Improving Lasso for model selection and prediction

It is known that the Thresholded Lasso (TL), SCAD or MCP correct intrinsic estimation bias of Lasso. In this paper we propose an alternative method improving for predictive models with general convex loss functions which encompass normal linear models, logistic regression, quantile support vector machines. For a given penalty order absolute values nonzero coefficients and then select final model from small nested family by Generalized Information Criterion. We derive exponential upper bounds on selection error method. These results confirm that, at least our algorithm seems to be benchmark theory as it constructive, computationally efficient leads consistent under weak assumptions. Constructivity means in contrast TL, MCP, does not rely unknown parameters cone invertibility factor. Instead, only needs sample size, number predictors bound noise parameter. show numerical experiments synthetic real-world datasets implementation more accurate than implementations studied concave regularizations. Our procedure included R package DMRnet available CRAN repository.