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Bayesian Classification with Gaussian Processes

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Original languageEnglish
Pages (from-to)1342-1351
Number of pages10
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Issue number12
Publication statusPublished - Dec 1998


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 σ(y(x)), where σ(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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