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Estimating the Support of a High-Dimensional Distribution

Estimating the Support of a High-Dimensional Distribution
Estimating the Support of a High-Dimensional Distribution
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.
1443-1471
Sch"olkopf, B.
054f1e13-e210-4def-a083-72100a953a6c
Platt, J.C.
505163ae-8890-4ae4-add5-2e0ec29077ec
Shawe-Taylor, J.S.
455c50d6-e793-4695-8808-ee67a1d29e0b
Smola, A.J.
86322260-e1c1-43ab-b415-e003c18a2fe0
Williamson, R.C.
d25ad96f-f423-4edd-ad48-d47dc90cec89
Sch"olkopf, B.
054f1e13-e210-4def-a083-72100a953a6c
Platt, J.C.
505163ae-8890-4ae4-add5-2e0ec29077ec
Shawe-Taylor, J.S.
455c50d6-e793-4695-8808-ee67a1d29e0b
Smola, A.J.
86322260-e1c1-43ab-b415-e003c18a2fe0
Williamson, R.C.
d25ad96f-f423-4edd-ad48-d47dc90cec89

Sch"olkopf, 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), 1443-1471.

Record type: Article

Abstract

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

Identifiers

Local EPrints ID: 259007
URI: http://eprints.soton.ac.uk/id/eprint/259007
PURE UUID: 3c8f4a3f-0182-40e9-a9d8-64d071cd00ff

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Date deposited: 05 Mar 2004
Last modified: 16 Dec 2019 20:45

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Contributors

Author: B. Sch"olkopf
Author: J.C. Platt
Author: J.S. Shawe-Taylor
Author: A.J. Smola
Author: R.C. Williamson

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