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The Gaussian process latent variable model (GP-LVM) provides a flexibleapproach for non-linear dimensionality reduction that has been widely applied.However, the current approach for training GP-LVMs is based on maximumlikelihood, where the latent projection variables are maximized over ratherthan integrated out. In this paper we present a Bayesian method for trainingGP-LVMs by introducing a non-standard variational inference framework thatallows to approximately integrate out the latent variables and subsequentlytrain a GP-LVM by maximizing an analytic lower bound on the exact marginallikelihood. We apply this method for learning a GP-LVM from iid observationsand for learning non-linear dynamical systems where the observations aretemporally correlated. We show that a benefit of the variational Bayesianprocedure is its robustness to overfitting and its ability to automaticallyselect the dimensionality of the nonlinear latent space. The resultingframework is generic, flexible and easy to extend for other purposes, such asGaussian process regression with uncertain inputs and semi-supervised Gaussianprocesses. We demonstrate our method on synthetic data and standard machinelearning benchmarks, as well as challenging real world datasets, including highresolution video data.

Variational Inference for Uncertainty on the Inputs of Gaussian Process Models