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. [3,11]), they mainly only consider variables over finite fields or real variables with no roundoff 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 paper we consider the other extreme: namely, we consider the case where the coefficients of the polynomial are (polynomial) functions of a single parameter.
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H.C., S.C. (2000). Learning from Approximate Data. In: Du, DZ., Eades, P., Estivill-Castro, V., Lin, X., Sharma, A. (eds) Computing and Combinatorics. COCOON 2000. Lecture Notes in Computer Science, vol 1858. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44968-X_40
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DOI: https://doi.org/10.1007/3-540-44968-X_40
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