Pseudo-marginal Bayesian inference for Gaussian process latent variable models

A Bayesian inference framework for supervised Gaussian process latent variable models is introduced. The overcomes the high correlations between variables and hyperparameters by collapsing statistical model through approximate integration of variables. Using an unbiased pseudo estimate marginal likelihood, exact hyperparameter posterior can then be explored using collapsed Gibbs sampling and, conditional on these samples, elliptical slice sampling. tested both simulated real examples. When compared with standard approach based variational inference, this leads to significant improvements in predictive accuracy quantification uncertainty, as well a deeper insight into challenges performing class models.