High-Dimensional Statistics: A Non-Asymptotic Viewpoint

ISBN-13: 9781108498029 / Angielski / Twarda / 2019 / 568 str.

Martin J. Wainwright

Opis

A coherent introductory text from a groundbreaking researcher, focusing on clarity and motivation to build intuition and understanding.

Recenzje

'An excellent statistical masterpiece is in the hands of the reader, which is a must read book for all graduate students in both mathematical statistics and mathematical machine learning.' Rózsa Horváth-Bokor, ZB Math Reviews

Spis treści

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.