Abstract
We would like here to complement the analysis of Vapnik–Chervonenkis bounds made by L. Bottou in Chap. 9 and by K.V. Vorontsov in (Comput Math Math Phys 44(11):1997–2009, 2004, Pattern Recognit Image Anal 18(2):243–259, 2008, Pattern Recognit Image Anal 20(3):269–285, 2010), pointing out the connections with transductive PAC-Bayes bounds (The Thermodynamics of Statistical Learning, 2007, McAllester, Proceedings of the 11th Annual Conference on Computational Learning Theory, 1998, McAllester, Proceedings of the 12th Annual Conference on Computational Learning Theory, 1999) as another way to come to the same kind of conclusions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Catoni, O.: PAC-Bayesian Supervised Classification: The Thermodynamics of Statistical Learning. IMS Lecture Notes Monograph Series, vol. 56. Institute of Mathematical Statistics (2007)
McAllester, D.A.: Some PAC-Bayesian theorems. In: Proceedings of the 11th Annual Conference on Computational Learning Theory, pp. 164–170 (1998)
McAllester, D.A.: PAC-Bayesian model averaging. In: Proceedings of the 12th Annual Conference on Computational Learning Theory, pp. 230–234 (1999)
Vapnik, V.: Estimation of Dependences Based on Empirical Data. Springer, Berlin (1982)
Vapnik, V., Chervonenkis, A.: On the uniform convergence of relative frequencies of events to their probabilities. Theory Probab. Appl. 16(2), 264–280 (1971) (This volume, Chap. 3)
Vorontsov, K.V.: Combinatorial substantiation of learning algorithms. Comput. Math. Math. Phys. 44(11), 1997–2009 (2004)
Vorontsov, K.V.: Combinatorial probability and the tightness of generalization bounds. Pattern Recognit. Image Anal. 18(2), 243–259 (2008)
Vorontsov, K.V.: Exact combinatorial bounds on the probability of overfitting for empirical risk minimization. Pattern Recognit. Image Anal. 20(3), 269–285 (2010)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Catoni, O. (2015). Comment: Transductive PAC-Bayes Bounds Seen as a Generalization of Vapnik–Chervonenkis Bounds. In: Vovk, V., Papadopoulos, H., Gammerman, A. (eds) Measures of Complexity. Springer, Cham. https://doi.org/10.1007/978-3-319-21852-6_10
Download citation
DOI: https://doi.org/10.1007/978-3-319-21852-6_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-21851-9
Online ISBN: 978-3-319-21852-6
eBook Packages: Computer ScienceComputer Science (R0)