Theory of linear and integer programming
Theory of linear and integer programming
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
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
Condition numbers for polyhedra with real number data
Operations Research Letters
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We provide an algorithm to PAC learn multivariate polynomials with real coefficients. The instance space from which labeled samples are drawn is IRN 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.