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Title: The CCP selector: Best subset selection for sparse regression from chance-constrained programming Authors:  Xinwei Deng - Virginia Tech (United States) [presenting]
Abstract: Sparse regression and variable selection for large-scale data have been rapidly developed in the past decades. The focus is on considering the exact $L_0$ norm to pursue the sparse regression. We pave out a theoretical foundation to understand why many existing approaches may not work well for this problem, in particular on large scale datasets. Inspired by reformulating the problem as a chance-constrained program, we derive a novel mixed integer second order conic (MISOC) reformulation. Based the reformulation, we develop new scalable algorithms for sparse ridge regression with desirable theoretical properties. The proposed algorithms are proved to yield near-optimal solutions under mild conditions. The merits of the proposed methods are elaborated through a set of numerical examples in comparison with several existing ones.