Learning from rounded-off data

Authors:
Dennis Cheung;Felipe Cucker
Affiliations:
Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong;Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong
Venue:
Information and Computation
Year:
2003

Citing 5
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On the computational complexity and geometry of the first-order theory of the reals. Par I: Introduction. Preliminaries. The geometry of semi-algebraic sets. The decision problem for the existential theory of the reals

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An introduction to computational learning theory

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Bounding the Vapnik-Chervonenkis Dimension of Concept Classes Parameterized by Real Numbers

Machine Learning - Special issue on COLT '93

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Abstract

We provide an algorithm to PAC learn multivariate polynomials with real coefficients. The instance space from which labeled samples are drawn is RN but the coordinates of such samples are known only approximately. The algorithm is iterative and the main ingredient of its complexity, the number of iterations it performs, is estimated using the condition number of a linear programming problem associated to the sample. To the best of our knowledge, this is the first study of PAC learning concepts parameterized by real numbers from approximate data.