Abstract
Transductive Confidence Machine (TCM) is a way of converting standard machine-learning algorithms into algorithms that output predictive regions rather than point predictions. It has been shown recently that TCM is well-calibrated when used in the on-line mode: at any confidence level 1 - σ, the long-run relative frequency of errors is guaranteed not to exceed σ provided the examples are generated independently from the same probability distribution P. Therefore, the number of “uncertain” predictive regions (i.e., those containing more than one label) becomes the sole measure of performance. The main result of this paper is that for any probability distribution P (assumed to generate the examples), it is possible to construct a TCM (guaranteed to be wellcalibrated even if the assumption is wrong) that performs asymptotically as well as the best region predictor under P.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bourbaki, N.: Eléments de mathématique, Livre IV, Fonctions d’une variable réelle (théorie élémentaire). 2nd edn. Hermann, Paris (1958)
Devroye, L., Györ., L., Lugosi, G.: A Probabilistic Theory of Pattern Recognition. Springer, New York (1996)
Lehmann, E.: Testing Statistical Hypotheses. Wiley, New York (1959)
Melluish, T., Saunders, C., Nouretdinov, I., Vovk, V.: Comparing the Bayes and typicalness frameworks. In: De Raedt, L., Flash, P. (eds.): Machine Learning: ECML 2001. Proceedings of the 12th European Conference on Machine Learning. Lecture Notes in Artificial Intelligence, Vol. 2167, Springer (2001) 360–371. Full version published as Technical Report CLRC-TR-01-05, Computer Learning ResearchCentre, Royal Holloway, University of London, http://www.clrc.rhul.ac.uk
Saunders, C., Gammerman, A., Vovk, V.: Transduction with confidence and credibility. In: Proceedings of the 16th International Joint Conference on Artificial Intelligence (1999) 722–726
Shiryaev, A. N.: Probability. 2nd edn. Springer, New York (1996)
Vapnik, V. N.: Statistical Learning Theory. Wiley, New York (1998)
Vovk, V., Gammerman, A., Saunders, C.: Machine-learning applications of algorithmic randomness. In: Proceedings of the 16th International Conference on Machine Learning (1999) 444–453
Vovk, V.: De-Bayesing Bayesian prediction algorithms. Manuscript (June 2000)
Vovk, V.: On-line Confidence Machines are well-calibrated. In: Proceedings of FOCS’2002. Full version published as Technical Report CLRC-TR-02-01, Computer Learning Research Centre, Royal Holloway, University of London, http://www.clrc.rhul.ac.uk (April 2002). Additional information can be found at http://www.cs.rhul.ac.uk/~vovk/cm
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Vovk, V. (2002). Asymptotic Optimality of Transductive Confidence Machine. In: Cesa-Bianchi, N., Numao, M., Reischuk, R. (eds) Algorithmic Learning Theory. ALT 2002. Lecture Notes in Computer Science(), vol 2533. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36169-3_27
Download citation
DOI: https://doi.org/10.1007/3-540-36169-3_27
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-00170-6
Online ISBN: 978-3-540-36169-5
eBook Packages: Springer Book Archive