Related papers: Efficient Numerical Methods to Solve Sparse Linear…
Based on a new atomic norm, we propose a new convex formulation for sparse matrix factorization problems in which the number of nonzero elements of the factors is assumed fixed and known. The formulation counts sparse PCA with multiple…
We study algorithms for estimating the statistical leverage scores of rectangular dense or sparse matrices of arbitrary rank. Our approach is based on combining rank revealing methods with compositions of dense and sparse randomized…
We investigate implicit regularization schemes for gradient descent methods applied to unpenalized least squares regression to solve the problem of reconstructing a sparse signal from an underdetermined system of linear measurements under…
The problem of minimizing a polynomial over a set of polynomial inequalities is an NP-hard non-convex problem. Thanks to powerful results from real algebraic geometry, one can convert this problem into a nested sequence of…
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…
We address the problem of estimating a sparse low-rank matrix from its noisy observation. We propose an objective function consisting of a data-fidelity term and two parameterized non-convex penalty functions. Further, we show how to set…
The problem of estimating sparse eigenvectors of a symmetric matrix attracts a lot of attention in many applications, especially those with high dimensional data set. While classical eigenvectors can be obtained as the solution of a…
Even distribution of irregular workload to processing units is crucial for efficient parallelization in many applications. In this work, we are concerned with a spatial partitioning called rectilinear partitioning (also known as generalized…
We present a simple, accurate method for solving consistent, rank-deficient linear systems, with or without addi- tional rank-completing constraints. Such problems arise in a variety of applications, such as the computation of the…
Recovery of low-rank matrices has recently seen significant activity in many areas of science and engineering, motivated by recent theoretical results for exact reconstruction guarantees and interesting practical applications. A number of…
This paper considers the sparse eigenvalue problem, which is to extract dominant (largest) sparse eigenvectors with at most $k$ non-zero components. We propose a simple yet effective solution called truncated power method that can…
In this paper, the estimation problem for sparse reduced rank regression (SRRR) model is considered. The SRRR model is widely used for dimension reduction and variable selection with applications in signal processing, econometrics, etc. The…
While matrix variate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional and noisy…
The paper is devoted to new modifications of recently proposed adaptive methods of Mirror Descent for convex minimization problems in the case of several convex functional constraints. Methods for problems of two classes are considered. The…
Sparse regression methods have been proven effective in a wide range of signal processing problems such as image compression, speech coding, channel equalization, linear regression and classification. In this paper a new convex method of…
In this paper, we investigate the problem of optimization multivariate performance measures, and propose a novel algorithm for it. Different from traditional machine learning methods which optimize simple loss functions to learn prediction…
The article is devoted to the development of numerical methods for solving saddle point problems and variational inequalities with simplified requirements for the smoothness conditions of functionals. Recently there were proposed some…
In this paper, we consider a recursive estimation problem for linear regression where the signal to be estimated admits a sparse representation and measurement samples are only sequentially available. We propose a convergent parallel…
Variational formulations of reconstruction in computed tomography have the notable drawback of requiring repeated evaluations of both the forward Radon transform and either its adjoint or an approximate inverse transform which are…
This paper examines a variety of classical optimization problems, including well-known minimization tasks and more general variational inequalities. We consider a stochastic formulation of these problems, and unlike most previous work, we…