High-dimensional statistics : a non-asymptotic viewpoint
著者
書誌事項
High-dimensional statistics : a non-asymptotic viewpoint
（Cambridge series on statistical and probabilistic mathematics, 48）
Cambridge University Press, 2019
- : hardback
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注記
Includes bibliographical references (p. 524-539) and indexes
内容説明・目次
内容説明
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.
目次
- 1. Introduction
- 2. Basic tail and concentration bounds
- 3. Concentration of measure
- 4. Uniform laws of large numbers
- 5. Metric entropy and its uses
- 6. Random matrices and covariance estimation
- 7. Sparse linear models in high dimensions
- 8. Principal component analysis in high dimensions
- 9. Decomposability and restricted strong convexity
- 10. Matrix estimation with rank constraints
- 11. Graphical models for high-dimensional data
- 12. Reproducing kernel Hilbert spaces
- 13. Nonparametric least squares
- 14. Localization and uniform laws
- 15. Minimax lower bounds
- References
- Author index
- Subject index.
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