Lectures on Empirical Processes PDF Download

Author: Eustasio Del Barrio
Publisher: Transaction Publishers
ISBN: 9783037190272
Category : Mathematics
Languages : en
Pages : 268

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Author: David Pollard
Publisher: IMS
ISBN: 9780940600164
Category : Distribution (Probability theory).
Languages : en
Pages : 100

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Book Description

Author: Roman Vershynin
Publisher: Cambridge University Press
ISBN: 1108415199
Category : Business & Economics
Languages : en
Pages : 299

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Book Description
An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

Author: D. Pollard
Publisher: David Pollard
ISBN: 0387909907
Category : Mathematics
Languages : en
Pages : 223

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Book Description
Functionals on stochastic processes; Uniform convergence of empirical measures; Convergence in distribution in euclidean spaces; Convergence in distribution in metric spaces; The uniform metric on space of cadlag functions; The skorohod metric on D [0, oo); Central limit teorems; Martingales.

Author: EUSTASIO DEL BARRIO; PAUL DEHEUVELS; SARA VAN DE G.
Publisher:
ISBN: 9783037195277
Category :
Languages : en
Pages :

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Author: Shahar Mendelson
Publisher: Springer
ISBN: 354036434X
Category : Computers
Languages : en
Pages : 267

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Book Description
Machine Learning has become a key enabling technology for many engineering applications and theoretical problems alike. To further discussions and to dis- minate new results, a Summer School was held on February 11–22, 2002 at the Australian National University. The current book contains a collection of the main talks held during those two weeks in February, presented as tutorial chapters on topics such as Boosting, Data Mining, Kernel Methods, Logic, Reinforcement Learning, and Statistical Learning Theory. The papers provide an in-depth overview of these exciting new areas, contain a large set of references, and thereby provide the interested reader with further information to start or to pursue his own research in these directions. Complementary to the book, a recorded video of the presentations during the Summer School can be obtained at http://mlg. anu. edu. au/summer2002 It is our hope that graduate students, lecturers, and researchers alike will ?nd this book useful in learning and teaching Machine Learning, thereby continuing the mission of the Summer School. Canberra, November 2002 Shahar Mendelson Alexander Smola Research School of Information Sciences and Engineering, The Australian National University Thanks and Acknowledgments We gratefully thank all the individuals and organizations responsible for the success of the workshop.

Author: Victor H. Peña
Publisher: Springer Science & Business Media
ISBN: 3540856366
Category : Mathematics
Languages : en
Pages : 273

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Book Description
Self-normalized processes are of common occurrence in probabilistic and statistical studies. A prototypical example is Student's t-statistic introduced in 1908 by Gosset, whose portrait is on the front cover. Due to the highly non-linear nature of these processes, the theory experienced a long period of slow development. In recent years there have been a number of important advances in the theory and applications of self-normalized processes. Some of these developments are closely linked to the study of central limit theorems, which imply that self-normalized processes are approximate pivots for statistical inference. The present volume covers recent developments in the area, including self-normalized large and moderate deviations, and laws of the iterated logarithms for self-normalized martingales. This is the first book that systematically treats the theory and applications of self-normalization.

Author: Pascal Massart
Publisher: Springer
ISBN: 3540485031
Category : Mathematics
Languages : en
Pages : 346

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Book Description
Concentration inequalities have been recognized as fundamental tools in several domains such as geometry of Banach spaces or random combinatorics. They also turn to be essential tools to develop a non asymptotic theory in statistics. This volume provides an overview of a non asymptotic theory for model selection. It also discusses some selected applications to variable selection, change points detection and statistical learning.

Author: Vladimir Koltchinskii
Publisher: Springer
ISBN: 3642221475
Category : Mathematics
Languages : en
Pages : 259

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Book Description
The purpose of these lecture notes is to provide an introduction to the general theory of empirical risk minimization with an emphasis on excess risk bounds and oracle inequalities in penalized problems. In recent years, there have been new developments in this area motivated by the study of new classes of methods in machine learning such as large margin classification methods (boosting, kernel machines). The main probabilistic tools involved in the analysis of these problems are concentration and deviation inequalities by Talagrand along with other methods of empirical processes theory (symmetrization inequalities, contraction inequality for Rademacher sums, entropy and generic chaining bounds). Sparse recovery based on l_1-type penalization and low rank matrix recovery based on the nuclear norm penalization are other active areas of research, where the main problems can be stated in the framework of penalized empirical risk minimization, and concentration inequalities and empirical processes tools have proved to be very useful.

Author: Lucien Le Cam
Publisher: Springer Science & Business Media
ISBN: 1461249465
Category : Mathematics
Languages : en
Pages : 767

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Book Description
This book grew out of lectures delivered at the University of California, Berkeley, over many years. The subject is a part of asymptotics in statistics, organized around a few central ideas. The presentation proceeds from the general to the particular since this seemed the best way to emphasize the basic concepts. The reader is expected to have been exposed to statistical thinking and methodology, as expounded for instance in the book by H. Cramer [1946] or the more recent text by P. Bickel and K. Doksum [1977]. Another pos sibility, closer to the present in spirit, is Ferguson [1967]. Otherwise the reader is expected to possess some mathematical maturity, but not really a great deal of detailed mathematical knowledge. Very few mathematical objects are used; their assumed properties are simple; the results are almost always immediate consequences of the definitions. Some objects, such as vector lattices, may not have been included in the standard background of a student of statistics. For these we have provided a summary of relevant facts in the Appendix. The basic structures in the whole affair are systems that Blackwell called "experiments" and "transitions" between them. An "experiment" is a mathe matical abstraction intended to describe the basic features of an observational process if that process is contemplated in advance of its implementation. Typically, an experiment consists of a set E> of theories about what may happen in the observational process.