Related papers: GAP Safe screening rules for sparse multi-task and…
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…
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.…
In high dimensional settings, sparse structures are crucial for efficiency, either in term of memory, computation or performance. In some contexts, it is natural to handle more refined structures than pure sparsity, such as for instance…
In a high-dimensional setting, sparse model has shown its power in computational and statistical efficiency. We consider variables selection problem with a broad class of simultaneous sparsity regularization, enforcing both feature-wise and…
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…
In logistic regression, it is often desirable to utilize regularization to promote sparse solutions, particularly for problems with a large number of features compared to available labels. In this paper, we present screening rules that…
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…
Sparse optimization problems are ubiquitous in many fields such as statistics, signal/image processing and machine learning. This has led to the birth of many iterative algorithms to solve them. A powerful strategy to boost the performance…
Distributed optimization has been widely used as one of the most efficient approaches for model training with massive samples. However, large-scale learning problems with both massive samples and high-dimensional features widely exist in…
Convex sparsity-inducing regularizations are ubiquitous in high-dimensional machine learning, but solving the resulting optimization problems can be slow. To accelerate solvers, state-of-the-art approaches consist in reducing the size of…
Sparse linear regression -- finding an unknown vector from linear measurements -- is now known to be possible with fewer samples than variables, via methods like the LASSO. We consider the multiple sparse linear regression problem, where…
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…
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 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…
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…
Tuning the regularization parameter in penalized regression models is an expensive task, requiring multiple models to be fit along a path of parameters. Strong screening rules drastically reduce computational costs by lowering the…
Sparse logistic regression is for classification and feature selection simultaneously. Although many studies have been done to solve $\ell_1$-regularized logistic regression, there is no equivalently abundant work on solving sparse logistic…
We consider high-dimensional multiclass classification by sparse multinomial logistic regression. Unlike binary classification, in the multiclass setup one can think about an entire spectrum of possible notions of sparsity associated with…
The l1-regularized logistic regression (or sparse logistic regression) is a widely used method for simultaneous classification and feature selection. Although many recent efforts have been devoted to its efficient implementation, its…
Leveraging on the convexity of the Lasso problem , screening rules help in accelerating solvers by discarding irrelevant variables, during the optimization process. However, because they provide better theoretical guarantees in identifying…