Multi-class Semi-supervised Learning with the $\epsilon$-truncated Multinomial Probit Gaussian Process
; Gaussian Processes in Practice, PMLR 1:17-32, 2007.
Recently, the null category noise model has been proposed as a simple and elegant solution to the problem of incorporating unlabeled data into a Gaussian process (GP) classification model. In this paper, we show how this binary likelihood model can be generalised to the multi-class setting through the use of the multinomial probit GP classifier. We present a Gibbs sampling scheme for sampling the GP parameters and also derive a more efficient variational updating scheme. We find that the performance improvement is roughly consistent with that observed in binary classification and that there is no significant difference in classification performance between the Gibbs sampling and variational schemes.