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Abstract: We prove upper and lower bounds on the VC dimension of sparse univariate polynomials over reals, and apply these results to prove uniform learnability of sparse polynomials and rational functions. As another application we solve an open problem of Vapnik ([Vapnik 82]) on uniform approximation of the general regression functions, a central problem of computational statistics (cf. [Vapnik 82]), p. 256). Department of Computer Science, University of Bonn, and International Computer Science... (Update)
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.... Approximative unbound interpolation arises also naturally in issues of computational learnability of sparse rational functions (cf. [21]) The present authors have previously studied the problem of interpolation of rational functions in [10] but the algorithm presented...
.... Approximative unbound interpolation arises also naturally in issues of computational learnability of sparse rational functions (cf. [20]) The present authors have previously studied the problem of interpolation of rational functions in [10] but the algorithm presented...
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BibTeX entry: (Update)
Karpinski, M. and Werther, T., VC Dimension and Learnability of Sparse Polynomials and Rational Functions, University of Bonn (1989), Research Report No. 8537-CS. http://citeseer.ist.psu.edu/karpinski89vc.html More
@techreport{ karpinski89vc,
author = "Marek Karpinski and Thorsten Werther",
title = "{VC} Dimension and Learnability of Sparse Polynomials and Rational Functions",
number = "8537-CS",
year = "1989",
url = "citeseer.ist.psu.edu/karpinski89vc.html" }
Citations (may not include all citations):537 A Theory of the Learnable (context) - Valiant - 1984
454 the Uniform Convergence of Relative Frequencies of Events an.. (context) - Vapnik, Chervonenkis - 1971
348 Estimation of Dependences Based on Empirical Data (context) - Vapnik - 1982
318 Convergence of Stochastic Processes (context) - Pollard - 1984
184 Cryptographic Limitations on Learning Boolean Formulae and F.. - Kearns, Valiant - 1989
38 A Deterministic Algorithm for Sparse Multivariate Polynomial.. (context) - Ben-Or, Tiwari - 1988
35 Fast Parallel Algorithms for Sparse Multivariate Polynomial .. (context) - Grigoriev, Yu et al. - 1988
21 The Matching Problem for Bipartite Graphs with Polynomially .. (context) - Grigoriev, Yu - 1987
18 the Decidability of Sparse Univariate Polynomial Interpolati.. (context) - Borodin, Tiwari - 1989
18 Inductive Principles of the Search for Empirical Dependences (context) - Vapnik - 1989
12 Space-Bounded Learning and the Vapnik-Chervonenkis Dimension (context) - Floyd - 1989
2 Generalizing the PAC Model: Sample Size Bounds From Metric D.. (context) - Hausler - 1989
2 UC Santa Cruz (context) - Blumer, Ehrenfeucht et al. - 1987
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