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We continue studying the problem of analytic approximation of matrix functions. We introduce the notion of a partial canonical factorization of a badly approximable matrix function $\Phi$ and the notion of a canonical factorization of a…

Functional Analysis · Mathematics 2007-05-23 R. B. Alexeev , V. V. Peller

This paper focuses on the Matrix Factorization based Clustering (MFC) method which is one of the few closed form algorithms for the subspace clustering problem. Despite being simple, closed-form, and computation-efficient, MFC can…

Machine Learning · Computer Science 2022-01-11 Mostafa Rahmani

We present an approximate algorithm for matrix multiplication based on matrix sketching techniques. First one of the matrix is chosen and sparsified using the online matrix sketching algorithm, and then the matrix product is calculated…

Numerical Analysis · Computer Science 2014-06-12 Huan Wang , Christos Boutsidis , Edo Liberty , Daniel Hsu

We extend the theory of matrix completion to the case where we make Poisson observations for a subset of entries of a low-rank matrix. We consider the (now) usual matrix recovery formulation through maximum likelihood with proper…

Machine Learning · Statistics 2015-03-26 Yang Cao , Yao Xie

We study the problem of computing maximin share guarantees, a recently introduced fairness notion. Given a set of $n$ agents and a set of goods, the maximin share of a single agent is the best that she can guarantee to herself, if she would…

Computer Science and Game Theory · Computer Science 2018-06-12 Georgios Amanatidis , Evangelos Markakis , Afshin Nikzad , Amin Saberi

Dropout is a simple yet effective algorithm for regularizing neural networks by randomly dropping out units through Bernoulli multiplicative noise, and for some restricted problem classes, such as linear or logistic regression, several…

Machine Learning · Computer Science 2017-10-12 Jacopo Cavazza , Connor Lane , Benjamin D. Haeffele , Vittorio Murino , René Vidal

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…

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

With the rapid development of information technology, "information overload" has become the main theme that plagues people's online life. As an effective tool to help users quickly search for useful information, a personalized…

Information Retrieval · Computer Science 2022-06-03 Peiyu Liu , Junping Du , Zhe Xue , Ang Li

The sparse linear regression problem is difficult to handle with usual sparse optimization models when both predictors and measurements are either quantized or represented in low-precision, due to non-convexity. In this paper, we provide a…

Optimization and Control · Mathematics 2019-03-22 Vito Cerone , Sophie M. Fosson , Diego Regruto

This survey describes probabilistic algorithms for linear algebra computations, such as factorizing matrices and solving linear systems. It focuses on techniques that have a proven track record for real-world problem instances. The paper…

Numerical Analysis · Mathematics 2021-03-17 Per-Gunnar Martinsson , Joel Tropp

We analyze a simple randomized subgradient method for approximating solutions to stochastic systems of convex functional constraints, the only input to the algorithm being the size of minibatches. By introducing a new notion of what is…

Optimization and Control · Mathematics 2021-08-30 James Renegar , Song Zhou

Many tasks in data mining and related fields can be formalized as matching between objects in two heterogeneous domains, including collaborative filtering, link prediction, image tagging, and web search. Machine learning techniques,…

Machine Learning · Computer Science 2014-10-24 Jingbo Shang , Tianqi Chen , Hang Li , Zhengdong Lu , Yong Yu

This article introduces new multiplicative updates for nonnegative matrix factorization with the $\beta$-divergence and sparse regularization of one of the two factors (say, the activation matrix). It is well known that the norm of the…

Machine Learning · Computer Science 2024-03-13 Arthur Marmin , José Henrique de Morais Goulart , Cédric Févotte

With the recent success of representation learning methods, which includes deep learning as a special case, there has been considerable interest in developing representation learning techniques that can incorporate known physical…

Machine Learning · Computer Science 2021-09-10 Harsha Vardhan Tetali , Joel B. Harley , Benjamin D. Haeffele

In this paper we study submodular maximization under a matroid constraint in the adaptive complexity model. This model was recently introduced in the context of submodular optimization in [BS18a] to quantify the information theoretic…

Data Structures and Algorithms · Computer Science 2018-11-09 Eric Balkanski , Aviad Rubinstein , Yaron Singer

We study a variant of classical clustering formulations in the context of algorithmic fairness, known as diversity-aware clustering. In this variant we are given a collection of facility subsets, and a solution must contain at least a…

Data Structures and Algorithms · Computer Science 2022-10-25 Suhas Thejaswi , Ameet Gadekar , Bruno Ordozgoiti , Michal Osadnik

The closest vector problem (CVP) is a fundamental optimization problem in lattice-based cryptography and its conjectured hardness underpins the security of lattice-based cryptosystems. Furthermore, Schnorr's lattice-based factoring…

Cryptography and Security · Computer Science 2025-10-23 Max O. Al-Hasso , Marko von der Leyen

We propose a fast greedy algorithm to compute sparse representations of signals from continuous dictionaries that are factorizable, i.e., with atoms that can be separated as a product of sub-atoms. Existing algorithms strongly reduce the…

Signal Processing · Electrical Eng. & Systems 2020-12-01 Gilles Monnoyer de Galland , Luc Vandendorpe , Laurent Jacques

We study the problem of finding a superoptimal solution to the four block problem. Given a bounded block matrix function $\left(\begin{array}{cc}\Phi_{11} &\Phi_{12}\\\Phi_{21}&\Phi_{22}\end{array}\right)$ on the unit circle the four block…

Classical Analysis and ODEs · Mathematics 2008-02-03 Vladimir Peller , Sergei Treil

Techniques of matrix completion aim to impute a large portion of missing entries in a data matrix through a small portion of observed ones. In practice including collaborative filtering, prior information and special structures are usually…

Statistics Theory · Mathematics 2022-03-09 Ji Chen , Xiaodong Li , Zongming Ma