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Among the most popular variable selection procedures in high-dimensional regression, Lasso provides a solution path to rank the variables and determines a cut-off position on the path to select variables and estimate coefficients. In this…

Shrinkage estimators that possess the ability to produce sparse solutions have become increasingly important to the analysis of today's complex datasets. Examples include the LASSO, the Elastic-Net and their adaptive counterparts.…

The lasso has become an important practical tool for high dimensional regression as well as the object of intense theoretical investigation. But despite the availability of efficient algorithms, the lasso remains computationally demanding…

In this paper, for Lasso penalized linear regression models in high-dimensional settings, we propose a modified cross-validation method for selecting the penalty parameter. The methodology is extended to other penalties, such as Elastic…

The goal of this paper is to contrast and survey the major advances in two of the most commonly used high-dimensional techniques, namely, the Lasso and horseshoe regularization. Lasso is a gold standard for predictor selection while…

Variable selection in linear regression models has been a problem since hypothesis testing began. Which variables to include or exclude from a model is not an easy task. Techniques such as Forward, Back ward, Stepwise Regression…

We consider the problem of automatic variable selection in a linear model with asymmetric or heavy-tailed errors when the number of explanatory variables diverges with the sample size. For this high-dimensional model, the penalized least…

Detecting influential features in non-linear and/or high-dimensional data is a challenging and increasingly important task in machine learning. Variable selection methods have thus been gaining much attention as well as post-selection…

Regression with the lasso penalty is a popular tool for performing dimension reduction when the number of covariates is large. In many applications of the lasso, like in genomics, covariates are subject to measurement error. We study the…

Penalized regression is an attractive framework for variable selection problems. Often, variables possess a grouping structure, and the relevant selection problem is that of selecting groups, not individual variables. The group lasso has…

In high-dimensional survival analysis, effective variable selection is crucial for both model interpretation and predictive performance. This paper investigates Cox regression with lasso and adaptive lasso penalties in genomic datasets…

This article introduces lassopack, a suite of programs for regularized regression in Stata. lassopack implements lasso, square-root lasso, elastic net, ridge regression, adaptive lasso and post-estimation OLS. The methods are suitable for…

The lasso is a popular tool for sparse linear regression, especially for problems in which the number of variables p exceeds the number of observations n. But when p>n, the lasso criterion is not strictly convex, and hence it may not have a…

This article describes a full Bayesian treatment for simultaneous fixed-effect selection and parameter estimation in high-dimensional generalized linear mixed models. The approach consists of using a Bayesian adaptive Lasso penalty for…

The $\ell_1$-penalized method, or the Lasso, has emerged as an important tool for the analysis of large data sets. Many important results have been obtained for the Lasso in linear regression which have led to a deeper understanding of…

High-dimensional prediction typically comprises two steps: variable selection and subsequent least-squares refitting on the selected variables. However, the standard variable selection procedures, such as the lasso, hinge on tuning…

In this article we investigate consistency of selection in regression models via the popular Lasso method. Here we depart from the traditional linear regression assumption and consider approximations of the regression function $f$ with…

Despite its prevalence in statistical datasets, heteroscedasticity (non-constant sample variances) has been largely ignored in the high-dimensional statistics literature. Recently, studies have shown that the Lasso can accommodate…

Random forests are a statistical learning technique that use bootstrap aggregation to average high-variance and low-bias trees. Improvements to random forests, such as applying Lasso regression to the tree predictions, have been proposed in…

Penalized likelihood approaches are widely used for high-dimensional regression. Although many methods have been proposed and the associated theory is now well-developed, the relative efficacy of different approaches in finite-sample…