  Gaussian processes (GPs), or distributions over arbitrary functions in a
continuous domain, can be generalized to the multi-output case: a linear model
of coregionalization (LMC) is one approach. LMCs estimate and exploit
correlations across the multiple outputs. While model estimation can be
performed efficiently for single-output GPs, these assume stationarity, but in
the multi-output case the cross-covariance interaction is not stationary. We
propose Large Linear GP (LLGP), which circumvents the need for stationarity by
inducing structure in the LMC kernel through a common grid of inputs shared
between outputs, enabling optimization of GP hyperparameters for
multi-dimensional outputs and low-dimensional inputs. When applied to synthetic
two-dimensional and real time series data, we find our theoretical improvement
relative to the current solutions for multi-output GPs is realized with LLGP
reducing training time while improving or maintaining predictive mean accuracy.
Moreover, by using a direct likelihood approximation rather than a variational
one, model confidence estimates are significantly improved.
