Related papers: Screening Rules for Lasso with Non-Convex Sparse R…
Screening rules allow to early discard irrelevant variables from the optimization in Lasso problems, or its derivatives, making solvers faster. In this paper, we propose new versions of the so-called $\textit{safe rules}$ for the Lasso.…
We propose a new framework for deriving screening rules for convex optimization problems. Our approach covers a large class of constrained and penalized optimization formulations, and works in two steps. First, given any approximate point,…
The lasso is a popular method to induce shrinkage and sparsity in the solution vector (coefficients) of regression problems, particularly when there are many predictors relative to the number of observations. Solving the lasso in this…
The conditional gradient method (CGM) is widely used in large-scale sparse convex optimization, having a low per iteration computational cost for structured sparse regularizers and a greedy approach to collecting nonzeros. We explore the…
Convex sparsity-promoting regularizations are ubiquitous in modern statistical learning. By construction, they yield solutions with few non-zero coefficients, which correspond to saturated constraints in the dual optimization formulation.…
The problems of Lasso regression and optimal design of experiments share a critical property: their optimal solutions are typically \emph{sparse}, i.e., only a small fraction of the optimal variables are non-zero. Therefore, the…
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…
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…
In this paper, we develop a simple yet effective screening rule strategy to improve the computational efficiency in solving structured optimization involving nonconvex $\ell_{q,p}$ regularization. Based on an iteratively reweighted $\ell_1$…
Predictor screening rules, which discard predictors before fitting a model, have had considerable impact on the speed with which sparse regression problems, such as the lasso, can be solved. In this paper we present a new screening rule for…
We give safe screening rules to eliminate variables from regression with $\ell_0$ regularization or cardinality constraint. These rules are based on guarantees that a feature may or may not be selected in an optimal solution. The screening…
This paper considers a large class of problems where we seek to recover a low rank matrix and/or sparse vector from some set of measurements. While methods based on convex relaxations suffer from a (possibly large) estimator bias, and other…
A number of recent work studied the effectiveness of feature selection using Lasso. It is known that under the restricted isometry properties (RIP), Lasso does not generally lead to the exact recovery of the set of nonzero coefficients, due…
A recently introduced technique for a sparse optimization problem called "safe screening" allows us to identify irrelevant variables in the early stage of optimization. In this paper, we first propose a flexible framework for safe screening…
In high dimensional regression settings, sparsity enforcing penalties have proved useful to regularize the data-fitting term. A recently introduced technique called screening rules propose to ignore some variables in the optimization…
Sparse learning techniques have been routinely used for feature selection as the resulting model usually has a small number of non-zero entries. Safe screening, which eliminates the features that are guaranteed to have zero coefficients for…
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…
High dimensional regression benefits from sparsity promoting regularizations. Screening rules leverage the known sparsity of the solution by ignoring some variables in the optimization, hence speeding up solvers. When the procedure is…
This paper considers the problem of recovering either a low rank matrix or a sparse vector from observations of linear combinations of the vector or matrix elements. Recent methods replace the non-convex regularization with $\ell_1$ or…
In this work, we consider a class of differentiable criteria for sparse image computing problems, where a nonconvex regularization is applied to an arbitrary linear transform of the target image. As special cases, it includes…