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A randomized algorithm for computing a compressed representation of a given rank-structured matrix $A \in \mathbb{R}^{N\times N}$ is presented. The algorithm interacts with $A$ only through its action on vectors. Specifically, it draws two…

Numerical Analysis · Mathematics 2024-06-25 James Levitt , Per-Gunnar Martinsson

We study ranked enumeration of join-query results according to very general orders defined by selective dioids. Our main contribution is a framework for ranked enumeration over a class of dynamic programming problems that generalizes…

Databases · Computer Science 2020-09-15 Nikolaos Tziavelis , Deepak Ajwani , Wolfgang Gatterbauer , Mirek Riedewald , Xiaofeng Yang

In this paper, we study the problem of matrix recovery, which aims to restore a target matrix of authentic samples from grossly corrupted observations. Most of the existing methods, such as the well-known Robust Principal Component Analysis…

Computer Vision and Pattern Recognition · Computer Science 2018-11-12 Xingyu Xie , Jianlong Wu , Guangcan Liu , Jun Wang

An effective technique for solving optimization problems over massive data sets is to partition the data into smaller pieces, solve the problem on each piece and compute a representative solution from it, and finally obtain a solution…

Data Structures and Algorithms · Computer Science 2015-06-23 Vahab Mirrokni , Morteza Zadimoghaddam

In this paper, we consider the challenge of reconstructing jointly sparse vectors from linear measurements. Firstly, we show that by utilizing the rank of the output data matrix we can reduce the problem to a full column rank case. This…

Numerical Analysis · Mathematics 2019-05-28 Armenak Petrosyan , Hoang Tran , Clayton Webster

We investigate the problem of heterogeneous task assignment in crowdsourcing markets from the point of view of the requester, who has a collection of tasks. Workers arrive online one by one, and each declare a set of feasible tasks they can…

Data Structures and Algorithms · Computer Science 2015-08-17 Sepehr Assadi , Justin Hsu , Shahin Jabbari

This paper is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a low-rank component and a sparse component. Can we recover each component individually? We prove that under some suitable assumptions,…

Information Theory · Computer Science 2009-12-21 Emmanuel J. Candes , Xiaodong Li , Yi Ma , John Wright

As graph data becomes more ubiquitous, the need for robust inferential graph algorithms to operate in these complex data domains is crucial. In many cases of interest, inference is further complicated by the presence of adversarial data…

Machine Learning · Statistics 2022-08-23 Sheyda Peyman , Minh Tang , Vince Lyzinski

In this paper, we study streaming and online algorithms in the context of randomness in the input. For several problems, a random order of the input sequence---as opposed to the worst-case order---appears to be a necessary evil in order to…

Data Structures and Algorithms · Computer Science 2020-04-28 Paritosh Garg , Sagar Kale , Lars Rohwedder , Ola Svensson

In the matroid buyback problem, an algorithm observes a sequence of bids and must decide whether to accept each bid at the moment it arrives, subject to a matroid constraint on the set of accepted bids. Decisions to reject bids are…

Computer Science and Game Theory · Computer Science 2009-11-30 Ashwinkumar B. V. , Robert Kleinberg

We consider the $M$-ary classification problem via crowdsourcing, where crowd workers respond to simple binary questions and the answers are aggregated via decision fusion. The workers have a reject option to skip answering a question when…

Human-Computer Interaction · Computer Science 2020-08-26 Baocheng Geng , Qunwei Li , Pramod K. Varshney

Motivated by the philosophy and phenomenal success of compressed sensing, the problem of reconstructing a matrix from a sampling of its entries has attracted much attention recently. Such a problem can be viewed as an information-theoretic…

Information Theory · Computer Science 2009-05-15 Zhisu Zhu , Anthony Man-Cho So , Yinyu Ye

This paper is concerned with the problem of recovering an unknown matrix from a small fraction of its entries. This is known as the matrix completion problem, and comes up in a great number of applications, including the famous Netflix…

Information Theory · Computer Science 2009-03-10 Emmanuel J. Candes , Terence Tao

Harnessing human computation for solving complex problems call spawns the issue of finding the unknown competitive group of solvers. In this paper, we propose an approach called Friendlysourcing to build up teams from social network…

Social and Information Networks · Computer Science 2013-05-30 Iheb Ben Amor , Athman Bougetteya , Mourad Ouziri , Salima Benbernou , Mohamed Nadif

We study low rank matrix and tensor completion and propose novel algorithms that employ adaptive sampling schemes to obtain strong performance guarantees. Our algorithms exploit adaptivity to identify entries that are highly informative for…

Machine Learning · Statistics 2013-11-12 Akshay Krishnamurthy , Aarti Singh

In this paper, we study the problem of image recovery from given partial (corrupted) observations. Recovering an image using a low-rank model has been an active research area in data analysis and machine learning. But often, images are not…

Computer Vision and Pattern Recognition · Computer Science 2020-03-13 Pawan Goyal , Hussam Al Daas , Peter Benner

We consider the classic problem of establishing a statistical ranking of a set of n items given a set of inconsistent and incomplete pairwise comparisons between such items. Instantiations of this problem occur in numerous applications in…

Machine Learning · Computer Science 2015-04-07 Mihai Cucuringu

In this work, we propose a robust framework that employs adversarially robust training to safeguard the ML models against perturbed testing data. Our contributions can be seen from both computational and statistical perspectives. Firstly,…

Machine Learning · Computer Science 2024-11-26 Deepak Maurya , Adarsh Barik , Jean Honorio

Alternating Minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems. Theoretical guarantees for Alternating Minimization have been hard to come by and are still…

Machine Learning · Computer Science 2014-05-15 Moritz Hardt

Matrix recovery is the problem of recovering a low-rank matrix from a few linear measurements. Recently, this problem has gained a lot of attention as it is employed in many applications such as Netflix prize problem, seismic data…

Information Theory · Computer Science 2019-07-30 Hamideh. S Fazael Ardakani , Sajad Daei , Farzan Haddadi
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