Matrix analysis
Bayesian Classification With Gaussian Processes
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multicategory Classification by Support Vector Machines
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part I
Bayesian Learning for Neural Networks
Bayesian Learning for Neural Networks
Statistics and Computing
Sparse on-line Gaussian processes
Neural Computation
Machine Learning
On the algorithmic implementation of multiclass kernel-based vector machines
The Journal of Machine Learning Research
Pac-bayesian generalisation error bounds for gaussian process classification
The Journal of Machine Learning Research
In Defense of One-Vs-All Classification
The Journal of Machine Learning Research
ICML '06 Proceedings of the 23rd international conference on Machine learning
Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)
Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)
Bayesian Gaussian Process Classification with the EM-EP Algorithm
IEEE Transactions on Pattern Analysis and Machine Intelligence
MSVMpack: A Multi-Class Support Vector Machine Package
The Journal of Machine Learning Research
A comparison of methods for multiclass support vector machines
IEEE Transactions on Neural Networks
Nested expectation propagation for Gaussian process classification
The Journal of Machine Learning Research
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Gaussian process prior with an appropriate likelihood function is a flexible non-parametric model for a variety of learning tasks. One important and standard task is multi-class classification, which is the categorization of an item into one of several fixed classes. A usual likelihood function for this is the multinomial logistic likelihood function. However, exact inference with this model has proved to be difficult because high-dimensional integrations are required. In this paper, we propose a variational approximation to this model, and we describe the optimization of the variational parameters. Experiments have shown our approximation to be tight. In addition, we provide data-independent bounds on the marginal likelihood of the model, one of which is shown to be much tighter than the existing variational mean-field bound in the experiments. We also derive a proper lower bound on the predictive likelihood that involves the Kullback-Leibler divergence between the approximating and the true posterior. We combine our approach with a recently proposed sparse approximation to give a variational sparse approximation to the Gaussian process multi-class model. We also derive criteria which can be used to select the inducing set, and we show the effectiveness of these criteria over random selection in an experiment.