M. Talagrand: Sharper bounds for Gaussian and empirical processes, Annals of Probability, 22(1), 28-76, 1994. Home/Search Document Not in Database Summary Related Articles Check |
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A few notes on Statistical Learning Theory - Mendelson (2003) (2 citations) (Correct)
....#, F s n , L# (s n ) K fat c# (F ) log 1 # where K p and c p are constants which depend only on p. The significance of these entropy estimates goes far beyond learning theory. They are essential in solving highly non trivial problems in convex geometry and in empirical processes [23, 26, 32, 33]. Using the bounds on the uniform entropy numbers and theorem 2.3, one can establish the following sample complexity estimates. Theorem 2.19 There is an absolute constant C such that for every class F and every 0 #, # 1, fat # 8 (F ) ....
....one has additional data on the variance of the random variable Z, which leads to potentially sharper bounds. It has been a long standing open question whether a similar result can be obtained when replacing Z by sup f#F . This functional inequality was first established by Talagrand [33], and later was modified and partially improved by Ledoux [15] Massart [18] Rio [28] and Bousquet [3] Theorem 2.21 [18] Let be a probability measure on # and let X 1 , X n be independent random variables distributed according to . Given a class of functions F , set Z = f(X i ) E ....
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M. Talagrand: Sharper bounds for Gaussian and empirical processes, Annals of Probability, 22(1), 28-76, 1994.
Geometric Methods in the Analysis of Glivenko-Cantelli Classes - Mendelson (Correct)
....) We use a concentration result which yields an estimate on the deviation of the empirical means from the actual mean in terms of the Rademacher averages. We show that rav (F ) measures the sample complexity of the class F . Recall the following concentration result, which is due to Talagrand [15]: Theorem 8. There are two absolute constants K and a 1 with the following property: consider a class of functions F whose range is a subset of [0; 1] such that sup f2F E(f Ef) 2 a. If is any probability measure on and p n K R n; M K R n; then P r ( sup f2F jE n f ....
M. Talagrand: Sharper bounds for Gaussian and empirical processes, Annals of Probability, 22(1), 28-76, 1994.
Rademacher averages and phase transitions in Glivenko-Cantelli.. - Mendelson (2001) (1 citation) (Correct)
....convex hull of a set, in terms of the original fat shattering dimension. Another application of that lower bound enables us to provide a new partial solution to a question in the geometry of Banach spaces which was posed by Elton [8] Finally, we use one of Talagrand s concentration inequalities [19] and prove complexity estimates with respect to any L q norm, for 1 q 1. The estimate we obtain in the polynomial scale is O( maxf2;pg ) up to a logarithmic factor in 1= and 1= The results we have are sharper than the known estimates, and we show that they are optimal. Here too, we ....
....then apply the estimates on those averages in terms of the fat shattering dimension obtained is section 3.2 and improve the known complexity estimates. It turns out that rav (F ) measures precisely the sample complexity. We begin with the following concentration result which is due to Talagrand [19]: 22 Theorem 5.1 There are two absolute constants K and a 1 with the following property: consider a class of functions F whose range is a subset of [0; 1] such that sup f2F E(f Ef) 2 a. If is any probability measure on and n 1 2 K R n; M K R n; then P r ( sup f2F ....
M. Talagrand: Sharper bounds for Gaussian and empirical processes, Annals of Probability, 22(1), 28-76, 1994.
On Almost Sure Convergence of Vector Valued Pramarts .. - Ahmed.. Self-citation (Talagrand Results) (Correct)
.... Bellow [3] Blake [4] Chatterji [10] Castaing [5] Castaing and Ezzaki [8] Choukairi ( 11] 12] 14] Daures [15] Bagchi [1] Hiai and Umegaki [20] Hess [19] Egghe ( 17] 18] Millet and Sucheston [26] Lavie [22] Luu ( 23] 24] 25] Slaby [28] Derras [16] Neveu [27] Talagrand [29], and many others. New convergence results for bounded pramarts in L 1 E and in the space L 1 wc(E) of integrably bounded multifunction with convex weakly compact values are presented. The main purpose of this paper is to obtain the Linear topology convergence (introduced by Beer [2] and ....
M. Talagrand: Some structure results for martingales in the limit and pramarts. The annals of probability. vol. 13, no. 4 (1985).
Geometric Parameters of Kernel Machines - Mendelson (Correct)
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M. Talagrand: Sharper bounds for Gaussian and empirical processes, Annals of Probability, 22(1), 28-76, 1994.
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