  We consider evidence integration from potentially dependent observation
processes under varying spatio-temporal sampling resolutions and noise levels.
We develop a multi-resolution multi-task (MRGP) framework while allowing for
both inter-task and intra-task multi-resolution and multi-fidelity. We develop
shallow Gaussian Process (GP) mixtures that approximate the difficult to
estimate joint likelihood with a composite one and deep GP constructions that
naturally handle biases in the mean. By doing so, we generalize and outperform
state of the art GP compositions and offer information-theoretic corrections
and efficient variational approximations. We demonstrate the competitiveness of
MRGPs on synthetic settings and on the challenging problem of hyper-local
estimation of air pollution levels across London from multiple sensing
modalities operating at disparate spatio-temporal resolutions.
