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" High-dimensional statistics : "
Martin J. Wainwright, University of California, Berkeley.
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BL
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| Record Number
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839616
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| Main Entry
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Wainwright, Martin, (Martin J.)
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| Title & Author
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High-dimensional statistics : : a non-asymptotic viewpoint /\ Martin J. Wainwright, University of California, Berkeley.
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| Publication Statement
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Cambridge, United Kingdom ;New York, NY, USA :: Cambridge University Press,, 2019.
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, ©2019
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| Series Statement
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Cambridge series in statistical and probabilistic mathematics ;; 48
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| Page. NO
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1 online resource (xvii, 552 pages) :: illustrations
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| ISBN
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1108627773
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: 9781108627771
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1108498027
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9781108498029
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| Bibliographies/Indexes
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Includes bibliographical references and indexes.
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| Contents
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Introduction -- Basic tail and concentration bounds -- Concentration of measure -- Uniform laws of large numbers -- Metric entropy and its uses -- Random matrices and covariance estimation -- Sparse linear models in high dimensions -- Principal component analysis in high dimensions -- Decomposability and restricted strong convexity -- Matrix estimation with rank constraints -- Graphical models for high-dimensional data -- Reproducing kernel Hilbert spaces -- Nonparametric least squares -- Localization and uniform laws -- Minimax lower bounds.
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| Abstract
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Recent years have witnessed an explosion in the volume and variety of data collected in all scientific disciplines and industrial settings. Such massive data sets present a number of challenges to researchers in statistics and machine learning. This book provides a self-contained introduction to the area of high-dimensional statistics, aimed at the first-year graduate level. It includes chapters that are focused on core methodology and theory - including tail bounds, concentration inequalities, uniform laws and empirical process, and random matrices - as well as chapters devoted to in-depth exploration of particular model classes - including sparse linear models, matrix models with rank constraints, graphical models, and various types of non-parametric models. With hundreds of worked examples and exercises, this text is intended both for courses and for self-study by graduate students and researchers in statistics, machine learning, and related fields who must understand, apply, and adapt modern statistical methods suited to large-scale data.
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| Subject
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Big data.
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Mathematical statistics, Textbooks.
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Big data.
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Mathematical statistics.
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| Dewey Classification
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519.5
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| LC Classification
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QA276.18.W35 2019
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