02558 2200253 4500003002100000005001700021008004100038020001800079040002500097082002000122100003500142245008300177260002000260300003600280490006600316504005000382505060400432520106301036650002802099650001302127942001502140952013002155999001902285ISI Library, Kolkata20240909163101.0210303b ||||| |||| 00| 0 eng d a9781108498029 aISI LibrarybEnglish04223aSA.01bW1411 aWainwright, Martin J. eauthor10aHigh-Dimensional statistics:ba non-asymptotic viewpoint/cMartin J Wainwright aUK:bCUP,c2019 axvii, 552 pages,bill;c26 cm. 0 aCambridge Series in Statistical and Probabilistic Mathematics aIncludes bibliographical references and index a1. 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 aRecent 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. 4aMathematical Statistics 4aBig Data 2ddccBK02 00104070aMAINbMAINd2021-02-04e424g4922.24l5m3oSA.01 W141p138498q2024-08-15r2024-07-16 14:36:16s2024-07-16yBKw c427955d427955