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Bayesian classification with Gaussian processes

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2 Author(s)
Williams, C.K.I. ; Dept. of Artificial Intelligence, Edinburgh Univ., UK ; Barber, D.

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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Pattern Analysis and Machine Intelligence, IEEE Transactions on  (Volume:20 ,  Issue: 12 )