SV estimation of a distribution’s support

Suppose you are given some dataset drawn from an underlying probability distribution È and you want to estimate a subset Ë of input space such that the probability that a test point drawn from È lies outside of Ë is bounded by some a priori specified ¼ ½. We propose an algorithm which approaches this problem by trying to estimate a function which is positive on Ë and negative on the complement. The functional form of 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 algorithm is a natural extension of the support vector algorithm to the case of unlabelled data.