Nettet1. sep. 2007 · The following lemma is a version of the well-known 'contraction principle' of the theory of Rademacher averages (see Theorem 4.12 of Ledoux & Talagrand, 1991, and Ambroladze, Parrado-Hernandez ... NettetA simple consequence of Hornik [1991]. I Also known as the “Universal Approximation Theorem”. Theorem 2 (Hornik) Assume that the function ˙ a is non constant and bounded. Let denote a probability measure on Rr, then NN 1is dense in L2(Rr; ). I Corollary: If for every p, p 2 p is a minimizer of inf 2 p E[j p(X; ) Yj 2]; (p(X; p)) p ...
[2007.05150] A supplement to the laws of large numbers and the …
NettetM. Ledoux, M. Talagrand, and other authors. The topic covered in this book is the study of metric and other close char-acteristics of di erent spaces and classes of random variables and the application of the entropy method to the investigation of properties of stochastic processes whose values, or whose increments, belong to given spaces. NettetLocal Rademacher complexities and oracle inequalities in risk minimization. Annals of\n\nStatistics, 34(6):2593\u20132656, 2006.\n\n[21] M. Ledoux. The Concentration of Measure Phenomenon. Mathematical Surveys and Monographs.\n\nAmerican Mathematical Society, Providence, RI, 2001.\n\n\f[22] M. Ledoux and M. Talagrand. easter activities for big kids
Michel Ledoux
Nettetwe comment and motivate the use of concentration arguments. Talagrand’s con-centration phenomenon for products of exponential distributions is one instance of a general phenomenon: concentration of measure in product spaces [Ledoux, 2001,Ledoux and Talagrand,1991]. The phenomenon may be summarised in Nettetis Talagrand's variance factor. If the random variables X1, X2, .. ., Xn are symmetric signs, then Z is the maximum of a Rademacher process and V = Vn. In that case Corollary 1.1 improves the known bounds on Var Z as soon as 2E(Z) < Vn. For Rademacher processes, the concentration inequality (4.10) in Ledoux and Talagrand (1991) yields Nettet1. jan. 2001 · Ledoux and Talagrand 1991. M. Ledoux, M. Talagrand. Probability in Banach Spaces, Springer, Berlin (1991) Google Scholar. Marcus 1998 Marcus, M., 1998. A sufficient condition for the continuity of high order Gaussian chaos processes. easter activities for babies in nursery