Elements of computer algebra with applications
Elements of computer algebra with applications
Learnability and the Vapnik-Chervonenkis dimension
Journal of the ACM (JACM)
Learning sparse multivariate polynomials over a field with queries and counterexamples
COLT '93 Proceedings of the sixth annual conference on Computational learning theory
An introduction to computational learning theory
An introduction to computational learning theory
Bounding the Vapnik-Chervonenkis Dimension of Concept Classes Parameterized by Real Numbers
Machine Learning - Special issue on COLT '93
Complexity and real computation
Complexity and real computation
Real Computations with Fake Numbers
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
On the combinatorial and algebraic complexity of quantifier elimination
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
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We give an algorithm to PAC-learn the coeffcients 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, 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. There, multivariate polynomials are learned under the assumption that the coeffcients are independent, eventually leading to a linear programming problem. In this paper we consider the other extreme: namely, we consider the case where the coeffcients of the polynomial are (polynomial) functions of a single parameter.