Related papers: Matrix Product Sketching via Coordinated Sampling
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…
Motivated by the study of matrix elimination orderings in combinatorial scientific computing, we utilize graph sketching and local sampling to give a data structure that provides access to approximate fill degrees of a matrix undergoing…
We consider the $\textit{Similarity Sketching}$ problem: Given a universe $[u] = \{0,\ldots, u-1\}$ we want a random function $S$ mapping subsets $A\subseteq [u]$ into vectors $S(A)$ of size $t$, such that the Jaccard similarity $J(A,B) =…
Linear algebraic operations are ubiquitous in engineering applications, and arise often in a variety of fields including statistical signal processing and machine learning. With contemporary large datasets, to perform linear algebraic…
Sketching is widely used in randomized linear algebra for low-rank matrix approximation, column subset selection, and many other problems, and it has gained significant traction in machine learning applications. However, sketching large…
We consider sketched approximate matrix multiplication and ridge regression in the novel setting of localized sketching, where at any given point, only part of the data matrix is available. This corresponds to a block diagonal structure on…
Bayesian computation of high dimensional linear regression models with a popular Gaussian scale mixture prior distribution using Markov Chain Monte Carlo (MCMC) or its variants can be extremely slow or completely prohibitive due to the…
Random projections or sketching are widely used in many algorithmic and learning contexts. Here we study the performance of iterative Hessian sketch for least-squares problems. By leveraging and extending recent results from random matrix…
With appropriately chosen sampling probabilities, sampling-based random projection can be used to implement large-scale statistical methods, substantially reducing computational cost while maintaining low statistical error. However,…
In this paper, we investigate effective sketching schemes via sparsification for high dimensional multilinear arrays or tensors. More specifically, we propose a novel tensor sparsification algorithm that retains a subset of the entries of a…
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…
Despite being a key bottleneck in many machine learning tasks, the cost of solving large linear systems has proven challenging to quantify due to problem-dependent quantities such as condition numbers. To tackle this, we consider a…
For an overdetermined system $\mathsf{A}\mathsf{x} \approx \mathsf{b}$ with $\mathsf{A}$ and $\mathsf{b}$ given, the least-square (LS) formulation $\min_x \, \|\mathsf{A}\mathsf{x}-\mathsf{b}\|_2$ is often used to find an acceptable…
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…
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…
In the subspace sketch problem one is given an $n\times d$ matrix $A$ with $O(\log(nd))$ bit entries, and would like to compress it in an arbitrary way to build a small space data structure $Q_p$, so that for any given $x \in \mathbb{R}^d$,…
Many real-world matrix datasets arrive as high-throughput vector streams, making it impractical to store or process them in their entirety. To enable real-time analytics under limited computational, memory, and communication resources,…
Randomized linear system solvers have become popular as they have the potential to reduce floating point complexity while still achieving desirable convergence rates. One particularly promising class of methods, random sketching solvers,…
Generalized matrix approximation plays a fundamental role in many machine learning problems, such as CUR decomposition, kernel approximation, and matrix low rank approximation. Especially with today's applications involved in larger and…
A substantial body of work in machine learning (ML) and randomized numerical linear algebra (RandNLA) has exploited various sorts of random sketching methodologies, including random sampling and random projection, with much of the analysis…