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In this tutorial we explain the inference procedures developed for the sparseGaussian 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 requirescollecting results from several different sources and a substantial amount ofalgebra to fill-in the gaps. Our main goal is thus to collect all the resultsand 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 tobe carried out in parallel. A secondary goal for this document is, therefore,to accompany our paper and open-source implementation of the parallel inferencescheme for the models. We hope that this document will bridge the gap betweenthe equations as implemented in code and those published in the originalpapers, in order to make it easier to extend existing work. We assume priorknowledge of Gaussian processes and variational inference, but we also includereferences for further reading where appropriate.

Variational Inference in Sparse Gaussian Process Regression and Latent Variable Models - a Gentle Tutorial