Low Rank Matrix Completion with Exponential Family Noise

author: Jean Lafond, Telecom ParisTech
published: Aug. 20, 2015,   recorded: July 2015,   views: 1886
Categories

Slides

Related content

Report a problem or upload files

If you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.
Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.
Lecture popularity: You need to login to cast your vote.
  Delicious Bibliography

Description

The matrix completion problem consists in reconstructing a matrix from a sample of entries observed with noise. A popular class of estimator, known as nuclear norm penalized estimators, are based on minimizing the sum of a data fitting term and a nuclear norm penalization. Here, we investigate the case where the noise distribution belongs to the exponential family, is sub-exponential and consider a general sampling scheme. We first consider an estimator defined as the minimizer of the sum of a log-likelihood term and a nuclear norm penalization and prove an upper bound on the Frobenius prediction risk. The rate obtained improves on previous works on exponential family completion. When the sampling distribution is known, we propose a second estimator and prove an oracle inequality on the Kullback-Leibler divergence risk, which translates immediatly into an upper bound on the Frobenius risk. Finally, we show that all the rates obtained are minimax optimal up to a logarithmic factor.

See Also:

Download slides icon Download slides: colt2015_lafond_family_noise_01.pdf (1.8 MB)


Help icon Streaming Video Help

Link this page

Would you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !

Write your own review or comment:

make sure you have javascript enabled or clear this field: