Bayesian classification with Gaussian processes

Williams, Christopher K. I. and Barber, David (1997). Bayesian classification with Gaussian processes. Technical Report. Aston University, Birmingham. (Unpublished)

Abstract

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

Divisions: ?? 13770100JJ ??
Uncontrolled Keywords: assigning,input vector,probability,Gaussian process,training data,predictions,Bayesian treatment prior,uncertainty,Laplace,approximation,multi-class problems,softmax function
Published Date: 1997-12-13

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