Related papers: Recursive Importance Sketching for Rank Constraine…

Convolutional neural networks (CNNs) have succeeded in many practical applications. However, their high computation and storage requirements often make them difficult to deploy on resource-constrained devices. In order to tackle this issue,…

Count-sketch is a popular matrix sketching algorithm that can produce a sketch of an input data matrix X in O(nnz(X))time where nnz(X) denotes the number of non-zero entries in X. The sketched matrix will be much smaller than X while…

Sketched gradient algorithms have been recently introduced for efficiently solving the large-scale constrained Least-squares regressions. In this paper we provide novel convergence analysis for the basic method {\it Gradient Projection…

Sketching-based preconditioners have been shown to accelerate the solution of dense least-squares problems with coefficient matrices having substantially more rows than columns. The cost of generating these preconditioners can be reduced by…

Given a persistence diagram with $n$ points, we give an algorithm that produces a sequence of $n$ persistence diagrams converging in bottleneck distance to the input diagram, the $i$th of which has $i$ distinct (weighted) points and is a…

Randomized sketching accelerates large-scale numerical linear algebra by reducing computational complexity. While the traditional sketch-and-solve approach reduces the problem size directly through sketching, the sketch-and-precondition…

We consider distributed optimization methods for problems where forming the Hessian is computationally challenging and communication is a significant bottleneck. We leverage randomized sketches for reducing the problem dimensions as well as…

Probabilistic ideas and tools have recently begun to permeate into several fields where they had traditionally not played a major role, including fields such as numerical linear algebra and optimization. One of the key ways in which these…

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…

This work considers the problem of learning the Markov parameters of a linear system from observed data. Recent non-asymptotic system identification results have characterized the sample complexity of this problem in the single and…

Learning-based low rank approximation algorithms can significantly improve the performance of randomized low rank approximation with sketch matrix. With the learned value and fixed non-zero positions for sketch matrices from learning-based…

The computation of accurate low-rank matrix approximations is central to improving the scalability of various techniques in machine learning, uncertainty quantification, and control. Traditionally, low-rank approximations are constructed…

This paper studies how to sketch element-wise functions of low-rank matrices. Formally, given low-rank matrix A = [Aij] and scalar non-linear function f, we aim for finding an approximated low-rank representation of the (possibly high-rank)…

Many relevant machine learning and scientific computing tasks involve high-dimensional linear operators accessible only via costly matrix-vector products. In this context, recent advances in sketched methods have enabled the construction of…

In this paper, we propose a novel approach to the rank minimization problem, termed rank residual constraint (RRC) model. Different from existing low-rank based approaches, such as the well-known nuclear norm minimization (NNM) and the…

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…

First-order optimizers are reliable but slow in sharp, anisotropic regions. We study a curvature-adaptive method that periodically sketches a low-rank Hessian subspace via Hessian--vector products and preconditions gradients only in that…

Pairwise alignment of DNA sequencing data is a ubiquitous task in bioinformatics and typically represents a heavy computational burden. A standard approach to speed up this task is to compute "sketches" of the DNA reads (typically via…

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 introduce a "learning-based" algorithm for the low-rank decomposition problem: given an $n \times d$ matrix $A$, and a parameter $k$, compute a rank-$k$ matrix $A'$ that minimizes the approximation loss $\|A-A'\|_F$. The algorithm uses a…