D. Pollard, Empirical Processes: Theory and Applications, vol. 2. NSF-CBMS Regional Conference Series in Probability and Statistics, Institute of Mathematical Statistics, 1990. Home/Search Document Not in Database Summary Related Articles Check |
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Exact Rates In Vapnik-Chervonenkis Bounds - Vayatis (Correct)
....to the control of the localized empirical process. Indeed we need to obtain a tractable exponential bound on the quantity Pr ( sup C2B(C ; jGn (C) Gamma Gn (C )j ffl 2 ) 20) The classical way to deal with suprema in empirical processes theory is to use the chaining trick (cf. [19], 22] 13] However, this cannot be done straightforwardly since the process involved here does not satisfy a subgaussian inequality. The argument developed here is due to Talagrand in [21] and it can also be found in [22] In the following Subsection 4.2, we shall prove EXACT RATES IN ....
, Empirical Processes : Theory and Applications, NSF-CBMS Regional Conference Series in Probability and Statistics, Institute of Mathematical Statistics, 1991.
On the Training Distortion of Vector Quantizers - Linder (2000) (1 citation) (Correct)
....D(Q ) Gamma c(B; d; k) p n for all X 2 P(B) where c(B; d; k) 96Bd 3=2 p k. The result is based on a nonasymptotic upper bound on E Phi sup Q2Q k Theta D(Q) Gamma D n (Q) Psi . At the core of the proof is a simple and elegant version of the classic metric entropy bound [14, 15] of empirical process theory, recently proved by Cesa Bianchi and Lugosi [16] which allows us to provide an explicit form of the constant c(B; d; k) In summary, Theorems 1 and 3 show that for independent training data of size n, the maximum difference D(Q ) Gamma E[D n (Q n ) of the ....
....s j s 2 S we have T s j T s with probability one. The following result gives an upper bound on the expected supremum of the random variables fT s : s 2 Sg in terms of the covering number of the index space. It provides a version of a classical result in empirical process theory (see, e.g. [15]) with an explicit constant. Lemma 2 ( 16, Proposition 3] If fT s : s 2 Sg is subgaussian and sample continuous in the metric ae, then E ae sup s2S T s oe 12 Z diam(S) 2 0 q ln N ae (S; ffl) dffl where diam(S) sup s;s 0 2S ae(s; s 0 ) is the diameter of S. To apply the above ....
D. Pollard, Empirical Processes: Theory and Applications. NSF-CBMS Regional Conference Series in Probability and Statistics, Institute of Mathematical Statistics, Hayward, CA, 1990.
Quantitative stability in stochastic programming: The method.. - Rachev, Römisch (2000) (2 citations) (Correct)
.... Whether a given class F is a Glivenko Cantelli class or whether even a rate of convergence of (d F ( n ( is valid, depends on the size of the class F measured in terms of covering or bracketing numbers or the corresponding metric entropy numbers de ned as their logarithms (see [10, 31, 53]) To introduce these concepts, let F be a subset of the normed space L p ( for some p 1) equipped with the usual norm k k p . The covering number N( F ; L p ( is the minimal number of open balls fg 2 L p ( kg fk p g needed to cover F . Given two functions f 1 and f 2 ....
D. Pollard, Empirical Processes: Theory and Applications, NSF-CBMS Regional Conference Series in Probability and Statistics Vol. 2, Institute of Mathematical Statistics, 1990.
Learning-Theoretic Methods in Vector Quantization - Linder (2001) (1 citation) Self-citation (Statistics) (Correct)
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D. Pollard. Empirical Processes: Theory and Applications. NSF-CBMS Regional Conference Series in Probability and Statistics, Institute of Mathematical Statistics, Hayward, CA, 1990.
Pattern Recognition as a Deterministic Problem: An Approach .. - Cervellera, Muselli (Correct)
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D. Pollard, Empirical Processes: Theory and Applications, vol. 2. NSF-CBMS Regional Conference Series in Probability and Statistics, Institute of Mathematical Statistics, 1990.
Deterministic Design for Neural Network Learning: - An Approach Based (Correct)
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D. Pollard, Empirical Processes: Theory and Applications. NSF-CBMS Regional Conference Series in Probability and Statistics, Institute of Mathematical Statistics, 1990, vol. 2.
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