Bayesian Classification With Gaussian Processes

Authors:
Christopher K. I. Williams;David Barber
Affiliations:
Univ. of Edinburgh, Edinburgh, Scotland, UK;Univ. of Nijmegen, Nijmegen, The Netherlands
Venue:
IEEE Transactions on Pattern Analysis and Machine Intelligence
Year:
1998

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Abstract

We consider the problem of assigning an input vector to one of m classes by predicting P(c|${\schmi x}$) for c = 1, ..., m. For a two-class problem, the probability of class one given ${\schmi x}$ is estimated by 驴(y(${\schmi x}$)), where 驴(y) = 1/(1 + e驴y). A Gaussian process prior is placed on y(${\schmi x}$), and is combined with the training data to obtain predictions for new ${\schmi x}$ 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.