Concentration-of-measure inequalities Lecture notes by Gábor Lugosi

This text contains some of the material presented at the Summer

[1]  G. Lugosi,et al.  Complexity regularization via localized random penalties , 2004, math/0410091.

[2]  Peter L. Bartlett,et al.  Model Selection and Error Estimation , 2000, Machine Learning.

[3]  D. Panchenko.  SYMMETRIZATION APPROACH TO CONCENTRATION INEQUALITIES FOR EMPIRICAL PROCESSES , 2003, math/0405354.

[4]  O. Bousquet.  New approaches to statistical learning theory , 2003 .

[5]  Colin McDiarmid,et al.  Concentration for locally acting permutations , 2003, Discret. Math..

[6]  Peter L. Bartlett,et al.  Localized Rademacher Complexities , 2002, COLT.

[7]  Piet Groeneboom.  Hydrodynamical methods for analyzing longest increasing subsequences , 2002 .

[8]  Colin McDiarmid.  Concentration For Independent Permutations , 2002, Comb. Probab. Comput..

[9]  V. Koltchinskii,et al.  Empirical margin distributions and bounding the generalization error of combined classifiers , 2002, math/0405343.

[10]  D. Panchenko.  Some Extensions of an Inequality of Vapnik and Chervonenkis , 2002, math/0405342.

[11]  P. MassartLedoux,et al.  Concentration Inequalities Using the Entropy Method , 2002 .

[12]  O. Bousquet.  A Bennett concentration inequality and its application to suprema of empirical processes , 2002 .

[13]  Gábor Lugosi,et al.  Pattern Classification and Learning Theory , 2002 .

[14]  Djalil CHAFAÏ.  On Φ-entropies and Φ-Sobolev inequalities , 2002 .

[15]  Peter L. Bartlett,et al.  Rademacher and Gaussian Complexities: Risk Bounds and Structural Results , 2003, J. Mach. Learn. Res..

[16]  D. Panchenko.  A Note on Talagrand's Concentration Inequality , 2001 .

[17]  A. W. van der Vaart,et al.  Uniform Central Limit Theorems , 2001 .

[18]  E. Rio,et al.  Inégalités de concentration pour les processus empiriques de classes de parties , 2001 .

[19]  M. Ledoux.  The concentration of measure phenomenon , 2001 .

[20]  Luc Devroye,et al.  Combinatorial methods in density estimation , 2001, Springer series in statistics.

[21]  Minimization Vladimir Koltchinskii.  Rademacher Penalties and Structural Risk , 2001 .

[22]  N. Alon,et al.  On the concentration of eigenvalues of random symmetric matrices , 2000, math-ph/0009032.

[23]  P. Massart,et al.  About the constants in Talagrand's concentration inequalities for empirical processes , 2000 .

[24]  R. Latala,et al.  Between Sobolev and Poincaré , 2000, math/0003043.

[25]  S. Boucheron,et al.  A sharp concentration inequality with applications , 1999, Random Struct. Algorithms.

[26]  P. Massart.  Some applications of concentration inequalities to statistics , 2000 .

[27]  Paul-Marie Samson,et al.  Concentration of measure inequalities for Markov chains and $\Phi$-mixing processes , 2000 .

[28]  Vladimir N. Vapnik,et al.  The Nature of Statistical Learning Theory , 2000, Statistics for Engineering and Information Science.

[29]  Peter L. Bartlett,et al.  Neural Network Learning - Theoretical Foundations , 1999 .

[30]  J. Baik,et al.  On the distribution of the length of the second row of a Young diagram under Plancherel measure , 1999, math/9901118.

[31]  M. Ledoux.  Concentration of measure and logarithmic Sobolev inequalities , 1999 .

[32]  Desh Ranjan,et al.  Balls and bins: A study in negative dependence , 1996, Random Struct. Algorithms.

[33]  Vladimir Vapnik,et al.  Statistical learning theory , 1998 .

[34]  A. Dembo.  Information inequalities and concentration of measure , 1997 .

