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Function Learning from Interpolation 1 Produced as Part of the Esprit Working Group in Neural and Computational Learning, Neurocolt 8556

In this paper, we study a statistical property of classes of real-valued functions that we call approximation from interpolated examples. We derive a characterization of function classes that have this property, in terms of their`fat-shattering function', a notion that has proven useful in computational learning theory. We discuss the implications for function learning of approximation from interpolated examples. Speciically, it can be interpreted as a problem of learning real-valued functions from random examples in which we require satisfactory performance from every algorithm that returns a function which approximately interpolates the training examples.