Related papers: Factorization-in-Loop: Proximal Fill-in Minimizati…

LU and Cholesky matrix factorization algorithms are core subroutines used to solve systems of linear equations (SLEs) encountered while solving an optimization problem. Standard factorization algorithms are highly efficient but remain…

Sequence models such as transformers require inputs to be represented as one-dimensional sequences. In vision, this typically involves flattening images using a fixed row-major (raster-scan) order. While full self-attention is…

Recovering low-rank and sparse matrices from incomplete or corrupted observations is an important problem in machine learning, statistics, bioinformatics, computer vision, as well as signal and image processing. In theory, this problem can…

Gradient descent optimizations and backpropagation are the most common methods for training neural networks, but they are computationally expensive for real time applications, need high memory resources, and are difficult to converge for…

Nonnegative matrix factorization arises widely in machine learning and data analysis. In this paper, for a given factorization of rank r, we consider the sparse stochastic matrix factorization (SSMF) of decomposing a prescribed m-by-n…

Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized…

Matrix factorization (MF) is a widely used collaborative filtering (CF) algorithm for recommendation systems (RSs), due to its high prediction accuracy, great flexibility and high efficiency in big data processing. However, with the…

Nonnegative Matrix Factorization consists in (approximately) factorizing a nonnegative data matrix by the product of two low-rank nonnegative matrices. It has been successfully applied as a data analysis technique in numerous domains, e.g.,…

We propose a method that meta-learns a knowledge on matrix factorization from various matrices, and uses the knowledge for factorizing unseen matrices. The proposed method uses a neural network that takes a matrix as input, and generates…

Nowadays, the availability of large-scale data in disparate application domains urges the deployment of sophisticated tools for extracting valuable knowledge out of this huge bulk of information. In that vein, low-rank representations…

Low-rank matrix approximation is a fundamental tool in data analysis for processing large datasets, reducing noise, and finding important signals. In this work, we present a novel truncated LU factorization called Spectrum-Revealing LU…

We investigate the problem of factorizing a matrix into several sparse matrices and propose an algorithm for this under randomness and sparsity assumptions. This problem can be viewed as a simplification of the deep learning problem where…

Motivated by applications in single-cell biology and metagenomics, we investigate the problem of matrix reordering based on a noisy disordered monotone Toeplitz matrix model. We establish the fundamental statistical limit for this problem…

Matrix factorization is an inference problem that has acquired importance due to its vast range of applications that go from dictionary learning to recommendation systems and machine learning with deep networks. The study of its fundamental…

LU-factorization of matrices is one of the fundamental algorithms of linear algebra. The widespread use of supercomputers with distributed memory requires a review of traditional algorithms, which were based on the common memory of a…

This article proposes a sparse computation-based method for optimizing neural networks for reinforcement learning (RL) tasks. This method combines two ideas: neural network pruning and taking into account input data correlations; it makes…

Matrix factorization exploits the idea that, in complex high-dimensional data, the actual signal typically lies in lower-dimensional structures. These lower dimensional objects provide useful insight, with interpretability favored by sparse…

Matrix factorization is a popular approach to solving matrix estimation problems based on partial observations. Existing matrix factorization is based on least squares and aims to yield a low-rank matrix to interpret the conditional sample…

Given a limited number of entries from the superposition of a low-rank matrix plus the product of a known fat compression matrix times a sparse matrix, recovery of the low-rank and sparse components is a fundamental task subsuming…

Predicting unobserved entries of a partially observed matrix has found wide applicability in several areas, such as recommender systems, computational biology, and computer vision. Many scalable methods with rigorous theoretical guarantees…