Related papers: More on the Power of Randomized Matrix Computation…
A Random SubMatrix method (RSM) is proposed to calculate the low-rank decomposition of large-scale matrices with known entry percentage \rho. RSM is very fast as the floating-point operations (flops) required are compared favorably with the…
We consider the problem of estimation of a low-rank matrix from a limited number of noisy rank-one projections. In particular, we propose two fast, non-convex \emph{proper} algorithms for matrix recovery and support them with rigorous…
Parametric stochastic simulators are ubiquitous in science, often featuring high-dimensional input parameters and/or an intractable likelihood. Performing Bayesian parameter inference in this context can be challenging. We present a neural…
Matrix factorization is a well-studied task in machine learning for compactly representing large, noisy data. In our approach, instead of using the traditional concept of matrix rank, we define a new notion of link-rank based on a…
Consider a random vector with finite second moments. If its precision matrix is an M-matrix, then all partial correlations are non-negative. If that random vector is additionally Gaussian, the corresponding Markov random field (GMRF) is…
Low-rank tensor approximations have shown great potential for uncertainty quantification in high dimensions, for example, to build surrogate models that can be used to speed up large-scale inference problems (Eigel et al., Inverse Problems…
We develop several efficient algorithms for the classical \emph{Matrix Scaling} problem, which is used in many diverse areas, from preconditioning linear systems to approximation of the permanent. On an input $n\times n$ matrix $A$, this…
The condition number of a diagonally scaled matrix, for appropriately chosen scaling matrices, is often less than that of the original. Equilibration scales a matrix so that the scaled matrix's row and column norms are equal. Scaling can be…
Since simulating quantum computers requires exponentially more classical resources, efficient algorithms are extremely helpful. We analyze algorithms that create single qubit and specific controlled qubit matrix representations of gates.…
A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. Unfortunately, the resulting submodular optimization…
Processes to automate the selection of appropriate algorithms for various matrix computations are described. In particular, processes to check for, and certify, various matrix properties of black box matrices are presented. These include…
We develop Bayesian predictive stacking for geostatistical models, where the primary inferential objective is to provide inference on the latent spatial random field and conduct spatial predictions at arbitrary locations. We exploit…
This paper presents a sequential randomized lowrank matrix factorization approach for incrementally predicting values of an unknown function at test points using the Gaussian Processes framework. It is well-known that in the Gaussian…
In this letter, we study the deterministic sampling patterns for the completion of low rank matrix, when corrupted with a sparse noise, also known as robust matrix completion. We extend the recent results on the deterministic sampling…
Recent work in machine learning community proposed multiple methods for performing lossy compression (quantization) of large matrices. This quantization is important for accelerating matrix multiplication (main component of large language…
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…
Matrices are typically considered over fields or rings. Motivated by applications in parametric differential equations and data-driven modeling, we suggest to study matrices with entries from a Hilbert space and present an elementary theory…
This paper presents a randomized algorithm for computing the near-optimal low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to compute low-rank matrix approximations at a fraction of the cost of…
We implement an Augmented Lagrangian method to minimize a constrained least-squares cost function designed to find polyadic decompositions of the matrix multiplication tensor. We use this method to obtain new discrete decompositions and…
This survey describes probabilistic algorithms for linear algebra computations, such as factorizing matrices and solving linear systems. It focuses on techniques that have a proven track record for real-world problem instances. The paper…