likelihood semidefinite relaxations. Proceedings of The 27th Conference on Learning Theory, in PMLR 35:1265-1267
Type of Material: Conference Article
Journal/Proceeding Title: Proceedings of The 27th Conference on Learning Theory
Version: Author's manuscript

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