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Publication Detail
A General Framework for Structured Sparsity via Proximal Optimization
  • Publication Type:
  • Authors:
    Baldassarre L, Morales J, Argyriou A, Pontil M
  • Published proceedings:
    Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics April 21-23, 2012 La Palma, Canary Islands
  • Editors:
    Lawrence N,Girolami M
  • Name of conference:
  • Conference place:
    La Palma, Canary Islands, Spain
  • Conference start date:
  • Conference finish date:
  • Keywords:
    structured sparsity, optimization, supervised learning, machine learning, linear model
We study a generalized framework for structured sparsity. It extends the well known methods of Lasso and Group Lasso by incorporating additional constraints on the variables as part of a convex optimization problem. This framework provides a straightforward way of favouring prescribed sparsity patterns, such as orderings, contiguous regions and overlapping groups, among others. Available optimization methods are limited to specific constraint sets and tend to not scale well with sample size and dimensionality. We propose a {\em first order proximal method}, which builds upon results on fixed points and successive approximations. The algorithm can be applied to a general class of conic and norm constraints sets and relies on a proximity operator subproblem which can be computed numerically. Experiments on different regression problems demonstrate state-of-the-art statistical performance, which improves over Lasso, Group Lasso and StructOMP. They also demonstrate the efficiency of the optimization algorithm and its scalability with the size of the problem.
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