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.


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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.

Item Type: Article
Organisations: Electronics & Computer Science
ePrint ID: 259789
Date :
Date Event
July 2001Published
Date Deposited: 17 Aug 2004
Last Modified: 17 Apr 2017 22:24
Further Information:Google Scholar

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