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Matrix factorization is a key component of collaborative filtering-based recommendation systems because it allows us to complete sparse user-by-item ratings matrices under a low-rank assumption that encodes the belief that similar users…

Machine Learning · Statistics 2016-04-22 Aleksandr Y. Aravkin , Kush R. Varshney , Liu Yang

We here introduce a novel classification approach adopted from the nonlinear model identification framework, which jointly addresses the feature selection and classifier design tasks. The classifier is constructed as a polynomial expansion…

Machine Learning · Computer Science 2016-07-29 Aida Brankovic , Alessandro Falsone , Maria Prandini , Luigi Piroddi

Matrix factorization (MF) is a common method for collaborative filtering. MF represents user preferences and item attributes by latent factors. Despite that MF is a powerful method, it suffers from not be able to identifying strong…

Information Retrieval · Computer Science 2021-05-13 Binh Nguyen , Atsuhiro Takasu

This paper describes a new approach, based on linear programming, for computing nonnegative matrix factorizations (NMFs). The key idea is a data-driven model for the factorization where the most salient features in the data are used to…

Optimization and Control · Mathematics 2013-02-05 Victor Bittorf , Benjamin Recht , Christopher Re , Joel A. Tropp

Collaborative filtering generates recommendations by exploiting user-item similarities based on rating data, which often contains numerous unrated items. To predict scores for unrated items, matrix factorization techniques such as…

Statistical Mechanics · Physics 2025-07-30 Yukino Terui , Yuka Inoue , Yohei Hamakawa , Kosuke Tatsumura , Kazue Kudo

Estimating the diagonal entries of a matrix, that is not directly accessible but only available as a linear operator in the form of a computer routine, is a common necessity in many computational applications, especially in image…

Instrumentation and Methods for Astrophysics · Physics 2015-03-19 Marco Selig , Niels Oppermann , Torsten A. Enßlin

We propose a new approximate factorization for solving linear systems with symmetric positive definite sparse matrices. In a nutshell the algorithm is to apply hierarchically block Gaussian elimination and additionally compress the fill-in.…

Numerical Analysis · Mathematics 2018-05-08 Daria A. Sushnikova , Ivan V. Oseledets

In this paper, we address a new problem of reversing the effect of an image filter, which can be linear or nonlinear. The assumption is that the algorithm of the filter is unknown and the filter is available as a black box. We formulate…

Image and Video Processing · Electrical Eng. & Systems 2021-12-15 Fernando J. Galetto , Guang Deng

Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…

Numerical Analysis · Mathematics 2016-06-07 Victor Y. Pan , Liang Zhao

In the last years, the success of kernel-based regularisation techniques in solving impulse response modelling tasks has revived the interest on linear system identification. In this work, an alternative perspective on the same problem is…

Systems and Control · Computer Science 2016-10-25 Anna Marconato , Maarten Schoukens , Johan Schoukens

We marry ideas from deep neural networks and approximate Bayesian inference to derive a generalised class of deep, directed generative models, endowed with a new algorithm for scalable inference and learning. Our algorithm introduces a…

Machine Learning · Statistics 2014-06-02 Danilo Jimenez Rezende , Shakir Mohamed , Daan Wierstra

We present a matrix factorization algorithm that scales to input matrices that are large in both dimensions (i.e., that contains morethan 1TB of data). The algorithm streams the matrix columns while subsampling them, resulting in low…

Optimization and Control · Mathematics 2016-12-04 Arthur Mensch , Julien Mairal , Gaël Varoquaux , Bertrand Thirion

Recommendation Systems apply Information Retrieval techniques to select the online information relevant to a given user. Collaborative Filtering is currently most widely used approach to build Recommendation System. CF techniques uses the…

Information Retrieval · Computer Science 2015-03-26 Dheeraj kumar Bokde , Sheetal Girase , Debajyoti Mukhopadhyay

The development of randomized algorithms for numerical linear algebra, e.g. for computing approximate QR and SVD factorizations, has recently become an intense area of research. This paper studies one of the most frequently discussed…

Numerical Analysis · Computer Science 2013-08-28 Rafi Witten , Emmanuel Candes

Predictive recursion is an accurate and computationally efficient algorithm for nonparametric estimation of mixing densities in mixture models. In semiparametric mixture models, however, the algorithm fails to account for any uncertainty in…

Methodology · Statistics 2015-03-19 Ryan Martin , Surya T. Tokdar

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…

Disordered Systems and Neural Networks · Physics 2023-08-01 Francesco Camilli , Marc Mézard

Randomized sampling has recently been demonstrated to be an efficient technique for computing approximate low-rank factorizations of matrices for which fast methods for computing matrix vector products are available. This paper describes an…

Numerical Analysis · Mathematics 2008-06-17 Per-Gunnar Martinsson

We consider the problem of estimation of a low-rank matrix from a limited number of noisy rank-one projections. In particular, we propose two fast, non-convex \emph{proper} algorithms for matrix recovery and support them with rigorous…

Machine Learning · Statistics 2017-05-23 Mohammadreza Soltani , Chinmay Hegde

We give a number of explicit matrix-algorithms for analysis/synthesis in multi-phase filtering; i.e., the operation on discrete-time signals which allow a separation into frequency-band components, one for each of the ranges of bands, say…

Functional Analysis · Mathematics 2014-12-10 Palle Jorgensen , Myung-Sin Song

A standard approach to approximate inference in state-space models isto apply a particle filter, e.g., the Condensation Algorithm.However, the performance of particle filters often varies significantlydue to their stochastic nature.We…

Artificial Intelligence · Computer Science 2013-01-14 Dirk Ormoneit , Christiane Lemieux , David J. Fleet