A PAC-Bayesian Margin Bound for Linear Classifiers: Why SVMs work

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A PAC-Bayesian Margin Bound for Linear Classifiers: Why SVMs work (2001) (Make Corrections) (6 citations)
Ralf Herbrich, Thore GraepelNIPS

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Abstract: We present a bound on the generalisation error of linear classiers in terms of a rened margin quantity on the training set. The result is obtained in a PACBayesian framework and is based on geometrical arguments in the space of linear classiers. The new bound constitutes an exponential improvement of the so far tightest margin bound by Shawe-Taylor et al. [8] and scales logarithmically in the inverse margin. Even in the case of less training examples than input dimensions suciently... (Update)

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4: Some PAC-Bayesian Theorems - McAllester - 1998
3: The Nature of Statistical Learning Theory (context) - Vapnik - 1995
3: Boosting the margin: A new explanation for the eectiveness of voting methods (context) - Schapire, Freund et al. - 1998

BibTeX entry: (Update)

R. Herbrich and T. Graepel. A PAC-Bayesian Margin Bound for Linear Classifiers: Why SVMs work. In Proceedings of NIPS, 2001. http://citeseer.ist.psu.edu/article/herbrich01pacbayesian.html More

@inproceedings{ herbrich00pacbayesian,
    author = "Ralf Herbrich and Thore Graepel",
    title = "A {PAC}-Bayesian Margin Bound for Linear Classifiers: Why {SVMs} work",
    booktitle = "{NIPS}",
    pages = "224-230",
    year = "2000",
    url = "citeseer.ist.psu.edu/article/herbrich01pacbayesian.html" }

Citations (may not include all citations):
1291 The Nature of Statistical Learning Theory (context) - Vapnik - 1995
493 Communications of the ACM (context) - Valiant, of et al. - 1984
454 the uniform convergence of relative frequencies of events to.. (context) - Vapnik, Chervonenkis - 1971
348 Estimation of Dependences Based on Empirical Data (context) - Vapnik - 1982
115 the density of families of sets (context) - Sauer - 1972
46 Some PAC Bayesian theorems - McAllester - 1998
31 uniform convergence and learnability (context) - Alon, Ben-David et al. - 1997
20 Bayesian learning in reproducing kernel Hilbert spaces - Herbrich, Graepel et al. - 1999
19 cient distribution-free learning of probabilistic concepts (context) - Kearns, Schapire - 1993
17 A PAC analysis of a Bayesian estimator (context) - Shawe-Taylor, Williamson - 1997
3 Learning Linear Classiers - Theory and Algorithms (context) - Herbrich - 2000
3 Boosting the margin: A new explanation for the eectiveness .. (context) - Schapire, Freund et al. - 1997

The graph only includes citing articles where the year of publication is known.

Documents on the same site (http://www.research.microsoft.com/users/rherb/herbrich-conference.htm): More
From Margin To Sparsity - Graepel, Herbrich, Williamson (2001) (Correct)
The Kernel Gibbs Sampler - Graepel, Herbrich (2001) (Correct)
Large Scale Bayes Point Machines - Herbrich, Graepel (2001) (Correct)

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