Related papers: A Count Sketch Kaczmarz Method For Solving Large O…
The Kaczmarz method is successfully used for solving discretizations of linear inverse problems, especially in computed tomography where it is known as ART. Practitioners often observe and appreciate its fast convergence in the first few…
The sampling Kaczmarz-Motzkin (SKM) method is a generalization of the randomized Kaczmarz and Motzkin methods. It first samples some rows of coefficient matrix randomly to build a set and then makes use of the maximum violation criterion…
Randomized iterative algorithms for solving a factorized linear system, $\mathbf A\mathbf B\mathbf x=\mathbf b$ with $\mathbf A\in{\mathbb{R}}^{m\times \ell}$, $\mathbf B\in{\mathbb{R}}^{\ell\times n}$, and $\mathbf b\in{\mathbb{R}}^m$,…
We propose a randomized algorithm with quadratic convergence rate for convex optimization problems with a self-concordant, composite, strongly convex objective function. Our method is based on performing an approximate Newton step using a…
Sketch-and-solve (SAS) is a very successful method to efficiently estimate the solution of heavily overdetermined large linear least squares problems. It uses random sketching to reduce the size of the problem, hence reducing the…
The sketch-and-project (SAP) framework for solving systems of linear equations has unified the theory behind popular projective iterative methods such as randomized Kaczmarz, randomized coordinate descent, and variants thereof. The…
We present a new class of preconditioned iterative methods for solving linear systems of the form $Ax = b$. Our methods are based on constructing a low-rank Nystr\"om approximation to $A$ using sparse random matrix sketching. This…
This paper presents a significant advancement in the estimation of the Composite Link Model within a penalized likelihood framework, specifically designed to address indirect observations of grouped count data. While the model is effective…
Matrices arising in scientific applications frequently admit linear low-rank approximations due to smoothness in the physical and/or temporal domain of the problem. In large-scale problems, computing an optimal low-rank approximation can be…
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…
This paper investigates the convergence of the randomized Kaczmarz algorithm for the problem of phase retrieval of complex-valued objects. While this algorithm has been studied for the real-valued case}, its generalization to the…
Stochastic iterative algorithms have gained recent interest in machine learning and signal processing for solving large-scale systems of equations, $Ax=b$. One such example is the Randomized Kaczmarz (RK) algorithm, which acts only on…
We introduce an algorithm based on a method of snapshots for computing approximate balanced truncations for discrete-time, stable, linear time-periodic systems. By construction, this algorithm is applicable to very high-dimensional systems,…
Coded computing is a distributed paradigm that uses coding theory to introduce \textit{redundancy} and overcome bottlenecks in large-scale systems. In the same vein, randomized numerical linear algebra employs probabilistic methods to…
We consider sketching algorithms which first quickly compress data by multiplication with a random sketch matrix, and then apply the sketch to quickly solve an optimization problem, e.g., low rank approximation. In the learning-based…
Kernel methods are learning algorithms that enjoy solid theoretical foundations while suffering from important computational limitations. Sketching, which consists in looking for solutions among a subspace of reduced dimension, is a well…
Randomized algorithms for very large matrix problems have received a great deal of attention in recent years. Much of this work was motivated by problems in large-scale data analysis, and this work was performed by individuals from many…
Stochastic computing (SC) is a promising candidate for fault tolerant computing in digital circuits. We present a novel stochastic computing estimation architecture allowing to solve a large group of estimation problems including least…
Recent work has explored transforming data sets into smaller, approximate summaries in order to scale Bayesian inference. We examine a related problem in which the parameters of a Bayesian model are very large and expensive to store in…
Learning parameters from voluminous data can be prohibitive in terms of memory and computational requirements. We propose a "compressive learning" framework where we estimate model parameters from a sketch of the training data. This sketch…