GAP Safe Screening Rules for Sparse-Group-Lasso

Abstract

In high dimensional settings, sparse structures are crucial for efficiency, either in term of memory, computation or performance. In some contexts, it is natural to handle more refined structures than pure sparsity, such as for instance group sparsity. Sparse-Group Lasso has recently been introduced in the context of linear regression to enforce sparsity both at the feature level and at the group level. We adapt to the case of Sparse-Group Lasso recent safe screening rules that discard early in the solver irrelevant features/groups. Such rules have led to important speed-ups for a wide range of iterative methods. Thanks to dual gap computations, we provide new safe screening rules for Sparse-Group Lasso and show significant gains in term of computing time for a coordinate descent implementation.

References in corpus (9)

• Pathwise coordinate optimization
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Cited by in corpus (11)

• Scaling Up Sparse Support Vector Machines by Simultaneous Feature and Sample Reduction
• Fast OSCAR and OWL Regression via Safe Screening Rules
• Expanding boundaries of Gap Safe screening
• Feedback-Controlled Sequential Lasso Screening
• A Fast, Principled Working Set Algorithm for Exploiting Piecewise Linear Structure in Convex Problems
• Learning Hierarchical Interactions at Scale: A Convex Optimization Approach
• Balancing Statistical and Computational Precision: A General Theory and Applications to Sparse Regression
• Screening Rules and its Complexity for Active Set Identification
• On Newton Screening
• Safe Element Screening for Submodular Function Minimization
• Safe Feature Elimination for Non-Negativity Constrained Convex Optimization