[35]  S. Bobkov,et al.  Poincaré’s inequalities and Talagrand’s concentration phenomenon for the exponential distribution , 1997 .

[36]  M. Ledoux.  On Talagrand's deviation inequalities for product measures , 1997 .

[37]  M. Talagrand.  New concentration inequalities in product spaces , 1996 .

[38]  K. Marton.  A measure concentration inequality for contracting markov chains , 1996 .

[39]  M. Talagrand.  A new look at independence , 1996 .

[40]  László Györfi,et al.  A Probabilistic Theory of Pattern Recognition , 1996, Stochastic Modelling and Applied Probability.

[41]  M. Ledoux,et al.  Isoperimetry and Gaussian analysis , 1996 .

[42]  M. Talagrand.  Concentration of measure and isoperimetric inequalities in product spaces , 1994, math/9406212.

[43]  Wansoo T. Rhee.  A Matching Problem and Subadditive Euclidean Functionals , 1993 .

[44]  Béla Bollobás,et al.  The Height of a Random Partial Order: Concentration of Measure , 1992 .

[45]  Alan Frieze,et al.  On the Length of the Longest Monotone Subsequence in a Random Permutation , 1991 .

[46]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[47]  L. Devroye.  Exponential Inequalities in Nonparametric Estimation , 1991 .

[48]  David Haussler,et al.  Learnability and the Vapnik-Chervonenkis dimension , 1989, JACM.

[49]  Colin McDiarmid,et al.  Surveys in Combinatorics, 1989: On the method of bounded differences , 1989 .

[50]  W. Beckner.  A generalized Poincaré inequality for Gaussian measures , 1989 .

[51]  L. Devroye.  The kernel estimate is relatively stable , 1988 .

[52]  Wansoo T. Rhee,et al.  Martingale Inequalities and NP-Complete Problems , 1987, Math. Oper. Res..

[53]  J. Steele.  Probability theory and combinatorial optimization , 1987 .

[54]  Joel H. Spencer,et al.  Sharp concentration of the chromatic number on random graphsGn, p , 1987, Comb..

[55]  Micha Hofri,et al.  Probabilistic Analysis of Algorithms , 1987, Texts and Monographs in Computer Science.

[56]  J. Steele.  An Efron-Stein inequality for nonsymmetric statistics , 1986 .

[57]  Katalin Marton,et al.  A simple proof of the blowing-up lemma , 1986, IEEE Trans. Inf. Theory.

[58]  V. Milman,et al.  Asymptotic Theory Of Finite Dimensional Normed Spaces , 1986 .

[59]  Michael J. Steele,et al.  Long Common Subsequences and the Proximity of two Random Strings. , 1982 .

[60]  B. Efron,et al.  The Jackknife Estimate of Variance , 1981 .

[61]  Joseph G. Deken.  Some limit results for longest common subsequences , 1979, Discret. Math..

[62]  Te Sun Han.  Nonnegative Entropy Measures of Multivariate Symmetric Correlations , 1978, Inf. Control..

[63]  B. Logan,et al.  A Variational Problem for Random Young Tableaux , 1977 .

[64]  P. Gács,et al.  Bounds on conditional probabilities with applications in multi-user communication , 1976 .

[65]  Vladimir Vapnik,et al.  Chervonenkis: On the uniform convergence of relative frequencies of events to their probabilities , 1971 .

[66]  G. Bennett.  Probability Inequalities for the Sum of Independent Random Variables , 1962 .

[67]  W. Hoeffding.  Probability inequalities for sum of bounded random variables , 1963 .

[68]  M. Okamoto.  Some inequalities relating to the partial sum of binomial probabilities , 1959 .

[69]  M. Sion.  On general minimax theorems , 1958 .

[70]  H. Chernoff.  A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations , 1952 .

[71]  A E Bostwick,et al.  THE THEORY OF PROBABILITIES. , 1896, Science.

[72]  C. McDiarmid.  Concentration , 1862, The Dental register.