Variational Inference in Sparse Gaussian Process Regression and Latent Variable Models - a Gentle Tutorial
It addresses the complexity and gaps in existing derivations for researchers and practitioners working with these models, making it easier to extend and apply them, though it is incremental as it primarily consolidates and clarifies prior work.
This tutorial compiles and explains the inference procedures for sparse Gaussian process regression and Gaussian process latent variable models, providing full derivations and a re-parametrization that enables parallel inference to aid understanding and implementation.
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.