## Neural Computation

Suppose you are given some data set drawn from an underlying probability 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 value between 0 and 1.

We propose a method to approach this problem by trying to estimate a function *f* that is positive on *S* and negative on the complement. The functional form of *f* is given by a kernel expansion in terms of a potentially small subset of the training data; it is regularized by controlling the length of the weight vector in an associated feature space. The expansion coefficients are found by solving a quadratic programming problem, which we do by carrying out sequential optimization over pairs of input patterns. We also 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 unlabeled data.