Estimating the support of a high-dimensional distribution

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.