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Title: Grouped variable selection with discrete optimization Authors:  Peter Radchenko - University of Sydney (Australia) [presenting]
Rahul Mazumder - MIT (United States)
Hussein Hazimeh - Massachusetts Institute of Technology (United States)
Abstract: The focus is on a new tractable framework for grouped variable selection with a cardinality constraint on the number of selected groups, leveraging tools in modern mathematical optimization. The proposed methodology covers both the case of high-dimensional linear regression and nonparametric sparse additive modelling. Computational experiments demonstrate the effectiveness of the proposal as an alternative method for sparse grouped variable selection - in terms of better predictive accuracy and greater model sparsity, at the cost of increased, but still reasonable, computation times. Empirical and theoretical evidence shows that the proposed estimators outperform their Group Lasso type counterparts in a wide variety of regimes.