  In this tutorial we explain the inference procedures developed for the sparse
Gaussian process (GP) regression and Gaussian process latent variable model
(GPLVM). Due to page limit the derivation given in Titsias (2009) and Titsias &
Lawrence (2010) is brief, hence getting a full picture of it requires
collecting results from several different sources and a substantial amount of
algebra to fill-in the gaps. Our main goal is thus to collect all the results
and full derivations into one place to help speed up understanding this work.
In doing so we present a re-parametrisation of the inference that allows it to
be carried out in parallel. A secondary goal for this document is, therefore,
to accompany our paper and open-source implementation of the parallel inference
scheme for the models. We hope that this document will bridge the gap between
the equations as implemented in code and those published in the original
papers, in order to make it easier to extend existing work. We assume prior
knowledge of Gaussian processes and variational inference, but we also include
references for further reading where appropriate.
