Learning from approximate data

Abstract

We give an algorithm to PAC-learn the coecients of a mul-tivariate polynomial from the signs of its values, over a sample of real points which are only known approximately. While there are several p-pers dealing with PAC-learning polynomials (e.g. [3,11]), they mainly only consider variables over nite elds or real variables with no round-o error. In particular, to the best of our knowledge, the only other work considering rounded-o real data is that of Dennis Cheung [6]. There, multivariate polynomials are learned under the assumption that the co-ecients are independent, eventually leading to a linear programming problem. In this paper we consider the other extreme: namely, we consider the case where the coecients of the polynomial are (polynomial) functions of a single parameter.