相关论文: Norming Sets for Tensor and Polynomial Sketching

Matrices arising in scientific applications frequently admit linear low-rank approximations due to smoothness in the physical and/or temporal domain of the problem. In large-scale problems, computing an optimal low-rank approximation can be…

In the last decade, tensors have shown their potential as valuable tools for various tasks in numerical linear algebra. While most of the research has been focusing on how to compress a given tensor in order to maintain information as well…

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 sketching algorithms which first compress data by multiplication with a random sketch matrix, and then apply the sketch to quickly solve an optimization problem, e.g., low-rank approximation and regression. In the learning-based…

We propose a new random sketching approach for embedding high-dimensional Hilbert-Schmidt operators, using random input-output pairs. Such operator can then be approximated in a low-dimensional subspace of operators by solving a small…

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…

We first propose the regular sketch-and-project method for solving tensor equations with respect to the popular t-product. Then, three adaptive sampling strategies and three corresponding adaptive sketch-and-project methods are derived. We…

The low-rank canonical polyadic tensor decomposition is useful in data analysis and can be computed by solving a sequence of overdetermined least squares subproblems. Motivated by consideration of sparse tensors, we propose sketching each…

We consider sketching algorithms which first quickly compress data by multiplication with a random sketch matrix, and then apply the sketch to quickly solve an optimization problem, e.g., low rank approximation. In the learning-based…

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 study the problem of residual error estimation for matrix and vector norms using a linear sketch. Such estimates can be used, for example, to quickly assess how useful a more expensive low-rank approximation computation will be. The…

Random sketching is a dimensionality reduction technique that approximately preserves norms and singular values up to some $O(1)$ distortion factor with high probability. The most popular sketches in literature are the Gaussian sketch and…

There is an increasing body of work exploring the integration of random projection into algorithms for numerical linear algebra. The primary motivation is to reduce the overall computational cost of processing large datasets. A suitably…

An outstanding open question posed by Guha and Indyk in 2006 asks to characterize metric spaces in which distances can be estimated using efficient sketches. Specifically, we say that a sketching algorithm is efficient if it achieves…

We describe a general framework -- compressive statistical learning -- for resource-efficient large-scale learning: the training collection is compressed in one pass into a low-dimensional sketch (a vector of random empirical generalized…

Focusing on implicit neural representations, we present a novel in situ training protocol that employs limited memory buffers of full and sketched data samples, where the sketched data are leveraged to prevent catastrophic forgetting. The…

We propose a hierarchical tensor-network approach for approximating high-dimensional probability density via empirical distribution. This leverages randomized singular value decomposition (SVD) techniques and involves solving linear…

In this work we propose a new paradigm for designing efficient deep unrolling networks using operator sketching. The deep unrolling networks are currently the state-of-the-art solutions for imaging inverse problems. However, for…

Learning distributed representations for nodes in graphs is a crucial primitive in network analysis with a wide spectrum of applications. Linear graph embedding methods learn such representations by optimizing the likelihood of both…

We initiate the study of data dimensionality reduction, or sketching, for the $q\to p$ norms. Given an $n \times d$ matrix $A$, the $q\to p$ norm, denoted $\|A\|_{q \to p} = \sup_{x \in \mathbb{R}^d \backslash \vec{0}}…