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Estimating the Support of a High-Dimensional Distribution (1999)
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| Citations: | 781 - 29 self |
BibTeX
@MISC{Schölkopf99estimatingthe,
author = {Bernhard Schölkopf and John C. Platt and John Shawe-taylor and Alex J. Smola and Robert C. Williamson},
title = {Estimating the Support of a High-Dimensional Distribution},
year = {1999}
}
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Abstract
Suppose you are given some dataset 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 is bounded by some a priori specified between 0 and 1. We propose a method to approach this problem by trying to estimate a function f which 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 preliminary theoretical analysis of the statistical performance of our algorithm. The algorithm is a natural extension of the support vector algorithm to the case of unlabelled d...
Keyphrases
high-dimensional distribution preliminary theoretical analysis statistical performance training data underlying probability distribution sequential optimization kernel expansion associated feature space input pattern expansion coefficient quadratic programming problem functional form natural extension weight vector support vector algorithm input space small subset test point drawn
