Estimating the support of a high-dimensional distribution

Citation
B. Scholkopf et al., Estimating the support of a high-dimensional distribution, NEURAL COMP, 13(7), 2001, pp. 1443-1471
Citations number
50
Categorie Soggetti
Neurosciences & Behavoir","AI Robotics and Automatic Control
Journal title
NEURAL COMPUTATION
ISSN journal
08997667 → ACNP
Volume
13
Issue
7
Year of publication
2001
Pages
1443 - 1471
Database
ISI
SICI code
0899-7667(200107)13:7<1443:ETSOAH>2.0.ZU;2-8
Abstract
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.