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.
|Pages (from-to)||1342 -1351|
|Number of pages||10|
|Journal||IEEE Transactions on Pattern Analysis and Machine Intelligence|
|Publication status||Published - 12 Dec 1998|
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- input vector
- Gaussian process
- training data
- Bayesian treatment prior
- multi-class problems
- softmax function