Related papers: Sparse Approximate Solutions to Max-Plus Equations…
We study the problem of estimating from data, a sparse approximation to the inverse covariance matrix. Estimating a sparsity constrained inverse covariance matrix is a key component in Gaussian graphical model learning, but one that is…
In this paper we propose a variant of the linear least squares model allowing practitioners to partition the input features into groups of variables that they require to contribute similarly to the final result. The output allows…
We develop two adaptive discretization algorithms for convex semi-infinite optimization, which terminate after finitely many iterations at approximate solutions of arbitrary precision. In particular, they terminate at a feasible point of…
Sparse regression models are increasingly prevalent due to their ease of interpretability and superior out-of-sample performance. However, the exact model of sparse regression with an $\ell_0$ constraint restricting the support of the…
We introduce a new method for sparse principal component analysis, based on the aggregation of eigenvector information from carefully-selected axis-aligned random projections of the sample covariance matrix. Unlike most alternative…
This paper addresses the problem of sparse phase retrieval, a fundamental inverse problem in applied mathematics, physics, and engineering, where a signal need to be reconstructed using only the magnitude of its transformation while phase…
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…
This paper presents a new algorithmic framework for computing sparse solutions to large-scale linear discrete ill-posed problems. The approach is motivated by recent perspectives on iteratively reweighted norm schemes, viewed through the…
We investigate how to solve smooth matrix optimization problems with general linear inequality constraints on the eigenvalues of a symmetric matrix. We present solution methods to obtain exact global minima for linear objective functions,…
The affine inverse eigenvalue problem consists of identifying a real symmetric matrix with a prescribed set of eigenvalues in an affine space. Due to its ubiquity in applications, various instances of the problem have been widely studied in…
In this paper, we study the solution uniqueness of an individual feasible vector of a class of convex optimization problems involving convex piecewise affine functions and subject to general polyhedral constraints. This class of problems…
In high-dimensional linear regression, the goal pursued here is to estimate an unknown regression function using linear combinations of a suitable set of covariates. One of the key assumptions for the success of any statistical procedure in…
Many problems in machine learning can be solved by rounding the solution of an appropriate linear program (LP). This paper shows that we can recover solutions of comparable quality by rounding an approximate LP solution instead of the ex-…
We consider a class of $\ell_0$-regularized linear-quadratic (LQ) optimal control problems. This class of problems is obtained by augmenting a penalizing sparsity measure to the cost objective of the standard linear-quadratic regulator…
We describe two algorithms for computing a sparse solution to a least-squares problem where the coefficient matrix can have arbitrary dimensions. We show that the solution vector obtained by our algorithms is close to the solution vector…
This paper deals with sparse phase retrieval, i.e., the problem of estimating a vector from quadratic measurements under the assumption that few components are nonzero. In particular, we consider the problem of finding the sparsest vector…
In this paper, we study the problem of sparse mixed linear regression on an unlabeled dataset that is generated from linear measurements from two different regression parameter vectors. Since the data is unlabeled, our task is not only to…
In recent years, there has been a growing interest in mathematical models leading to the minimization, in a symmetric matrix space, of a Bregman divergence coupled with a regularization term. We address problems of this type within a…
In exact sparse optimization problems on Rd (also known as sparsity constrained problems), one looks for solution that have few nonzero components. In this paper, we consider problems where sparsity is exactly measured either by the…
For the problem of multi-class linear classification and feature selection, we propose approximate message passing approaches to sparse multinomial logistic regression (MLR). First, we propose two algorithms based on the Hybrid Generalized…