Related papers: From safe screening rules to working sets for fast…

Sparse methods for supervised learning aim at finding good linear predictors from as few variables as possible, i.e., with small cardinality of their supports. This combinatorial selection problem is often turned into a convex optimization…

The Lasso is a method for high-dimensional regression, which is now commonly used when the number of covariates $p$ is of the same order or larger than the number of observations $n$. Classical asymptotic normality theory does not apply to…

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 analyze a class of norms defined via an optimal interpolation problem involving the composition of norms and a linear operator. This construction, known as infimal postcomposition in convex analysis, is shown to encompass various of…

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…

There has been significant recent work on the theory and application of randomized coordinate descent algorithms, beginning with the work of Nesterov [SIAM J. Optim., 22(2), 2012], who showed that a random-coordinate selection rule achieves…

The convolutional sparse model has recently gained increasing attention in the signal and image processing communities, and several methods have been proposed for solving the pursuit problem emerging from it -- in particular its convex…

Autonomous navigation requires an accurate model or map of the environment. While dramatic progress in the prior two decades has enabled large-scale SLAM, the majority of existing methods rely on non-linear optimization techniques to find…

We consider a class of sparse learning problems in high dimensional feature space regularized by a structured sparsity-inducing norm which incorporates prior knowledge of the group structure of the features. Such problems often pose a…

In genomic analysis, biomarker discovery, image recognition, and other systems involving machine learning, input variables can often be organized into different groups by their source or semantic category. Eliminating some groups of…

Extracting relevant features from data sets where the number of observations ($n$) is much smaller then the number of predictors ($p$) is a major challenge in modern statistics. Sorted L-One Penalized Estimation (SLOPE), a generalization of…

We investigate fast methods that allow to quickly eliminate variables (features) in supervised learning problems involving a convex loss function and a $l_1$-norm penalty, leading to a potentially substantial reduction in the number of…

When given a generalized matrix separation problem, which aims to recover a low rank matrix $L_0$ and a sparse matrix $S_0$ from $M_0=L_0+HS_0$, the work \cite{CW25} proposes a novel convex optimization problem whose objective function is…

We investigate the convergence rates and data sample sizes required for training a machine learning model using a stochastic gradient descent (SGD) algorithm, where data points are sampled based on either their loss value or uncertainty…

Flexible sparsity regularization means stably approximating sparse solutions of operator equations by using coefficient-dependent penalizations. We propose and analyse a general nonconvex approach in this respect, from both theoretical and…

We propose Expected Work Search (EWS), a new game solving algorithm. EWS combines win rate estimation, as used in Monte Carlo Tree Search, with proof size estimation, as used in Proof Number Search. The search efficiency of EWS stems from…

Recent computational strategies based on screening tests have been proposed to accelerate algorithms addressing penalized sparse regression problems such as the Lasso. Such approaches build upon the idea that it is worth dedicating some…

The theory of sampling and the reconstruction of data has a wide range of applications and a rich collection of techniques. For many methods a core problem is the estimation of the number of samples needed in order to secure a stable and…

Label smoothing regularization (LSR) has a great success in training deep neural networks by stochastic algorithms such as stochastic gradient descent and its variants. However, the theoretical understanding of its power from the view of…

It is essential for a robot to be able to detect revisits or loop closures for long-term visual navigation.A key insight explored in this work is that the loop-closing event inherently occurs sparsely, that is, the image currently being…