Recursive ${\ell }_{1,\infty }$ Group lasso

Abstract

We introduce a recursive adaptive group lasso algorithm for real-time penalized least squares prediction that produces a time sequence of optimal sparse predictor coefficient vectors. At each time index the proposed algorithm computes an exact update of the optimal ${\ell }_{1,\infty }$-penalized recursive least squares (RLS) predictor. Each update minimizes a convex but nondifferentiable function optimization problem. We develop an online homotopy method to reduce the computational complexity. Numerical simulations demonstrate that the proposed algorithm outperforms the ${\ell }_1$ regularized RLS algorithm for a group sparse system identification problem and has lower implementation complexity than direct group lasso solvers.

8 pages, double column, 6 figures

References in corpus (6)

• Compressed Sensing of Block-Sparse Signals: Uncertainty Relations and Efficient Recovery
• Consistency of the group Lasso and multiple kernel learning
• The composite absolute penalties family for grouped and hierarchical variable selection
• l_0 Norm Constraint LMS Algorithm for Sparse System Identification
• Sequential Compressed Sensing
• Regularized Least-Mean-Square Algorithms

Cited by in corpus (2)

• Recursive Recovery of Sparse Signal Sequences from Compressive Measurements: A Review
• An Online Parallel and Distributed Algorithm for Recursive Estimation of Sparse Signals