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Title: Learning from approximate data
Other Titles: Cong jin si zi liao xue xi
Authors: Cheung, Hung Ching (張紅靖)
Department: Dept. of Mathematics
Degree: Master of Philosophy
Issue Date: 2000
Publisher: Dept. of Mathematics, City University of Hong Kong
Subjects: Approximation theory
Notes: 37 leaves ; 30 cm.
CityU Call Number: QA221.C48 2000
Includes bibliographical references (leaves 36-37)
Thesis (M.Phil.)--City University of Hong Kong, 2000
Type: Thesis
Abstract: We give an algorithm to PAC learn the coefficients of a multivariate polynomial from the signs of its values, over a sample of real points which are only known approximately. While there are several papers dealing with PAC learning polynomials (e.g. [3, II]), they mainly only consider variables over finite fields or real variables with no round-off error. In particular, to the best of our knowledge, the only other work considering rounded-off real data is that of Dennis Cheung [6]. There, multivariate polynomials are learned under the assumption that the coefficients are independent, eventually leading to a linear programming problem. In this thesis we consider the other extreme: namely, we consider the case where the coefficients of the polynomial are (polynomial) functions of a single parameter. As we shall see, this leads to solving a non-linear system of polynomial inequalities in one variable. Our algorithm does so in a number of operations which is polynomial in the data size and the logarithm of the condition of the sample.
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