Part of Advances in Neural Information Processing Systems 12 (NIPS 1999)

*Bernhard Schölkopf, Robert C. Williamson, Alex Smola, John Shawe-Taylor, John Platt*

Suppose you are given some dataset drawn from an underlying probabil(cid:173) ity distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S equals some a priori specified l/ between 0 and 1. We propose a method to approach this problem by trying to estimate a function f which is positive on S and negative on the complement. The functional form of f is given by a kernel expansion in terms of a poten(cid:173) tially small subset of the training data; it is regularized by controlling the length of the weight vector in an associated feature space. We provide a theoretical analysis of the statistical performance of our algorithm. The algorithm is a natural extension of the support vector algorithm to the case of unlabelled data.

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