Gaussian processes are non-parametric models that can be used to carryout supervised and unsupervised learning tasks. As they are non-parametricmodels, their complexity grows with the number of data instances, and asa consequence, they can be used to explain complex phenomena associatedwith the training dataset. They are also very useful to introduce a prioriknowledge in the learning problem, because the characteristics that theycan describe are given by a covariance function. Finally, these models areBayesian models, thus they allow to obtain the uncertainty of the predictionsand perform model comparison in an automated way. Despite allthese advantages, in practice Gaussian processes have certain limitations.The first one is that the computations needed to train the model are onlytractable in regression problems with Gaussian additive noise, and for anyother case they need to be approximated. The other problem is their scalability,given that the training cost is cubic with respect to the number of observeddata points N. In this master thesis, we propose a method for multiclassclassification with Gaussian processes that scales well to very largedatasets. For that, it uses the Expectation Propagation algorithm, alongwith the Fully Independent Training Conditional approximation (which introducesM N pseudo-inputs), stochastic gradients and some extra assumptionsthat reduce the training cost to O(M3). Experimental resultsshow that this method is competitive with other approaches based on variationalinference.
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