Group lasso is a natural extension of lasso and selects variables in a grouped manner. However, group lasso suffers from estimation inefficiency and selection inconsistency. To remedy these problems, we propose the adaptive group lasso method. We show theoretically that the new method is able to identify the true model consistently, and the resulting estimator can be as efficient as oracle. Num...

The method of sparse principal component analysis (S-PCA) proposed by Zou, Hastie, and Tibshirani (2006) is an attractive approach to obtain sparse loadings in principal component analysis (PCA). S-PCA was motivated by reformulating PCA as a least-squares problem so that a lasso penalty on the loading coefficients can be applied. In this article, we propose new estimates to improve S-PCA in the...

The Lasso is an attractive approach to variable selection in sparse, highdimensional regression models. Much work has been done to study the selection and estimation properties of the Lasso in the context of least squares regression. However, the least squares based method is sensitive to outliers. An alternative to the least squares method is the least absolute deviations (LAD) method which is...

We study the validity of the pairs bootstrap for Lasso estimators in linear regression models with random covariates and heteroscedastic error terms. We show that the naive pairs bootstrap does not consistently estimate the distribution of the Lasso estimator. In particular, we identify two different sources for the failure of the bootstrap. First, in the bootstrap samples the Lasso estimator f...

This paper aims to study the convergence rate of a majorized alternating direction method of multiplier with indefinite proximal terms (iPADMM) for solving linearly constrained convex composite optimization problems. We establish the Q-linear rate convergence theorem for 2-block majorized iPADMM under mild conditions. Based on this result, the convergence rate analysis of symmetric Gaussian-Sei...

We propose the Bayesian adaptive Lasso (BaLasso) for variable selection and coefficient estimation in linear regression. The BaLasso is adaptive to the signal level by adopting different shrinkage for different coefficients. Furthermore, we provide a model selection machinery for the BaLasso by assessing the posterior conditional mode estimates, motivated by the hierarchical Bayesian interpreta...

We wholeheartedly congratulate Lockhart, Taylor, Tibshrani and Tibshrani on the stimulating paper, which provides insights into statistical inference based on the lasso solution path. The authors proposed novel covariance statistics for testing the significance of predictor variables as they enter the active set, which formalizes the data-adaptive test based on the lasso path. The observation t...

We discuss the behavior of penalized robust regression estimators in high-dimension and compare our theoretical predictions to simulations. Our results show the importance of the geometry of the dataset and shed light on the theoretical behavior of LASSO and much more involved methods.

The conserved threonine (Thr) residue in the penultimate position of the leader peptide of lasso peptides microcin J25 and capistruin can be effectively replaced by several amino acids close in size and shape to Thr. These findings suggest a model for lasso peptide biosynthesis in which the Thr sidechain is a recognition element for the lasso peptide maturation machinery.

Bayesian regression analysis has great importance in recent years, especially the Regularization method, Such as ridge, Lasso, adaptive lasso, elastic net methods, where choosing prior distribution of interested parameter is main idea analysis. By penalizing model, variance estimators are reduced notable and bias getting smaller. The tradeoff between penalized estimator consequently produce mor...