| Description |
1 online resource (xvii, 552 pages) : illustrations |
| Series |
Cambridge series in statistical and probabilistic mathematics ; 48 |
|
Cambridge series on statistical and probabilistic mathematics ; 48.
|
| Contents |
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 |
| Summary |
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 |
| Bibliography |
Includes bibliographical references and indexes |
| Notes |
Print version record |
| Subject |
Mathematical statistics -- Textbooks
|
|
Big data.
|
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Big data
|
|
Mathematical statistics
|
| Genre/Form |
Textbooks
|
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Textbooks.
|
| Form |
Electronic book
|
| ISBN |
9781108627771 |
|
1108627773 |
|
