Related papers: Bad estimation, good prediction: the Lasso in dens…

Nonconvex penalty methods for sparse modeling in linear regression have been a topic of fervent interest in recent years. Herein, we study a family of nonconvex penalty functions that we call the trimmed Lasso and that offers exact control…

It is well-known that the statistical performance of Lasso can suffer significantly when the covariates of interest have strong correlations. In particular, the prediction error of Lasso becomes much worse than computationally inefficient…

Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is done by solving an l_1-regularized linear regression problem, usually called Lasso. In this work we first combine the…

In high dimension, it is customary to consider Lasso-type estimators to enforce sparsity. For standard Lasso theory to hold, the regularization parameter should be proportional to the noise level, yet the latter is generally unknown in…

Learning sparse models from data is an important task in all those frameworks where relevant information should be identified within a large dataset. This can be achieved by formulating and solving suitable sparsity promoting optimization…

We study various constraints and conditions on the true coefficient vector and on the design matrix to establish non-asymptotic oracle inequalities for the prediction error, estimation accuracy and variable selection for the Lasso estimator…

The abundance of high-dimensional data in the modern sciences has generated tremendous interest in penalized estimators such as the lasso, scaled lasso, square-root lasso, elastic net, and many others. In this paper, we establish a general…

Least squares fitting is in general not useful for high-dimensional linear models, in which the number of predictors is of the same or even larger order of magnitude than the number of samples. Theory developed in recent years has coined a…

We consider the problem of identifying significant predictors in large data bases, where the response variable depends on the linear combination of explanatory variables through an unknown link function, corrupted with the noise from the…

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…

Censored data are quite common in statistics and have been studied in depth in the last years. In this paper we consider censored high-dimensional data. High-dimensional models are in some way more complex than their low-dimensional…

Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual…

Sparse linear regression with ill-conditioned Gaussian random designs is widely believed to exhibit a statistical/computational gap, but there is surprisingly little formal evidence for this belief, even in the form of examples that are…

Lasso, or $\ell^1$ regularized least squares, has been explored extensively for its remarkable sparsity properties. It is shown in this paper that the solution to Lasso, in addition to its sparsity, has robustness properties: it is the…

Bayesian predictive inference provides a coherent description of entire predictive uncertainty through predictive distributions. We examine several widely used sparsity priors from the predictive (as opposed to estimation) inference…

In high-dimensions, many variable selection methods, such as the lasso, are often limited by excessive variability and rank deficiency of the sample covariance matrix. Covariance sparsity is a natural phenomenon in high-dimensional…

High resolution microarrays and second-generation sequencing platforms are powerful tools to investigate genome-wide alterations in DNA copy number, methylation and gene expression associated with a disease. An integrated genomic profiling…

When we are interested in high-dimensional system and focus on classification performance, the $\ell_{1}$-penalized logistic regression is becoming important and popular. However, the Lasso estimates could be problematic when penalties of…

The popular Lasso approach for sparse estimation can be derived via marginalization of a joint density associated with a particular stochastic model. A different marginalization of the same probabilistic model leads to a different…

Meinshausen and Buhlmann [Ann. Statist. 34 (2006) 1436--1462] showed that, for neighborhood selection in Gaussian graphical models, under a neighborhood stability condition, the LASSO is consistent, even when the number of variables is of…