  We introduce a Bayesian Gaussian process latent variable model that
explicitly captures spatial correlations in data using a parameterized spatial
kernel and leveraging structure-exploiting algebra on the model covariance
matrices for computational tractability. Inference is made tractable through a
collapsed variational bound with similar computational complexity to that of
the traditional Bayesian GP-LVM. Inference over partially-observed test cases
is achieved by optimizing a "partially-collapsed" bound. Modeling
high-dimensional time series systems is enabled through use of a dynamical GP
latent variable prior. Examples imputing missing data on images and
super-resolution imputation of missing video frames demonstrate the model.
