High-Dimensional LASSO-Based Computational Regression Models: Regularization, Shrinkage, and Selection

Generalized Lasso Regularization for Regression Models

Regression Coefficient and Autoregressive Order Shrinkage and Selection via Lasso

The least absolute shrinkage and selection operator (lasso) has been widely used in regression shrinkage and selection. In this article, we extend its application to the REGression model with AutoRegressive errors (REGAR). Two types of lasso estimators are carefully studied. The first is similar to the traditional lasso estimator with only two tuning parameters (one for regression coefficients ...

Regression shrinkage and selection via the Lasso: a retrospective

Presented at the RSS annual meeting 2010, Brighton, U.K. The work discussed here represents collaborations with many people, especially Bradley Efron, Jerome Friedman, Trevor Hastie, Holger Hoefling, Iain Johnstone, Ryan Tibshirani and Daniela Witten I would like to thank the research section of the Royal Statistical Society for inviting me to present this retrospective paper. In this paper I g...

Adaptive Lasso for Sparse High-dimensional Regression Models

We study the asymptotic properties of the adaptive Lasso estimators in sparse, high-dimensional, linear regression models when the number of covariates may increase with the sample size. We consider variable selection using the adaptive Lasso, where the L1 norms in the penalty are re-weighted by data-dependent weights. We show that, if a reasonable initial estimator is available, under appropri...

High dimensional thresholded regression and shrinkage effect

High dimensional sparse modelling via regularization provides a powerful tool for analysing large-scale data sets and obtaining meaningful interpretable models.The use of nonconvex penalty functions shows advantage in selecting important features in high dimensions, but the global optimality of such methods still demands more understanding.We consider sparse regression with a hard thresholding ...