An accessible account of the rich theory surrounding concentration inequalities in probability theory, with applications from machine learning and statistics to high-dimensional geometry. This book introduces key ideas and presents a detailed summary of the state-of-the-art in the area, making it ideal for independent learning and as a reference.
An accessible account of the rich theory surrounding concentration inequalities in probability theory, with applications from machine learning and statistics to high-dimensional geometry. This book introduces key ideas and presents a detailed summary of the state-of-the-art in the area, making it ideal for independent learning and as a reference.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Stéphane Boucheron is a Professor in the Applied Mathematics and Statistics Department at Université Paris-Diderot, France. ; Gábor Lugosi is ICREA Research Professor in the Department of Economics at the Pompeu Fabra University in Barcelona, Spain. ; Pascal Massart is a Professor in the Department of Mathematics at Université de Paris-Sud, France.
Inhaltsangabe
Foreword 1: Introduction 2: Basic inequalities 3: Bounding the variance 4: Basic information inequalities 5: Logarithmic Sobolev inequalities 6: The entropy method 7: Concentration and isoperimetry 8: The transportation method 9: Influences and threshold phenomena 10: Isoperimetry on the hypercube and Gaussian spaces 11: The variance of suprema of empirical processes 12: Suprema of empirical processes: exponential inequalities 13: The expected value of suprema of empirical processes 14: ¿-entropies 15: Moment inequalities
Foreword 1: Introduction 2: Basic inequalities 3: Bounding the variance 4: Basic information inequalities 5: Logarithmic Sobolev inequalities 6: The entropy method 7: Concentration and isoperimetry 8: The transportation method 9: Influences and threshold phenomena 10: Isoperimetry on the hypercube and Gaussian spaces 11: The variance of suprema of empirical processes 12: Suprema of empirical processes: exponential inequalities 13: The expected value of suprema of empirical processes 14: ¿-entropies 15: Moment inequalities
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