Multi-resolution Multi-task Gaussian Processes

Abstract

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.

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• Multi-Fidelity High-Order Gaussian Processes for Physical Simulation
• Beyond the Mean-Field: Structured Deep Gaussian Processes Improve the Predictive Uncertainties
• Using Distance Correlation for Efficient Bayesian Optimization
• Deconditional Downscaling with Gaussian Processes