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Related papers: Butterfly factorization with error guarantees

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We consider the matrix completion problem where the aim is to esti-mate a large data matrix for which only a relatively small random subset of its entries is observed. Quite popular approaches to matrix completion problem are iterative…

Statistics Theory · Mathematics 2015-02-03 Olga Klopp

Parker and L\^e introduced random butterfly transforms (RBTs) as a preprocessing technique to replace pivoting in dense LU factorization. Unfortunately, their FFT-like recursive structure restricts the dimensions of the matrix. Furthermore,…

Numerical Analysis · Mathematics 2024-10-14 Neil Lindquist , Piotr Luszczek , Jack Dongarra

In this paper, a method via sparse-sparse iteration for computing a sparse incomplete factorization of the inverse of a symmetric positive definite matrix is proposed. The resulting factorized sparse approximate inverse is used as a…

Numerical Analysis · Mathematics 2008-08-03 Davod Khojasteh Salkuyeh , Faezeh Toutounian

Branes and defects in topological Landau-Ginzburg models are described by matrix factorisations. We revisit the problem of deforming them and discuss various deformation methods as well as their relations. We have implemented these…

High Energy Physics - Theory · Physics 2012-06-28 Nils Carqueville , Laura Dowdy , Andreas Recknagel

The behavior of many Bayesian models used in machine learning critically depends on the choice of prior distributions, controlled by some hyperparameters that are typically selected by Bayesian optimization or cross-validation. This…

Machine Learning · Statistics 2023-10-09 Eliezer de Souza da Silva , Tomasz Kuśmierczyk , Marcelo Hartmann , Arto Klami

Matrix Factorization (MF) on large scale matrices is computationally as well as memory intensive task. Alternative convergence techniques are needed when the size of the input matrix is higher than the available memory on a Central…

Machine Learning · Computer Science 2019-01-21 Prasad G Bhavana , Vineet C Nair

Incomplete factorizations have long been popular general-purpose algebraic preconditioners for solving large sparse linear systems of equations. Guaranteeing the factorization is breakdown free while computing a high quality preconditioner…

Numerical Analysis · Mathematics 2025-02-04 Jennifer Scott , Miroslav Tůma

We present a matrix-factorization algorithm that scales to input matrices with both huge number of rows and columns. Learned factors may be sparse or dense and/or non-negative, which makes our algorithm suitable for dictionary learning,…

Machine Learning · Statistics 2017-11-15 Arthur Mensch , Julien Mairal , Bertrand Thirion , Gael Varoquaux

The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…

Signal Processing · Electrical Eng. & Systems 2023-07-19 Xiao Fu , Nico Vervliet , Lieven De Lathauwer , Kejun Huang , Nicolas Gillis

Nonnegative matrix factorization (NMF), which is the approximation of a data matrix as the product of two nonnegative matrices, is a key issue in machine learning and data analysis. One approach to NMF is to formulate the problem as a…

Optimization and Control · Mathematics 2016-11-02 Hideaki Iiduka , Shizuka Nishino

Factorization machines (FMs) are a powerful tool for regression and classification in the context of sparse observations, that has been successfully applied to collaborative filtering, especially when side information over users or items is…

Machine Learning · Computer Science 2022-12-21 Jill-Jênn Vie , Tomas Rigaux , Hisashi Kashima

We provide a randomized linear time approximation scheme for a generic problem about clustering of binary vectors subject to additional constrains. The new constrained clustering problem encompasses a number of problems and by solving it,…

Data Structures and Algorithms · Computer Science 2018-07-20 Fedor V. Fomin , Petr A. Golovach , Daniel Lokshtanov , Fahad Panolan , Saket Saurabh

In the dictionary learning (or sparse coding) problem, we are given a collection of signals (vectors in $\mathbb{R}^d$), and the goal is to find a "basis" in which the signals have a sparse (approximate) representation. The problem has…

Machine Learning · Computer Science 2019-05-30 Aditya Bhaskara , Wai Ming Tai

Approximate computing is an emerging paradigm where design accuracy can be traded off for benefits in design metrics such as design area, power consumption or circuit complexity. In this work, we present a novel paradigm to synthesize…

Hardware Architecture · Computer Science 2018-05-17 Soheil Hashemi , Hokchhay Tann , Sherief Reda

Matrix factorization is an important mathematical problem encountered in the context of dictionary learning, recommendation systems and machine learning. We introduce a new `decimation' scheme that maps it to neural network models of…

Disordered Systems and Neural Networks · Physics 2023-07-12 Francesco Camilli , Marc Mézard

In this paper we consider a generalization of the well-known budgeted maximum coverage problem. We are given a ground set of elements and a set of bins. The goal is to find a subset of elements along with an associated set of bins, such…

Data Structures and Algorithms · Computer Science 2018-08-10 Francesco Cellinese , Gianlorenzo D'Angelo , Gianpiero Monaco , Yllka Velaj

Sparse regularization techniques are well-established in machine learning, yet their application in neural networks remains challenging due to the non-differentiability of penalties like the $L_1$ norm, which is incompatible with stochastic…

Machine Learning · Computer Science 2025-02-10 Chris Kolb , Tobias Weber , Bernd Bischl , David Rügamer

A symmetric nonnegative matrix factorization algorithm based on self-paced learning was proposed to improve the clustering performance of the model. It could make the model better distinguish normal samples from abnormal samples in an…

Machine Learning · Computer Science 2024-10-22 Lei Wang , Liang Du , Peng Zhou , Peng Wu

The problem of portfolio allocation in the context of stocks evolving in random environments, that is with volatility and returns depending on random factors, has attracted a lot of attention. The problem of maximizing a power utility at a…

Mathematical Finance · Quantitative Finance 2022-11-29 Maxim Bichuch , Jean-Pierre Fouque

We present a new approach to RSA factorization inspired by geometric interpretations and square differences. This method reformulates the problem in terms of the distance between perfect squares and provides a recurrence relation that…

Cryptography and Security · Computer Science 2025-06-24 Akihisa Yorozu