Abstract
We show that there exist individual lower bounds corresponding to the upper bounds on the rate of convergence of nonparametric pattern recognition which are arbitrarily close to Yang’s minimax lower bounds, if the a posteriori probability function is in the classes used by Stone and others. The rates equal to the ones on the corresponding regression estimation problem. Thus for these classes classification is not easier than regression estimation either in individual sense.
The author’s work was supported by a grant from the Hungarian Academy of Sciences (MTA SZTAKI).
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
Antos, A.: Függvényosztályok tulajdonságaiés szerepe az alakfelismerésben (in Hungarian) (Properties of classes of functions and their roles in pattern recognition). M.Sc. Thesis, Technical University of Budapest, Budapest, Hungary (1995)
Antos, A., Györff, L. and Kohler, M.: Lower bounds on the rate of convergence of nonparametric regression estimates. Preprint No. 98-11 (1998), Universität Stuttgart. Submitted
Antos, A. and Lugosi, G.: Strong minimax lower bounds for learning. Machine Learning 30 (1998) 31–56
Barron, A.R., Birgé, L. and Massart, P.: Risk bounds for model selection via penalization. Technical Report No. 95.54 (1995), Université Paris Sud. To appear in Probability Theory and Related Fields
Birgé, L.: On estimating a density using Hellinger distance and some other strange facts. Probability Theory and Related Fields 71 (1986) 271–291
Devroye, L., Györff, L. and Lugosi, G.: A Probabilistic Theory of Pattern Recognition Springer Verlag (1996)
Mammen, E. and Tsybakov, A. B.: Smooth discrimination analysis. Submitted
Stone, C. J.: Consistent nonparametric regression. Annals of Statistics 5 (1977) 595–645
Stone, C. J.: Optimal global rates of convergence for nonparametric regression. Annals of Statistics 10 (1982) 1040–1053
Yang, Y.: Minimax nonparametric classification Part I: Rates of convergence. Submitted
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Antos, A. (1999). Lower Bounds on the Rate of Convergence of Nonparametric Pattern Recognition. In: Fischer, P., Simon, H.U. (eds) Computational Learning Theory. EuroCOLT 1999. Lecture Notes in Computer Science(), vol 1572. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49097-3_19
Download citation
DOI: https://doi.org/10.1007/3-540-49097-3_19
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-65701-9
Online ISBN: 978-3-540-49097-5
eBook Packages: Springer Book Archive