Bayesian classification with Gaussian processes


We consider the problem of assigning an input vector to one of m classes by predicting P(c|x) for c=1,...,m. For a two-class problem, the probability of class one given x is estimated by s(y(x)), where s(y)=1/(1+e-y). A Gaussian process prior is placed on y(x), and is combined with the training data to obtain predictions for new x points. We provide a Bayesian treatment, integrating over uncertainty in y and in the parameters that control the Gaussian process prior the necessary integration over y is carried out using Laplace's approximation. The method is generalized to multiclass problems (m>2) using the softmax function. We demonstrate the effectiveness of the method on a number of datasets.

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Divisions: Aston University (General)
Additional Information: ©1998 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Uncontrolled Keywords: assigning,input vector,probability,Gaussian process,training data,predictions,Bayesian treatment prior,uncertainty,Laplace,approximation,multi-class problems,softmax function
Publication ISSN: 1939-3539
Last Modified: 14 Jun 2024 07:07
Date Deposited: 05 Oct 2009 11:49
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Related URLs: http://ieeexplo ... &isnumber=15842 (Publisher URL)
PURE Output Type: Article
Published Date: 1998-12-12
Authors: Williams, Christopher K. I.
Barber, David



Version: Published Version

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