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Estimating the Support of a High-Dimensional Distribution

Schölkopf, B., Platt, J.C., Shawe-Taylor, J.S., Smola, A.J. and Williamson, R.C. (2001) Estimating the Support of a High-Dimensional Distribution Neural Computation, 13, (7), pp. 1443-1471.

Record type: Article


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.

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Published date: July 2001
Organisations: Electronics & Computer Science


Local EPrints ID: 259789
PURE UUID: 10c8cdc0-bd58-48a6-8b9c-4ff678b1be3b

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Date deposited: 17 Aug 2004
Last modified: 18 Jul 2017 09:19

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Author: B. Schölkopf
Author: J.C. Platt
Author: J.S. Shawe-Taylor
Author: A.J. Smola
Author: R.C. Williamson

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