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- W2743133559 abstract "This paper studies a fundamental bicriteria optimization problem for variable selection in statistical learning; the two criteria are a loss/residual function and a model control (also called regularization, penalty). The former function measures the fitness of the learning model to data and the latter function is employed as a control of the complexity of the model. We focus on the case where the loss function is (strongly) convex and the model control function is a difference-of-convex (dc) sparsity measure. Our paper establishes some fundamental optimality and sparsity properties of directional stationary solutions to a nonconvex Lagrangian formulation of the bicriteria optimization problem, based on a specially structured dc representation of many well-known sparsity functions that can be profitably exploited in the analysis. We relate the Lagrangian optimization problem with the penalty constrained problem in terms of their respective d(irectional)-stationary solutions; this is in contrast to common ..." @default.
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- W2743133559 date "2017-01-01" @default.
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- W2743133559 title "Difference-of-Convex Learning: Directional Stationarity, Optimality, and Sparsity" @default.
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