Abstract
Non-convex sparsity-inducing penalties have recently received considerable attentions in sparse learning. Recent theoretical investigations have demonstrated their superiority over the convex counterparts in several sparse learning settings. However, solving the non-convex optimization problems associated with non-convex penalties remains a big challenge. A commonly used approach is the Multi-Stage (MS) convex relaxation (or DC programming), which relaxes the original non-convex problem to a sequence of convex problems. This approach is usually not very practical for large-scale problems because its computational cost is a multiple of solving a single convex problem. In this paper, we propose a General Iterative Shrinkage and Thresholding (GIST) algorithm to solve the nonconvex optimization problem for a large class of non-convex penalties. The GIST algorithm iteratively solves a proximal operator problem, which in turn has a closed-form solution for many commonly used penalties. At each outer iteration of the algorithm, we use a line search initialized by the Barzilai-Borwein (BB) rule that allows finding an appropriate step size quickly. The paper also presents a detailed convergence analysis of the GIST algorithm. The efficiency of the proposed algorithm is demonstrated by extensive experiments on large-scale data sets.
Original language | English (US) |
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Title of host publication | 30th International Conference on Machine Learning, ICML 2013 |
Publisher | International Machine Learning Society (IMLS) |
Pages | 696-704 |
Number of pages | 9 |
Edition | PART 1 |
State | Published - 2013 |
Event | 30th International Conference on Machine Learning, ICML 2013 - Atlanta, GA, United States Duration: Jun 16 2013 → Jun 21 2013 |
Other
Other | 30th International Conference on Machine Learning, ICML 2013 |
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Country/Territory | United States |
City | Atlanta, GA |
Period | 6/16/13 → 6/21/13 |
ASJC Scopus subject areas
- Human-Computer Interaction
- Sociology and Political Science