English
Related papers

Related papers: Matrix Approximation under Local Low-Rank Assumpti…

200 papers

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…

Numerical Analysis · Mathematics 2023-04-25 Sergey A. Matveev , Stanislav Budzinskiy

Reinforcement learning has gained wide popularity as a technique for simulation-driven approximate dynamic programming. A less known aspect is that the very reasons that make it effective in dynamic programming can also be leveraged for…

Machine Learning · Computer Science 2013-11-13 Vivek S. Borkar , Adwaitvedant S. Mathkar

We study the problem of learning a partially observed matrix under the low rank assumption in the presence of fully observed side information that depends linearly on the true underlying matrix. This problem consists of an important…

Machine Learning · Statistics 2026-02-05 Dimitris Bertsimas , Nicholas A. G. Johnson

We consider supervised learning problems within the positive-definite kernel framework, such as kernel ridge regression, kernel logistic regression or the support vector machine. With kernels leading to infinite-dimensional feature spaces,…

Machine Learning · Computer Science 2013-05-23 Francis Bach

Low-rank modeling has many important applications in computer vision and machine learning. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better empirical…

Machine Learning · Computer Science 2018-07-25 Quanming Yao , James T. Kwok , Taifeng Wang , Tie-Yan Liu

Low-rank approximation and column subset selection are two fundamental and related problems that are applied across a wealth of machine learning applications. In this paper, we study the question of socially fair low-rank approximation and…

Machine Learning · Computer Science 2024-12-10 Zhao Song , Ali Vakilian , David P. Woodruff , Samson Zhou

This paper, broadly speaking, covers the use of randomness in two main areas: low-rank approximation and kernel methods. Low-rank approximation is very important in numerical linear algebra. Many applications depend on matrix decomposition…

Numerical Analysis · Mathematics 2020-08-12 Rishi Advani , Madison Crim , Sean O'Hagan

Low-rank tensor approximation techniques attempt to mitigate the overwhelming complexity of linear algebra tasks arising from high-dimensional applications. In this work, we study the low-rank approximability of solutions to linear systems…

Numerical Analysis · Mathematics 2016-01-08 Daniel Kressner , André Uschmajew

Low-rank modeling plays a pivotal role in signal processing and machine learning, with applications ranging from collaborative filtering, video surveillance, medical imaging, to dimensionality reduction and adaptive filtering. Many modern…

Machine Learning · Statistics 2018-05-04 Yudong Chen , Yuejie Chi

We provide new approximation guarantees for greedy low rank matrix estimation under standard assumptions of restricted strong convexity and smoothness. Our novel analysis also uncovers previously unknown connections between the low rank…

Machine Learning · Statistics 2017-03-09 Rajiv Khanna , Ethan Elenberg , Alexandros G. Dimakis , Sahand Negahban

We study three fundamental problems of Linear Algebra, lying in the heart of various Machine Learning applications, namely: 1)"Low-rank Column-based Matrix Approximation". We are given a matrix A and a target rank k. The goal is to select a…

Data Structures and Algorithms · Computer Science 2011-05-05 Christos Boutsidis

Subspace inference for neural networks assumes that a subspace of their parameter space suffices to produce a reliable uncertainty quantification. In this work, we underpin the validity of this assumption by using low rank techniques. We…

Machine Learning · Computer Science 2026-04-13 Josua Faller , Jörg Martin

We propose a new technique for constructing low-rank approximations of matrices that arise in kernel methods for machine learning. Our approach pairs a novel automatically constructed analytic expansion of the underlying kernel function…

Machine Learning · Computer Science 2022-02-09 John Paul Ryan , Anil Damle

Matrix factorization is a popular approach for large-scale matrix completion. The optimization formulation based on matrix factorization can be solved very efficiently by standard algorithms in practice. However, due to the non-convexity…

Machine Learning · Computer Science 2016-11-18 Ruoyu Sun , Zhi-Quan Luo

In the construction of low-rank matrix approximation and maximum element search it is effective to use maxvol algorithm. Nevertheless, even in the case of rank 1 approximation the algorithm does not always converge to the maximum matrix…

Numerical Analysis · Mathematics 2023-09-04 Alexander Osinsky

Random sampling has become a critical tool in solving massive matrix problems. For linear regression, a small, manageable set of data rows can be randomly selected to approximate a tall, skinny data matrix, improving processing time…

Data Structures and Algorithms · Computer Science 2014-08-22 Michael B. Cohen , Yin Tat Lee , Cameron Musco , Christopher Musco , Richard Peng , Aaron Sidford

Matrix factorization is a widely adopted recommender system technique that fits scalar rating values by dot products of user feature vectors and item feature vectors. However, the formulation of matrix factorization as a scalar fitting…

Information Retrieval · Computer Science 2021-12-07 Hao Wang

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…

Numerical Analysis · Computer Science 2016-09-09 Haishan Ye , Qiaoming Ye , Zhihua Zhang

CUR and low-rank approximations are among most fundamental subjects of numerical linear algebra, with a wide range of applications to a variety of highly important areas of modern computing, which range from the machine learning theory and…

Numerical Analysis · Mathematics 2016-12-20 Victor Y. Pan

Low-rank Matrix Completion (LRMC) describes the problem where we wish to recover missing entries of partially observed low-rank matrix. Most existing matrix completion work deals with sampling procedures that are independent of the…

Machine Learning · Computer Science 2025-04-15 Rishhabh Naik , Nisarg Trivedi , Davoud Ataee Tarzanagh , Laura Balzano