Issue No. 09 - Sept. (2013 vol. 35)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TPAMI.2013.17
Lei Yuan , Dept. of Comput. Sci. & Eng., Arizona State Univ., Tempe, AZ, USA
Jun Liu , Siemens Corp. Res., Princeton, NJ, USA
Jieping Ye , Dept. of Comput. Sci. & Eng., Arizona State Univ., Tempe, AZ, USA
The group Lasso is an extension of the Lasso for feature selection on (predefined) nonoverlapping groups of features. The nonoverlapping group structure limits its applicability in practice. There have been several recent attempts to study a more general formulation where groups of features are given, potentially with overlaps between the groups. The resulting optimization is, however, much more challenging to solve due to the group overlaps. In this paper, we consider the efficient optimization of the overlapping group Lasso penalized problem. We reveal several key properties of the proximal operator associated with the overlapping group Lasso, and compute the proximal operator by solving the smooth and convex dual problem, which allows the use of the gradient descent type of algorithms for the optimization. Our methods and theoretical results are then generalized to tackle the general overlapping group Lasso formulation based on the eq norm. We further extend our algorithm to solve a nonconvex overlapping group Lasso formulation based on the capped norm regularization, which reduces the estimation bias introduced by the convex penalty. We have performed empirical evaluations using both a synthetic and the breast cancer gene expression dataset, which consists of 8,141 genes organized into (overlapping) gene sets. Experimental results show that the proposed algorithm is more efficient than existing state-of-the-art algorithms. Results also demonstrate the effectiveness of the nonconvex formulation for overlapping group Lasso.
Optimization, Convergence, Indexes, Algorithm design and analysis, Acceleration, Silicon, Convex functions
Lei Yuan, Jun Liu and Jieping Ye, "Efficient Methods for Overlapping Group Lasso," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 35, no. 9, pp. 2104-2116, 2013.