Stephane Boucheron, Laboratoire de Probabilites et Modeles Aleatoires, Universite Paris-Diderot,Gabor Lugosi, ICREA Research Professor, Pompeu Fabra University,Pascal Massart, Laboratoire de Mathematiques, Universite Paris Sud and Institut Universitaire de France
Stephane Boucheron is a Professor in the Applied Mathematics and Statistics Department at Universite Paris-Diderot, France.
Gabor 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 Universite de Paris-Sud, France.
Concentration inequalities for functions of independent random variables is an area of probability theory that has witnessed a great revolution in the last few decades, and has applications in a wide variety of areas such as machine learning, statistics, discrete mathematics, and high-dimensional geometry. Roughly speaking, if a function of many independent random variables does not depend too much on any of the variables then it is concentrated in the sense that with high probability, it is close to its expected value. This book offers a host of inequalities to illustrate this rich theory in an accessible way by covering the key developments and applications in the field. The authors describe the interplay between the probabilistic structure (independence) and a variety of tools ranging from functional inequalities to transportation arguments to information theory. Applications to the study of empirical processes, random projections, random matrix theory, and threshold phenomena are also presented. A self-contained introduction to concentration inequalities, it includes a survey of concentration of sums of independent random variables, variance bounds, the entropy method, and the transportation method. Deep connections with isoperimetric problems are revealed whilst special attention is paid to applications to the supremum of empirical processes. Written by leading experts in the field and containing extensive exercise sections this book will be an invaluable resource for researchers and graduate students in mathematics, theoretical computer science, and engineering.
發表於2024-12-23
Concentration Inequalities 2024 pdf epub mobi 電子書 下載
圖書標籤: Statistics 數學 learning-theory concentration_inequality Probability, Inequalities, Concentration-of-Measure, 學術
其實這個書挺好的, 當reference book算是非常好的 (雖然有些應該齣現在正文的被relegate到習題裏瞭, 比如generic chaining), 不過字體是palantino吧, 看著真是不舒服...
評分隻是因為Concentration的書比較少,這本書纔有它的價值。事實上,本書的最大缺點不是奇怪的字體(事實上看久瞭之後還覺得挺順眼的),而是它的詳略不分。雖然一本書做到“全”也是一件非常值得稱贊的事情,但是本書並沒有做到“全”,例如Chaining在本書中就沒有得到體現。較前沿的一本教材,應該盡可能地“突齣主綫”,減去旁枝末節的東西,簡明扼要地闡述本領域的主要方法、工具,然後再展示其主要應用。不幸地是,本書在每一章的後半部分,幾乎都與主綫方法無關,且本書的第六章以後的部分,也開始逐漸脫離主綫瞭。既然如此,為什麼不將各個專題,如Random Graph,VC-Dimension中的應用等,直接刪掉,留在Notes中進行簡要說明即可呢?
評分隻是因為Concentration的書比較少,這本書纔有它的價值。事實上,本書的最大缺點不是奇怪的字體(事實上看久瞭之後還覺得挺順眼的),而是它的詳略不分。雖然一本書做到“全”也是一件非常值得稱贊的事情,但是本書並沒有做到“全”,例如Chaining在本書中就沒有得到體現。較前沿的一本教材,應該盡可能地“突齣主綫”,減去旁枝末節的東西,簡明扼要地闡述本領域的主要方法、工具,然後再展示其主要應用。不幸地是,本書在每一章的後半部分,幾乎都與主綫方法無關,且本書的第六章以後的部分,也開始逐漸脫離主綫瞭。既然如此,為什麼不將各個專題,如Random Graph,VC-Dimension中的應用等,直接刪掉,留在Notes中進行簡要說明即可呢?
評分隻是因為Concentration的書比較少,這本書纔有它的價值。事實上,本書的最大缺點不是奇怪的字體(事實上看久瞭之後還覺得挺順眼的),而是它的詳略不分。雖然一本書做到“全”也是一件非常值得稱贊的事情,但是本書並沒有做到“全”,例如Chaining在本書中就沒有得到體現。較前沿的一本教材,應該盡可能地“突齣主綫”,減去旁枝末節的東西,簡明扼要地闡述本領域的主要方法、工具,然後再展示其主要應用。不幸地是,本書在每一章的後半部分,幾乎都與主綫方法無關,且本書的第六章以後的部分,也開始逐漸脫離主綫瞭。既然如此,為什麼不將各個專題,如Random Graph,VC-Dimension中的應用等,直接刪掉,留在Notes中進行簡要說明即可呢?
評分其實這個書挺好的, 當reference book算是非常好的 (雖然有些應該齣現在正文的被relegate到習題裏瞭, 比如generic chaining), 不過字體是palantino吧, 看著真是不舒服...
Concentration Inequalities 2024 pdf epub mobi 電子書 下載