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On the minimax risk of dictionary learning

WebIn particular, we analyze the minimax risk of the dictionary learning problem which governs the mean squared error (MSE) performance of any learning scheme, regardless of its computational complexity. WebThis paper identifies minimax rates of CSDL in terms of reconstruction risk, providing both lower and upper bounds in a variety of settings. Our results make minimal assumptions, …

Sample complexity bounds for dictionary learning of tensor data

WebDictionary learning is the problem of estimating the collection of atomic elements that provide a sparse representation of measured/collected signals or data. This paper finds fundamental limits on the sample complexity of estimating dictionaries for tensor data by proving a lower bound on the minimax risk. Web15 de jul. de 2016 · The focus of this paper is on second-order tensor data, with the underlying dictionaries constructed by taking the Kronecker product of two smaller … cite young goodman brown https://ryangriffithmusic.com

On the Minimax Risk of Dictionary Learning - IEEE Journals

Web20 de jul. de 2015 · On the Minimax Risk of Dictionary Learning arXiv Authors: Alexander Jung Aalto University Yonina Eldar Weizmann Institute of Science Norbert Görtz Abstract … WebIt is assumed the data are generated by linear combinations of these structured dictionary atoms and observed through white Gaussian noise. This work first provides a general lower bound on the minimax risk of dictionary learning for such tensor data and then adapts the proof techniques for specialized results in the case of sparse and sparse-Gaussian … WebWe consider the problem of dictionary learning under the assumption that the observed signals can be represented as sparse linear combinations of the columns of a single … cite yourself apa 7

On the Minimax Risk of Dictionary Learning - IEEE Journals

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On the minimax risk of dictionary learning

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WebCORE is not-for-profit service delivered by the Open University and Jisc. Web8 de fev. de 2024 · Jung, A., Eldar, Y. C., & Görtz, N. (2016). On the Minimax Risk of Dictionary Learning. IEEE Transactions on Information Theory, 62, 62

On the minimax risk of dictionary learning

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Web: (7) A. Minimax risk analysis We are interested in lower bounding the minimax risk for estimating D based on observations Y, which is defined as the worst-case mean squared error (MSE) that can be obtained by the best KS dictionary estimator Db(Y). That is, " = inf Db sup 2X(0;r) E Y n Db(Y) D 2 F WebWe consider the problem of learning a dictionary matrix from a number of observed signals, which are assumed to be generated via a linear model with a common... Skip to …

http://www.inspirelab.us/wp-content/uploads/2024/07/ShakeriSarwateEtAl.BookChInfoTh21-Preprint.pdf Web1 de abr. de 2024 · This work first provides a general lower bound on the minimax risk of dictionary learning for such tensor data and then adapts the proof techniques for specialized results in the case of sparse and sparse-Gaussian linear combinations.

http://spars2024.lx.it.pt/index_files/papers/SPARS2024_Paper_10.pdf WebMinimax lower bounds for Kronecker-structured dictionary learning. Authors: Zahra Shakeri. Dept. of Electrical and Computer Engineering, Rutgers University, Piscataway, New Jersey 08854, United States ...

Web9 de ago. de 2016 · This work first provides a general lower bound on the minimax risk of dictionary learning for such tensor data and then adapts the proof techniques for …

WebDictionary learning is the problem of estimating the collection of atomic elements that provide a sparse representation of measured/collected signals or data. This paper finds fundamental limits on the sample complexity of estimating dictionaries for tensor data by proving a lower bound on the minimax risk. This lower bound depends on the … cite your sources properly in researchWebThis paper identifies minimax rates of CSDL in terms of reconstruction risk, providing both lower and upper bounds in a variety of settings, and makes minimal assumptions, … cite yourself mlaWeb17 de fev. de 2014 · By following an established information-theoretic method based on Fanos inequality, we derive a lower bound on the minimax risk for a given dictionary learning problem. This lower bound yields a characterization of the sample-complexity, i.e., a lower bound on the required number of observations such that consistent dictionary … cite youtube apa formatWebWe consider the problem of learning a dictionary matrix from a number of observed signals, which are assumed to be generated via a linear model with a common ... diane stackhouseWeb29 de ago. de 2024 · On the Minimax Risk of Dictionary Learning Article Full-text available Jul 2015 IEEE T INFORM THEORY Alexander Jung Yonina Eldar Norbert Goertz We consider the problem of learning a... dianes steakhouseWebKS dictionary. The risk decreases with larger Nand K; in particular, larger Kfor fixed mpmeans more structure, which simplifies the estimation problem. The results for … citezenship in education ukWebWe consider the problem of learning a dictionary matrix from a number of observed signals, which are assumed to be generated via a linear model with a common underlying … diane stackhouse cambridge narrows