Universal algorithms for learning theory. Part II: Piecewise polynomial functions

Constructive Approximation

Volumn 26, Issue 2, 2007, Pages 127-152

  Binev, Peter ^a   Cohen, Albert ^b   Dahmen, Wolfgang ^c   Devore, Ronald ^a  

^a UNIVERSITY OF SOUTH CAROLINA   (United States)

^b UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

^c RWTH AACHEN UNIVERSITY   (Germany)

Author keywords

Adaptive methods; Distribution free; Learning theory; Optimal rates

Indexed keywords

EID: 34547472681     PISSN: 01764276     EISSN: 14320940     Source Type: Journal    
DOI: 10.1007/s00365-006-0658-z     Document Type: Article

References (9)

1. P. BINEV, A. COHEN, W. DAHMEN, R. DEVORE, V. TEMLYAKOV (2005): Universal algorithms in learning theory - Part I: Piecewise constant functions. J. Mach. Learn. Res., 6:1297-1321.
2. C. BENNETT, R. SHARPLEY (1988): Interpolation of Operators. Pure and Applied Mathematics, Vol. 129. New York: Academic Press.
3. L. BREIMAN, J. H. FRIEDMAN, R. A. OLSHEN, C. J. STONE (1984): Classification and Regression Trees. Belmont, CA: Wadsworth International.
4. A. COHEN, W. DAHMEN, I. DAUBECHIES, R. DEVORE (2001): Tree-structured approximation and optimal encoding. Appl. Comput. Harmonic Anal., 11:192-226.
5. A. COHEN, R. DEVORE, G. KERKYACHARIAN, D. PICARD (2001): Maximal spaces with given rate of convergence for thresholding algorithms. Appl. Comput. Harmonic Anal., 11:167-191.
6. R. DEVORE, G. KERKYACHARIAN, D. PICARD, V. TEMLYAKOV (2006): Mathematical methods for supervised learning. Found. Comput. Math., 6:3-58.
7. D. L. DONOHO (1997): CART and best-ortho-basis: A connection. Ann. Statist., 25:1870-1911.
8. L. GYÖRFI, M. KOHLER, A. KRZYZAK, H. WALK (2002): A Distribution-Free Theory of Nonparametric Regression. Berlin: Springer-Verlag.
9. V. TEMLYAKOV (2005): Approximation in learning theory. IMI preprints 05:05. University of South. Carolina, pp. 1-42.