  A simple and widely adopted approach to extend Gaussian processes (GPs) to
multiple outputs is to model each output as a linear combination of a
collection of shared, unobserved latent GPs. An issue with this approach is
choosing the number of latent processes and their kernels. These choices are
typically done manually, which can be time consuming and prone to human biases.
We propose Gaussian Process Automatic Latent Process Selection (GP-ALPS), which
automatically chooses the latent processes by turning off those that do not
meaningfully contribute to explaining the data. We develop a variational
inference scheme, assess the quality of the variational posterior by comparing
it against the gold standard MCMC, and demonstrate the suitability of GP-ALPS
in a set of preliminary experiments.
