Bayesian Classiication with Gaussian Processes
reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. Abstract We consider the problem of assigning an input vector x to one of m classes by predicting P(cjx) for c = 1; : : : ; m. For a two-class problem , the probability of class 1 given x is estimated by (y(x)), where (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. 1 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 multi-class problems (m > 2) using the softmax function. We demonstrate the eeectiveness of the method on a number of datasets.