Related papers: CAPPA: Continuous-time Accelerated Proximal Point …

We formulate the sparse classification problem of $n$ samples with $p$ features as a binary convex optimization problem and propose a cutting-plane algorithm to solve it exactly. For sparse logistic regression and sparse SVM, our algorithm…

Sparse Principal Component Analysis (SPCA) and Sparse Linear Regression (SLR) have a wide range of applications and have attracted a tremendous amount of attention in the last two decades as canonical examples of statistical problems in…

Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel…

In this paper, we propose exact passive-aggressive (PA) online algorithms for learning to rank. The proposed algorithms can be used even when we have interval labels instead of actual labels for examples. The proposed algorithms solve a…

This work examines the compressed sensor caching problem in wireless sensor networks and devises efficient distributed sparse data recovery algorithms to enable collaboration among multiple caches. In this problem, each cache is only…

A recursive algorithm named Zero-point Attracting Projection (ZAP) is proposed recently for sparse signal reconstruction. Compared with the reference algorithms, ZAP demonstrates rather good performance in recovery precision and robustness.…

This paper establishes several convergence results about flows of the dynamical system LCA (Locally Competitive Algorithm) to the mixed $\ell_2$-$\ell_1$ minimization problem LASSO and the constrained version, called CLASSO here, where the…

It has recently been shown that ISTA, an unaccelerated optimization method, presents sparse updates for the $\ell_1$-regularized personalized PageRank problem, leading to cheap iteration complexity and providing the same guarantees as the…

In many real-world problems, recovering sparse signals from underdetermined linear systems remains a fundamental challenge. Although $\ell_1$ norm minimization is widely used, it suffers from estimation bias that prevents it from reaching…

The classical Canonical Correlation Analysis (CCA) identifies the correlations between two sets of multivariate variables based on their covariance, which has been widely applied in diverse fields such as computer vision, natural language…

We develop a new efficient sequential approximate leverage score algorithm, SALSA, using methods from randomized numerical linear algebra (RandNLA) for large matrices. We demonstrate that, with high probability, the accuracy of SALSA's…

Compressed sensing deals with the recovery of sparse signals from linear measurements. Without any additional information, it is possible to recover an $s$-sparse signal using $m \gtrsim s \log(d/s)$ measurements in a robust and stable way.…

Sparse Principal Component Analysis (PCA) is a prevalent tool across a plethora of subfields of applied statistics. While several results have characterized the recovery error of the principal eigenvectors, these are typically in spectral…

Recent studies of under-determined linear systems of equations with sparse solutions showed a great practical and theoretical efficiency of a particular technique called $\ell_1$-optimization. Seminal works \cite{CRT,DOnoho06CS} rigorously…

This paper presents an algorithm tailored for the efficient recovery of sparse probability measures incorporating $\ell_0$-sparse regularization within the probability simplex constraint. Employing the Bregman proximal gradient method, our…

Sparsity and rank functions are important ways of regularizing under-determined linear systems. Optimization of the resulting formulations is made difficult since both these penalties are non-convex and discontinuous. The most common remedy…

Sparsity constrained minimization captures a wide spectrum of applications in both machine learning and signal processing. This class of problems is difficult to solve since it is NP-hard and existing solutions are primarily based on…

Principal component analysis (PCA) is one of the most widely used dimensionality reduction methods in scientific data analysis. In many applications, for additional interpretability, it is desirable for the factor loadings to be sparse,…

We consider the problem of recovering sparse vectors from underdetermined linear measurements via $\ell_p$-constrained basis pursuit. Previous analyses of this problem based on generalized restricted isometry properties have suggested that…

Sparse principal component analysis (PCA) improves interpretability of the classic PCA by introducing sparsity into the dimension-reduction process. Optimization models for sparse PCA, however, are generally non-convex, non-smooth and more…