Related papers: Safe Feature Elimination in Sparse Supervised Lear…

In this paper we consider the dictionary learning problem for sparse representation. We first show that this problem is NP-hard by polynomial time reduction of the densest cut problem. Then, using successive convex approximation strategies,…

We present the backbone method, a generic framework that enables sparse and interpretable supervised machine learning methods to scale to ultra-high dimensional problems. We solve sparse regression problems with $10^7$ features in minutes…

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…

In dictionary learning, also known as sparse coding, the algorithm is given samples of the form $y = Ax$ where $x\in \mathbb{R}^m$ is an unknown random sparse vector and $A$ is an unknown dictionary matrix in $\mathbb{R}^{n\times m}$…

We study the data deletion problem for convex models. By leveraging techniques from convex optimization and reservoir sampling, we give the first data deletion algorithms that are able to handle an arbitrarily long sequence of adversarial…

We present a new approach to solve the sparse approximation or best subset selection problem, namely find a $k$-sparse vector ${\bf x}\in\mathbb{R}^d$ that minimizes the $\ell_2$ residual $\lVert A{\bf x}-{\bf y} \rVert_2$. We consider a…

We consider a non-convex constrained Lagrangian formulation of a fundamental bi-criteria optimization problem for variable selection in statistical learning; the two criteria are a smooth (possibly) nonconvex loss function, measuring the…

As the data-driven decision process becomes dominating for industrial applications, fairness-aware machine learning arouses great attention in various areas. This work proposes fairness penalties learned by neural networks with a simple…

We present a novel binary convex reformulation of the sparse regression problem that constitutes a new duality perspective. We devise a new cutting plane method and provide evidence that it can solve to provable optimality the sparse…

Sparse sampling schemes have the potential to dramatically reduce image acquisition time while simultaneously reducing radiation damage to samples. However, for a sparse sampling scheme to be useful it is important that we are able to…

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…

The sparse factorization of a large matrix is fundamental in modern statistical learning. In particular, the sparse singular value decomposition and its variants have been utilized in multivariate regression, factor analysis, biclustering,…

We study the problem of variable selection in convex nonparametric regression. Under the assumption that the true regression function is convex and sparse, we develop a screening procedure to select a subset of variables that contains the…

In statistical machine learning, kernel methods allow to consider infinite dimensional feature spaces with a computational cost that only depends on the number of observations. This is usually done by solving an optimization problem…

We study the problem of selecting limited features to observe such that models trained on them can perform well simultaneously across multiple subpopulations. This problem has applications in settings where collecting each feature is…

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…

In this paper we study the sparse coding problem in the context of sparse dictionary learning for image recovery. To this end, we consider and compare several state-of-the-art sparse optimization methods constructed using the shrinkage…

We consider the problem of sparse estimation in a factor analysis model. A traditional estimation procedure in use is the following two-step approach: the model is estimated by maximum likelihood method and then a rotation technique is…

We study variable selection (also called support recovery) in high-dimensional sparse linear regression when one has external information on which variables are likely to be associated with the response. Consistent recovery is only possible…

We give two provably accurate feature-selection techniques for the linear SVM. The algorithms run in deterministic and randomized time respectively. Our algorithms can be used in an unsupervised or supervised setting. The supervised…