Related papers: Matroid Regression
We propose a two-level nested preconditioned iterative scheme for solving sparse linear systems of equations in which the coefficient matrix is symmetric and indefinite with relatively small number of negative eigenvalues. The proposed…
The recovery of signals with finite-valued components from few linear measurements is a problem with widespread applications and interesting mathematical characteristics. In the compressed sensing framework, tailored methods have been…
Multi-view data have been routinely collected in various fields of science and engineering. A general problem is to study the predictive association between multivariate responses and multi-view predictor sets, all of which can be of high…
Finding the solutions to a system of multivariate polynomial equations is a fundamental problem in mathematics and computer science. It involves evaluating the polynomials at many points, often chosen from a grid. In most current methods,…
The sparse linear regression problem is difficult to handle with usual sparse optimization models when both predictors and measurements are either quantized or represented in low-precision, due to non-convexity. In this paper, we provide a…
An l0-regularized linear regression for a sparse signal reconstruction is implemented based on the quadratic unconstrained binary optimization (QUBO) formulation. In this method, the signal values are quantized and expressed as bit…
Noisy matrix completion has attracted significant attention due to its applications in recommendation systems, signal processing and image restoration. Most existing works rely on (weighted) least squares methods under various low-rank…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
Many important problems are characterized by the eigenvalues of a large matrix. For example, the difficulty of many optimization problems, such as those arising from the fitting of large models in statistics and machine learning, can be…
Nowadays sparse systems of equations occur frequently in science and engineering. In this contribution we deal with sparse systems common in cryptanalysis. Given a cipher system, one converts it into a system of sparse equations, and then…
This paper proposes an efficient general alternating-direction implicit (GADI) framework for solving large sparse linear systems. The convergence property of the GADI framework is discussed. Most of the existing ADI methods can be viewed as…
Deep learning has yielded extraordinary results in vision and natural language processing, but this achievement comes at a cost. Most models require enormous resources during training, both in terms of computation and in human labeling…
We consider the problem of estimating the parameters of a Gaussian or binary distribution in such a way that the resulting undirected graphical model is sparse. Our approach is to solve a maximum likelihood problem with an added l_1-norm…
We present a new adaptive method for electronic structure calculations based on novel fast algorithms for reduction of multivariate mixtures. In our calculations, spatial orbitals are maintained as Gaussian mixtures whose terms are selected…
The non-negative solution to an underdetermined linear system can be uniquely recovered sometimes, even without imposing any additional sparsity constraints. In this paper, we derive conditions under which a unique non-negative solution for…
In compressed sensing one measures sparse signals directly in a compressed form via a linear transform and then reconstructs the original signal. However, it is often the case that the linear transform itself is known only approximately, a…
Estimation of the precision matrix (or inverse covariance matrix) is of great importance in statistical data analysis and machine learning. However, as the number of parameters scales quadratically with the dimension $p$, computation…
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…
Multigrid methods have proven to be an invaluable tool to efficiently solve large sparse linear systems arising in the discretization of partial differential equations (PDEs). Algebraic multigrid methods and in particular adaptive algebraic…
Given a sample covariance matrix, we examine the problem of maximizing the variance explained by a linear combination of the input variables while constraining the number of nonzero coefficients in this combination. This is known as sparse…