  Zero-inflated datasets, which have an excess of zero outputs, are commonly
encountered in problems such as climate or rare event modelling. Conventional
machine learning approaches tend to overestimate the non-zeros leading to poor
performance. We propose a novel model family of zero-inflated Gaussian
processes (ZiGP) for such zero-inflated datasets, produced by sparse kernels
through learning a latent probit Gaussian process that can zero out kernel rows
and columns whenever the signal is absent. The ZiGPs are particularly useful
for making the powerful Gaussian process networks more interpretable. We
introduce sparse GP networks where variable-order latent modelling is achieved
through sparse mixing signals. We derive the non-trivial stochastic variational
inference tractably for scalable learning of the sparse kernels in both models.
The novel output-sparse approach improves both prediction of zero-inflated data
and interpretability of latent mixing models.
