Algorithmic Strategies for Non-convex Optimization in Sparse Learning

author: Tong Zhang, Department of Statistics, Rutgers, The State University of New Jersey
published: May 6, 2009,   recorded: April 2009,   views: 1291
Categories

See Also:

Download slides icon Download slides: smls09_zhang_asfnc_01.pdf (359.3┬áKB)


Help icon Streaming Video Help

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

We consider optimization formulations with non-convex regularization that are natural for learning sparse linear models. There are two approaches to this problem: 1. Heuristic methods such as gradient descent that only find a local minimum; a drawback of this approach is the lack of theoretical guarantee showing that the local minimum gives a good solution. 2. Convex relaxation such as L1-regularization that solves the problem under some conditions, but often leads to sub-optimal sparsity in reality.

This talk tries to remedy the above gap between theory and practice by presenting two algorithms for direct optimization of non-convex objectives in sparse learning, for which performance guarantees can be established. The first method is a multi-stage convex relaxation scheme that iteratively refines the L1-regularization. The second approach is a greedy procedure for solving non-convex sparse regularization. We show that under appropriate conditions, both procedures lead to desirable local solutions of sparse non-convex formulations that are superior to the global solution of L1-regularization.

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: