Safe Subspace Screening for Nuclear Norm Regularized Least Squares Problems
published: Sept. 27, 2015, recorded: July 2015, views: 35
Report a problem or upload filesIf 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.
Nuclear norm regularization has been shown very promising for pursing a low rank matrix solution in various machine learning problems. Many efforts have been devoted to develop efficient algorithms for solving the optimization problem in nuclear norm regularization. Solving it for large-scale matrix variables, however, is still a challenging task since the complexity grows fast with the size of matrix variable. In this work, we propose a novel method called safe subspace screening (SSS), to improve the efficiency of the solver for nuclear norm regularized least squares problems. Motivated by the fact that the low rank solution can be represented by a few subspaces, the proposed method accurately discards a predominant percentage of inactive subspaces prior to solving the problem to reduce problem size. Consequently, a much smaller problem is required to solve, making it more efficient than optimizing the original problem. The proposed SSS is safe, in that its solution is identical to the solution from the solver. In addition, the proposed SSS can be used together with any existing nuclear norm solver since it is independent of the solver. Extensive results on several synthetic and real data sets show that the proposed SSS is very effective in inactive subspace screening.
Link this pageWould you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !