Related papers: A Statistical Perspective on Randomized Sketching …

The Dirac-Frenkel variational principle is a widely used building block for using nonlinear parametrizations in the context of model reduction and numerically solving partial differential equations; however, it typically leads to…

Linear sketching and recovery of sparse vectors with randomly constructed sparse matrices has numerous applications in several areas, including compressive sensing, data stream computing, graph sketching, and combinatorial group testing.…

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…

The sliding window model of computation captures scenarios in which data are continually arriving in the form of a stream, and only the most recent $w$ items are used for analysis. In this setting, an algorithm needs to accurately track…

We consider least-squares problems with quadratic regularization and propose novel sketching-based iterative methods with an adaptive sketch size. The sketch size can be as small as the effective dimension of the data matrix to guarantee…

Stream monitoring is fundamental in many data stream applications, such as financial data trackers, security, anomaly detection, and load balancing. In that respect, quantiles are of particular interest, as they often capture the user's…

We develop and analyze stochastic optimization algorithms for problems in which the expected loss is strongly convex, and the optimum is (approximately) sparse. Previous approaches are able to exploit only one of these two structures,…

In recent years, randomized algorithms have established themselves as fundamental tools in computational linear algebra, with applications in scientific computing, machine learning, and quantum information science. Many randomized matrix…

The Count-Min sketch is an important and well-studied data summarization method. It allows one to estimate the count of any item in a stream using a small, fixed size data sketch. However, the accuracy of the sketch depends on…

Sketching is one of the most fundamental tools in large-scale machine learning. It enables runtime and memory saving via randomly compressing the original large problem into lower dimensions. In this paper, we propose a novel sketching…

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…

Among randomized numerical linear algebra strategies, so-called sketching procedures are emerging as effective reduction means to accelerate the computation of Krylov subspace methods for, e.g., the solution of linear systems, eigenvalue…

Large, distributed data streams are now ubiquitous. High-accuracy sketches with low memory overhead have become the de facto method for analyzing this data. For instance, if we wish to group data by some label and report the largest counts…

It is often desirable to reduce the dimensionality of a large dataset by projecting it onto a low-dimensional subspace. Matrix sketching has emerged as a powerful technique for performing such dimensionality reduction very efficiently. Even…

Detecting emergence of a low-rank signal from high-dimensional data is an important problem arising from many applications such as camera surveillance and swarm monitoring using sensors. We consider a procedure based on the largest…

Matrices with low-rank structure are ubiquitous in scientific computing. Choosing an appropriate rank is a key step in many computational algorithms that exploit low-rank structure. However, estimating the rank has been done largely in an…

Compressive learning is an approach to efficient large scale learning based on sketching an entire dataset to a single mean embedding (the sketch), i.e. a vector of generalized moments. The learning task is then approximately solved as an…

This paper explores and analyzes two randomized designs for robust Principal Component Analysis (PCA) employing low-dimensional data sketching. In one design, a data sketch is constructed using random column sampling followed by low…

This article considers stochastic algorithms for efficiently solving a class of large scale non-linear least squares (NLS) problems which frequently arise in applications. We propose eight variants of a practical randomized algorithm where…

Matrix sketching is aimed at finding close approximations of a matrix by factors of much smaller dimensions, which has important applications in optimization and machine learning. Given a matrix A of size m by n, state-of-the-art randomized…