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Title: Best subset selection via continuous optimization Authors:  Sarat Moka - Macquarie University (Australia)
Houying Zhu - Macquarie University (Australia)
Samuel Muller - Macquarie University (Australia)
Benoit Liquet - Macquary University (Australia) [presenting]
Abstract: Recent rapid developments in information technology have enabled the collection of high-dimensional complex data including in engineering, economics, finance, biology, and health sciences. High-dimensional means that the number of features is large and often far higher than the number of collected data samples. Several optimization and search methods have been proposed in the literature to tackle the problem of identifying or selecting the set of important predictors. These methods include forward stepwise, Lasso, and mixed-integer optimization. We will briefly review existing methods, and then present an L0 continuous optimization-based solution, a novel approach that tackles the challenging task of best subset selection for linear models, especially when the number of features is very large. Simulation results are presented to highlight the performance of the proposed method in comparison to the existing methods. Our new formulation for best subset selection in linear regression models promises to open new research avenues for feature extraction for a large variety of models.