Suppose you are given some data set drawn from an underlying probability di
stribution P and you want to estimate a "simple" subset S of input space su
ch that the probability that a test point drawn from P lies outside of S eq
uals some a priori specified value between 0 and 1.
We propose a method to approach this problem by trying to estimate a functi
on f that is positive on S and negative on the complement. The functional f
orm of f is given by a kernel expansion in terms of a potentially small sub
set of the training data; it is regularized by controlling the length of th
e weight vector in an associated feature space. The expansion coefficients
are found by solving a quadratic programming problem, which we do by carryi
ng out sequential optimization over pairs of input patterns. We also provid
e 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.