Related papers: Semi-randomized block Kaczmarz methods with simple…
It is known that any continuous multivariate function can be represented exactly by a composition functions of a single variable - the so-called Kolmogorov-Arnold representation. It can be a convenient tool for tasks where it is required to…
The Sparse Kaczmarz method is a famous and widely used iterative method for solving the regularized basis pursuit problem. A general scheme of the surrogate hyperplane sparse Kaczmarz method is proposed. In particular, a class of…
We consider the problem of phase retrieval, i.e. that of solving systems of quadratic equations. A simple variant of the randomized Kaczmarz method was recently proposed for phase retrieval, and it was shown numerically to have a…
In this paper we present a convergence rate analysis of inexact variants of several randomized iterative methods. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic…
The randomized coordinate descent (RCD) method is a classical algorithm with simple, lightweight iterations that is widely used for various optimization problems, including the solution of positive semidefinite linear systems. As a linear…
The latent block model is used to simultaneously rank the rows and columns of a matrix to reveal a block structure. The algorithms used for estimation are often time consuming. However, recent work shows that the log-likelihood ratios are…
Sparse and low rank tensor recovery has emerged as a significant area of research with applications in many fields such as computer vision. However, minimizing the $\ell_0$-norm of a vector or the rank of a matrix is NP-hard. Instead, their…
The Kaczmarz method is a popular iterative method for solving consistent, overdetermined linear system such as medical imaging in computerized tomography. The Kaczmarz's iteration repeatedly scans all equations in order, which leads to…
The low rank approximation of matrices is a crucial component in many data mining applications today. A competitive algorithm for this class of problems is the randomized block Lanczos algorithm - an amalgamation of the traditional block…
We propose a computationally intensive method, the random lasso method, for variable selection in linear models. The method consists of two major steps. In step 1, the lasso method is applied to many bootstrap samples, each using a set of…
Large-scale linear systems of the form $Ax=b$ are often doubly-noisy, in the sense that both its measurement matrix $A$ and measurement vector $b$ are noisy. In this paper, we extend the relaxed greedy randomized Kaczmarz (RGRK) method to…
A novel matrix approximation problem is considered herein: observations based on a few fully sampled columns and quasi-polynomial structural side information are exploited. The framework is motivated by quantum chemistry problems wherein…
Sampling from very large spatial populations is challenging. The solutions suggested in recent literature on this subject often require that the randomly selected units are well distributed across the study region by using complex…
Randomized algorithms provide solutions to two ubiquitous problems: (1) the distributed calculation of a principal component analysis or singular value decomposition of a highly rectangular matrix, and (2) the distributed calculation of a…
This article explores and analyzes the unsupervised clustering of large partially observed graphs. We propose a scalable and provable randomized framework for clustering graphs generated from the stochastic block model. The clustering is…
Asynchronous methods for solving systems of linear equations have been researched since Chazan and Miranker's pioneering 1969 paper on chaotic relaxation. The underlying idea of asynchronous methods is to avoid processor idle time by…
We investigate modified steepest descent methods coupled with a loping Kaczmarz strategy for obtaining stable solutions of nonlinear systems of ill-posed operator equations. We show that the proposed method is a convergent regularization…
We propose a novel stochastic algorithm that randomly samples entire rows and columns of the matrix as a way to approximate an arbitrary matrix function using the power series expansion. This contrasts with existing Monte Carlo methods,…
We explore the impact of coarse quantization on low-rank matrix sensing in the extreme scenario of dithered one-bit sampling, where the high-resolution measurements are compared with random time-varying threshold levels. To recover the…
Iteration method is commonly used in solving linear systems of equations. We present quantum algorithms for the relaxed row and column iteration methods by constructing unitary matrices in the iterative processes, which generalize row and…