Classification with Sparse Overlapping Groups
This work addresses the need for more flexible feature selection in high-dimensional applications like fMRI and gene analysis, though it is incremental as it generalizes existing sparse group lasso methods.
The paper tackles the problem of structured sparse feature selection for classification by introducing Sparse Overlapping Group (SOG) lasso, a convex optimization method that allows overlapping groups of features, and establishes model selection error bounds, demonstrating advantages over lasso and group lasso in experiments with real and synthetic data.
Classification with a sparsity constraint on the solution plays a central role in many high dimensional machine learning applications. In some cases, the features can be grouped together so that entire subsets of features can be selected or not selected. In many applications, however, this can be too restrictive. In this paper, we are interested in a less restrictive form of structured sparse feature selection: we assume that while features can be grouped according to some notion of similarity, not all features in a group need be selected for the task at hand. When the groups are comprised of disjoint sets of features, this is sometimes referred to as the "sparse group" lasso, and it allows for working with a richer class of models than traditional group lasso methods. Our framework generalizes conventional sparse group lasso further by allowing for overlapping groups, an additional flexiblity needed in many applications and one that presents further challenges. The main contribution of this paper is a new procedure called Sparse Overlapping Group (SOG) lasso, a convex optimization program that automatically selects similar features for classification in high dimensions. We establish model selection error bounds for SOGlasso classification problems under a fairly general setting. In particular, the error bounds are the first such results for classification using the sparse group lasso. Furthermore, the general SOGlasso bound specializes to results for the lasso and the group lasso, some known and some new. The SOGlasso is motivated by multi-subject fMRI studies in which functional activity is classified using brain voxels as features, source localization problems in Magnetoencephalography (MEG), and analyzing gene activation patterns in microarray data analysis. Experiments with real and synthetic data demonstrate the advantages of SOGlasso compared to the lasso and group lasso.