Related papers: The Well Tempered Lasso
The regularization path of the Lasso can be shown to be piecewise linear, making it possible to "follow" and explicitly compute the entire path. We analyze in this paper this popular strategy, and prove that its worst case complexity is…
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…
In recent years, a rich variety of regularization procedures have been proposed for high dimensional regression problems. However, tuning parameter choice and computational efficiency in ultra-high dimensional problems remain vexing issues.…
Many least squares problems involve affine equality and inequality constraints. Although there are variety of methods for solving such problems, most statisticians find constrained estimation challenging. The current paper proposes a new…
Nowadays, l1 penalized likelihood has absorbed a high amount of consideration due to its simplicity and well developed theoretical properties. This method is known as a reliable method in order to apply in a broad range of applications…
Regularized regression approaches such as the Lasso have been widely adopted for constructing sparse linear models in high-dimensional datasets. A complexity in fitting these models is the tuning of the parameters which control the level of…
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…
The LASSO is an attractive regularisation method for linear regression that combines variable selection with an efficient computation procedure. This paper is concerned with enhancing the performance of LASSO for square-free hierarchical…
A reciprocal LASSO (rLASSO) regularization employs a decreasing penalty function as opposed to conventional penalization approaches that use increasing penalties on the coefficients, leading to stronger parsimony and superior model…
The Lasso is a very well known penalized regression model, which adds an $L_{1}$ penalty with parameter $\lambda_{1}$ on the coefficients to the squared error loss function. The Fused Lasso extends this model by also putting an $L_{1}$…
We consider the least-square linear regression problem with regularization by the $\ell^1$-norm, a problem usually referred to as the Lasso. In this paper, we first present a detailed asymptotic analysis of model consistency of the Lasso in…
Analysis sparsity is a common prior in inverse problem or machine learning including special cases such as Total Variation regularization, Edge Lasso and Fused Lasso. We study the geometry of the solution set (a polyhedron) of the analysis…
Regularization is widely used in statistics and machine learning to prevent overfitting and gear solution towards prior information. In general, a regularized estimation problem minimizes the sum of a loss function and a penalty term. The…
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…
Modern technologies are producing a wealth of data with complex structures. For instance, in two-dimensional digital imaging, flow cytometry, and electroencephalography, matrix type covariates frequently arise when measurements are obtained…
The Lasso is a computationally efficient regression regularization procedure that can produce sparse estimators when the number of predictors (p) is large. Oracle inequalities provide probability loss bounds for the Lasso estimator at a…
For many algorithms, parameter tuning remains a challenging and critical task, which becomes tedious and infeasible in a multi-parameter setting. Multi-penalty regularization, successfully used for solving undetermined sparse regression of…
We consider the least-square linear regression problem with regularization by the l1-norm, a problem usually referred to as the Lasso. In this paper, we present a detailed asymptotic analysis of model consistency of the Lasso. For various…
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…
Within the statistical and machine learning literature, regularization techniques are often used to construct sparse (predictive) models. Most regularization strategies only work for data where all predictors are treated identically, such…