Learning from rounded-off data

We provide an algorithm to PAC learn multivariate polynomials with real coefficients. The instance space from which labeled samples are drawn is ℝ^V 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.