TY - GEN

T1 - Safe subspace screening for nuclear norm regularized least squares problems

AU - Zhou, Qiang

AU - Zhao, Qi

PY - 2015/1/1

Y1 - 2015/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84969835003&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84969835003&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84969835003

T3 - 32nd International Conference on Machine Learning, ICML 2015

SP - 1103

EP - 1112

BT - 32nd International Conference on Machine Learning, ICML 2015

A2 - Blei, David

A2 - Bach, Francis

PB - International Machine Learning Society (IMLS)

T2 - 32nd International Conference on Machine Learning, ICML 2015

Y2 - 6 July 2015 through 11 July 2015

ER -