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Neural Computation

July 1, 2001, Vol. 13, No. 7, Pages 1443-1471
(doi: 10.1162/089976601750264965)
© 2001 Massachusetts Institute of Technology
Estimating the Support of a High-Dimensional Distribution
Article PDF (1.43 MB)

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.