MPGL: An Efficient Matching Pursuit Method for Generalized LASSO

Unlike traditional LASSO enforcing sparsity on the variables, Generalized LASSO (GL) enforces sparsity on a linear transformation of the variables, gaining flexibility and success in many applications. However, many existing GL algorithms do not scale up to high-dimensional problems, and/or only work well for a specific choice of the transformation. We propose an efficient Matching Pursuit Generalized LASSO (MPGL) method, which overcomes these issues, and is guaranteed to converge to a global optimum. We formulate the GL problem as a convex quadratic constrained linear programming (QCLP) problem and tailor-make a cutting plane method. More specifically, our MPGL iteratively activates a subset of nonzero elements of the transformed variables, and solves a subproblem involving only the activated elements thus gaining significant speed-up. Moreover, MPGL is less sensitive to the choice of the trade-off hyper-parameter between data fitting and regularization, and mitigates the longstanding hyper-parameter tuning issue in many existing methods. Experiments demonstrate the superior efficiency and accuracy of the proposed method over the state-of-the-arts in both classification and image processing tasks.

Authors

• Dong Gong
• Mingkui Tan South China University of Technology
• Yanning Zhang Northwestern Polytechnical University
• Anton van den Hengel Amazon
• Qinfeng Shi

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