Related papers: A novel greedy Gauss-Seidel method for solving lar…
In this paper, we consider a subset selection problem in a spatial field where we seek to find a set of k locations whose observations provide the best estimate of the field value at a finite set of prediction locations. The measurements…
In this paper, we consider a novel two-dimensional randomized Kaczmarz method and its improved version with simple random sampling, which chooses two active rows with probability proportional to the square of their cross-product-like…
High dimensional unconstrained quadratic programs (UQPs) involving massive datasets are now common in application areas such as web, social networks, etc. Unless computational resources that match up to these datasets are available, solving…
In this paper, we develop a new Randomized Global Generalized Minimum Residual (RGlGMRES) algorithm for efficiently computing solutions to large scale linear systems with multiple right hand sides.The proposed method builds on a recently…
We consider the problem of breaking a multivariate (vector) time series into segments over which the data is well explained as independent samples from a Gaussian distribution. We formulate this as a covariance-regularized maximum…
This paper introduces the Multiple Greedy Quasi-Newton (MGSR1-SP) method, a novel approach to solving strongly-convex-strongly-concave (SCSC) saddle point problems. Our method enhances the approximation of the squared indefinite Hessian…
Least squares method is one of the simplest and most popular techniques applied in data fitting, imaging processing and high dimension data analysis. The classic methods like QR and SVD decomposition for solving least squares problems has a…
We describe the Greedy Sparse Subspace Clustering (GSSC) algorithm providing an efficient method for clustering data belonging to a few low-dimensional linear or affine subspaces from incomplete corrupted and noisy data. We provide…
Coordinate descent with random coordinate selection is the current state of the art for many large scale optimization problems. However, greedy selection of the steepest coordinate on smooth problems can yield convergence rates independent…
A parameter-free method, namely the generalization of the Gauss-Seidel (GGS) method, is developed to solve generalized absolute value equations. Convergence of the proposed method is analyzed. Numerical results are given to demonstrate the…
A class of fast greedy block Kaczmarz methods combined with general greedy strategy and average technique are proposed for solving large consistent linear systems. Theoretical analysis of the convergence of the proposed method is given in…
In this work we propose and analyze a weighted proper orthogonal decomposition method to solve elliptic partial differential equations depending on random input data, for stochastic problems that can be transformed into parametric systems.…
For solving the large-scale linear system by iteration methods, we utilize the Petrov-Galerkin conditions and relaxed greedy index selection technique and provide two relaxed greedy deterministic row (RGDR) and column (RGDC) iterative…
The Kaczmarz method is a popular iterative scheme for solving large-scale linear systems. The randomized Kaczmarz method (RK) greatly improves the convergence rate of the Kaczmarz method, by using the rows of the coefficient matrix in…
We analyze greedy algorithms for the Hierarchical Aggregation (HAG) problem, a strategy introduced in [Jia et al., KDD 2020] for speeding up learning on Graph Neural Networks (GNNs). The idea of HAG is to identify and remove redundancies in…
In this article, we present two new greedy algorithms for the computation of the lowest eigenvalue (and an associated eigenvector) of a high-dimensional eigenvalue problem, and prove some convergence results for these algorithms and their…
We analyze a batched variant of Stochastic Gradient Descent (SGD) with weighted sampling distribution for smooth and non-smooth objective functions. We show that by distributing the batches computationally, a significant speedup in the…
In recent studies on sparse modeling, $l_q$ ($0<q<1$) regularized least squares regression ($l_q$LS) has received considerable attention due to its superiorities on sparsity-inducing and bias-reduction over the convex counterparts. In this…
In this article, we present a family of numerical approaches to solve high-dimensional linear non-symmetric problems. The principle of these methods is to approximate a function which depends on a large number of variates by a sum of tensor…
The Kaczmarz and Gauss-Seidel methods both solve a linear system $\bf{X}\bf{\beta} = \bf{y}$ by iteratively refining the solution estimate. Recent interest in these methods has been sparked by a proof of Strohmer and Vershynin which shows…