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Meeting-ID: 937 6054 7545

password: 946296

Abstract: We consider estimation methods in the context of high-dimensional regression models such as the Lasso and SLOPE, defined as solutions to a penalized optimization problem. The geometric object relevant for our investigation is the polytope that is dual to to the unit ball of the penalizing norm. We show that which models are accessible by such a procedure depends on what faces of the polytope are intersected by the row span of the regressor matrix. Moreover, these geometric considerations allow to derive a criterion for the uniqueness of the estimator that is both necessary and sufficient. We illustrate this approach for Lasso and SLOPE with the unit cube and the sign permutahedron as relevant polytopes.  Joint work with Patrick Tardivel (Université Bourgogne).