  The Multi-Output Gaussian Process is is a popular tool for modelling data
from multiple sources. A typical choice to build a covariance function for a
MOGP is the Linear Model of Coregionalization (LMC) which parametrically models
the covariance between outputs. The Latent Variable MOGP (LV-MOGP) generalises
this idea by modelling the covariance between outputs using a kernel applied to
latent variables, one per output, leading to a flexible MOGP model that allows
efficient generalization to new outputs with few data points. Computational
complexity in LV-MOGP grows linearly with the number of outputs, which makes it
unsuitable for problems with a large number of outputs. In this paper, we
propose a stochastic variational inference approach for the LV-MOGP that allows
mini-batches for both inputs and outputs, making computational complexity per
training iteration independent of the number of outputs.
