相关论文: Efficient error and variance estimation for random…

Statistical resampling methods have become feasible for parametric estimation, hypothesis testing, and model validation now that the computer is a ubiquitous tool for statisticians. This essay focuses on the resampling technique for…

A novel algorithm for the recovery of low-rank matrices acquired via compressive linear measurements is proposed and analyzed. The algorithm, a variation on the iterative hard thresholding algorithm for low-rank recovery, is designed to…

The Randomized Singular Value Decomposition (RSVD) is a widely used algorithm for efficiently computing low-rank approximations of large matrices, without the need to construct a full-blown SVD. Of interest, of course, is the approximation…

Generalized singular values (GSVs) play an essential role in the comparative analysis. In the real world data for comparative analysis, both data matrices are usually numerically low-rank. This paper proposes a randomized algorithm to first…

We give an efficient algorithm which can obtain a relative error approximation to the spectral norm of a matrix, combining the power iteration method with some techniques from matrix reconstruction which use random sampling.

Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to…

We introduce novel dynamical low-rank methods for solving large-scale matrix differential equations, motivated by algorithms from randomized numerical linear algebra. In terms of performance (cost and accuracy), our methods overperform…

While matrix variate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional and noisy…

Low-rank matrix approximations are often used to help scale standard machine learning algorithms to large-scale problems. Recently, matrix coherence has been used to characterize the ability to extract global information from a subset of…

Low-rank approximation of a matrix by means of structured random sampling has been consistently efficient in its extensive empirical studies around the globe, but adequate formal support for this empirical phenomenon has been missing so…

This survey explores modern approaches for computing low-rank approximations of high-dimensional matrices by means of the randomized SVD, randomized subspace iteration, and randomized block Krylov iteration. The paper compares the…

Over the course of the past decade, a variety of randomized algorithms have been proposed for computing approximate least-squares (LS) solutions in large-scale settings. A longstanding practical issue is that, for any given input, the user…

Randomized algorithms, such as randomized sketching or stochastic optimization, are a promising approach to ease the computational burden in analyzing large datasets. However, randomized algorithms also produce non-deterministic outputs,…

We reconsider randomized algorithms for the low-rank approximation of symmetric positive semi-definite (SPSD) matrices such as Laplacian and kernel matrices that arise in data analysis and machine learning applications. Our main results…

We propose new approximate alternating projection methods, based on randomized sketching, for the low-rank nonnegative matrix approximation problem: find a low-rank approximation of a nonnegative matrix that is nonnegative, but whose…

We propose algorithms for addressing the bias of the posterior mean when used as an estimator of parameters. These algorithms build upon the recently proposed Bayesian infinitesimal jackknife approximation (Giordano and Broderick (2023))…

In recent years, randomized methods for numerical linear algebra have received growing interest as a general approach to large-scale problems. Typically, the essential ingredient of these methods is some form of randomized dimension…

This paper argues that randomized linear sketching is a natural tool for on-the-fly compression of data matrices that arise from large-scale scientific simulations and data collection. The technical contribution consists in a new algorithm…

We provide computationally attractive methods to obtain jackknife-based cluster-robust variance matrix estimators (CRVEs) for linear regression models estimated by least squares. We also propose several new variants of the wild cluster…

Driven by applications in telecommunication networks, we explore the simulation task of estimating rare event probabilities for tandem queues in their steady state. Existing literature has recognized that importance sampling methods can be…