Regularization-free estimation in trace regression with symmetric positive semidefinite matrices

Martin Slawski, Ping Li, Matthias Hein

Research output: Contribution to journalConference article

1 Scopus citations


Trace regression models have received considerable attention in the context of matrix completion, quantum state tomography, and compressed sensing. Estimation of the underlying matrix from regularization-based approaches promoting low-rankedness, notably nuclear norm regularization, have enjoyed great popularity. In this paper, we argue that such regularization may no longer be necessary if the underlying matrix is symmetric positive semidefinite (spd) and the design satisfies certain conditions. In this situation, simple least squares estimation subject to an spd constraint may perform as well as regularization-based approaches with a proper choice of regularization parameter, which entails knowledge of the noise level and/or tuning. By contrast, constrained least squares estimation comes without any tuning parameter and may hence be preferred due to its simplicity.

Original languageEnglish (US)
Pages (from-to)2782-2790
Number of pages9
JournalAdvances in Neural Information Processing Systems
StatePublished - Jan 1 2015
Event29th Annual Conference on Neural Information Processing Systems, NIPS 2015 - Montreal, Canada
Duration: Dec 7 2015Dec 12 2015

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Signal Processing
  • Computer Networks and Communications

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