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Description

The grouping of features is highly beneficial in learning with high-dimensional data. It reduces the variance in the estimation and improves the stability of feature selection, leading to improved generalization. Moreover, it can also help in data understanding and interpretation. OSCAR is a recent sparse modeling tool that achieves this by using a $ell_1$-regularizer and a pairwise $ell_infty$-regularizer. However, its optimization is computationally expensive. In this paper, we propose an efficient solver based on the accelerated gradient methods. We show that its key projection step can be solved by a simple iterative group merging algorithm. It is highly efficient and reduces the empirical time complexity from $O(d^3 sim d^5)$ for the existing solvers to just $O(d)$, where $d$ is the number of features. Experimental results on toy and real-world data sets demonstrate that OSCAR is a competitive sparse modeling approach with the added ability of automatic feature grouping.

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