Quantization for nonparametric regression

IEEE Transactions on Information Theory

Volumn 54, Issue 2, 2008, Pages 867-874

  Györfi, László ^a   Wegkamp, Marten ^b  

^a BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

^b FLORIDA STATE UNIVERSITY   (United States)

Author keywords

Finite sample bounds; Least squares estimates; Regression estimation with restriction; Vector quantization

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; ESTIMATION; LEAST SQUARES APPROXIMATIONS; VECTOR QUANTIZATION;

FINITE-SAMPLE BOUNDS; LEAST SQUARES ESTIMATES; REGRESSION ESTIMATION;

REGRESSION ANALYSIS;

EID: 39849110135     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2007.913565     Document Type: Article

References (10)

1. M. Anthony and P. L. Bartlett, Neural Network Learning: Theoretical Foundations. Cambridge, U.K.: Cambrige University Press, 1999.
2. A. Antos, L. Györfi, and A. György, "Individual convergence rates in empirical vector quantizer design," IEEE Trans. Inf. Theory, vol. 51, pp. 4013-4022, 2005.
3. 1 error of partitioning estimates of a regression function," in Proc. Fourth Pannonian Symp. Math. Stat., F. Konecny, J. Mogyoródi, and W. Wetz, Eds., Budapest, Hungary, 1983, pp. 67-76.
4. L. Devroye and G. Lugosi, Combinatorial Methods in Density Estimation New York: Springer-Verlag, 2001.
5. L. Györfi, "Universal consistencies of regression estimate for unbounded regression functions," in Nonparametric Functional Estimation and Related Topics, G. Roussas, Ed. Dordrecht, Germany: Kluwer Academic, 1991, pp. 329-338.
6. L. Györfi, M. Kohler, A. Krzyzak, and H. Walk, A Distribution-Free Theory of Nonparametric Regression. New York: Springer-Verlag, 2002.
7. W. S. Lee, P. L. Bartlett, and R. C. Williamson, "Efficient agnostic learning of neural networks with bounded fan-in," IEEE Trans. Inf. Theory, vol. 42, pp. 2118-2132, 1996.
8. T. Linder, G. Lugosi, and K. Zeger, "Empirical quantizer design in the presence of source noise or channel noise," IEEE Trans. Inf. Theory vol. 43, pp. 612-623, 1997.
9. D. P. Pollard, "A central limit theorem for k-means clustering," Ann. Stat., vol. 16, pp. 919-926, 1982.
10. M. H. Wegkamp, Entropy Methods in Statistical Estimation. Amsterdam, The Netherlands: CWI, 1999, vol. 25.