Restricted Eigen Condition for Heavy Tailed Designs

author: Arindam Banerjee, Department of Computer Science and Engineering, University of Minnesota
published: Aug. 20, 2015,   recorded: July 2015,   views: 43
Categories

Slides

Related Open Educational Resources

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.
  Bibliography

Description

The restricted eigenvalue (RE) condition characterizes the sample complexity of accurate recovery in the context of high-dimensional estimators such as Lasso and Dantzig selector (Bickel et al., 2009). Recent work has shown that random design matrices drawn from any thin-tailed (subGaussian) distributions satisfy the RE condition with high probability, when the number of samples scale as the square of the Gaussian width of the restricted set (Banerjee et al., 2014; Tropp, 2015). We pose the equivalent question for heavy-tailed distributions: Given a random design matrix drawn from a heavy-tailed distribution satisfying the small-ball property (Mendelson, 2015), does the design matrix satisfy the RE condition with the same order of sample complexity as subGaussian distributions? An answer to the question will guide the design of high-dimensional estimators for heavy tailed problems.

See Also:

Download slides icon Download slides: colt2015_banerjee_tailed_designs_01.pdf (150.1┬áKB)


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: