On the minimax risk of dictionary learning

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August undefined, 2024

Web1 de mar. de 2024 · This paper provides fundamental limits on the sample complexity of estimating dictionaries for tensor data. The specific focus of this work is on $K$th-order tensor data and the case where the... 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 …

Minimax lower bounds for Kronecker-structured dictionary learning ...

WebKS dictionary. The risk decreases with larger Nand K; in particular, larger Kfor ﬁxed mpmeans more structure, which simpliﬁes the estimation problem. The results for … Web9 de mar. de 2024 · The lower bound follows from a lower bound on the minimax risk for general coefficient distributions and can be further specialized to sparse-Gaussian coefficients. This bound scales linearly with the sum of the product of the dimensions of the (smaller) coordinate dictionaries for tensor data. easikey 99

Minimax Lower Bounds on Dictionary Learning for Tensor Data

Web22 de mar. de 2024 · A new algorithm for dictionary learning based on tensor factorization using a TUCKER model, in which sparseness constraints are applied to the core tensor, of which the n-mode factors are learned from the input data in an alternate minimization manner using gradient descent. Expand 72 PDF View 1 excerpt, references methods Web17 de fev. de 2014 · Prior theoretical studies of dictionary learning have either focused on existing algorithms for non-KS dictionaries [5,[16][17][18][19][20][21] or lower bounds on … Web17 de mai. de 2016 · In this regard, the paper provides a general lower bound on the minimax risk and also adapts the proof techniques for equivalent results using sparse and Gaussian coefficient models. The reported results suggest that the sample complexity of dictionary learning for tensor data can be significantly lower than that for unstructured … easiject needles

[1507.05498] On the Minimax Risk of Dictionary Learning

IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 62, NO. 3, …

WebIndex Terms—Compressed sensing, dictionary learning, minimax risk, Fano inequality. I. INTRODUCTION A CCORDING to [1], the worldwide internet trafﬁc in 2016 will exceed the Zettabyte threshold.1 In view of the pervasive massive datasets generated at an ever increasing speed [2], [3], it is mandatory to be able to extract relevant WebCORE is not-for-profit service delivered by the Open University and Jisc. easii softwareWebThis 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, … ctyap

"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 comm. Skip to Main Content. IEEE.org; IEEE Xplore Digital Library; IEEE-SA; IEEE ... On the Minimax Risk of Dictionary Learning " - On the minimax risk of dictionary learning

On the minimax risk of dictionary learning

Sample complexity bounds for dictionary learning of tensor data

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 … WebBibliographic details on On the Minimax Risk of Dictionary Learning. DOI: — access: open type: Informal or Other Publication metadata version: 2024-08-13

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Web15 de jul. de 2016 · Minimax lower bounds for Kronecker-structured dictionary learning Abstract: Dictionary learning is the problem of estimating the collection of atomic elements that provide a sparse representation of measured/collected signals or data. 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 underlying …

Web17 de mai. de 2016 · Dictionary learning is the problem of estimating the collection of atomic elements that provide a sparse representation of measured/collected signals or … WebSparse decomposition has been widely used in gear local fault diagnosis due to its outstanding performance in feature extraction. The extraction results depend heavily on the similarity between dictionary atoms and fault feature signal. However, the transient impact signal aroused by gear local defect is usually submerged in meshing harmonics and …

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 ... 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

Webminimax risk have direct implications on the required sample size of accurate DL schemes. In particular our analysis reveals that, for a sufﬁciently incoherent underlying …

Web29 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... easihorse farmWebMinimax reconstruction risk of convolutional sparse dictionary learning. AISTATS, 2024. Yang Y, Gu Q, Zhang Y, Sasaki T, Crivello J, O'Neill R, Gilbert DM, and Ma J. Continuous-trait probabilistic model for comparing multi-species functional genomic data. Cell Systems, 7(2):208-218.e11 ... cty amphenolWeb12 de jan. de 2016 · On the Minimax Risk of Dictionary Learning Abstract: We consider the problem of learning a dictionary matrix from a number of observed signals, which … cty anvietconsWebUpload an image to customize your repository’s social media preview. Images should be at least 640×320px (1280×640px for best display). easikey instructionsWebDictionary 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. cty ansell vinaWebOn the Minimax Risk of Dictionary Learning Alexander Jung, Yonina C. Eldar,Fellow, IEEE, and Norbert Görtz,Senior Member, IEEE Abstract—We consider the problem of … cty apaWebthe information theory literature; these include restating the dictionary learning problem as a channel coding problem and connecting the analysis of minimax risk in statistical estimation to Fano’s inequality. In addition to highlighting the effects of different parameters on the sample complexity of dictionary learning, cty apeco