Nuclear norm penalized LAD estimator for low rank matrix recovery

In the thesis we propose a novel method for low rank matrix recovery. We study the framework using absolute deviation loss function and nuclear penalty. While nuclear norm penalty is widely utilized heuristic method for shrinkage to low rank solution, the absolute deviation loss function is rarely studied. We establish an near oracle optimal recovery bound and gave a proof using E-net covering argument under certain restricted isometry and restricted eigenvalue assumptions. The estimator is able to recover the underlying matrix with high probability with limited observations that the number of observation is more than the degree of freedom but less than a power of dimension. Our estimator has two advantages. First the theoretical tuning parameter does not depends on the knowledge of the noise level, and the bound can be derived even when noises have fatter tails than normal distribution. The second advantage is that absolute deviation loss function is robust compared with the popular square loss function.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2015

Author dc:creator

• Wei, Wenzhe

Advisor dc:contributor.advisor

• Lie Wang.

• Mathematics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/99320

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/99320