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Abstract.In this paper we demonstrate, how p -regularized univariate quadratic loss function can be effectively optimized (for 0 p 1) without approximation of penalty term and provide analytical solution for p = 1 2. Next we adapt this approach for important multivariate cases like linear and logistic regressions, using Coordinate Descent algorithm. At the end we compare sample complexity of 1 with p , 0 p < 1 regularized models for artificial and real datasets.

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