Near-Optimal Active Learning of Multi-Output Gaussian Processes

This paperaddresses the problem of active learning of a multi-output Gaussian process (MOGP) model repre-senting multiple types of coexisting correlated environ-mental phenomena. In contrast to existing works, our active learning problem involves selecting not just the most informative sampling locations to be observed but also the types of measurements at each selected location for minimizing the predictive uncertainty (i.e., posterior joint entropy) of a target phenomenon of interest given a sampling budget. Unfortunately, such an entropy crite-rion scales poorly in the numbers of candidate sampling locations and selected observations when optimized. To resolve this issue, we first exploit a structure common to sparse MOGP models for deriving a novel active learn-ing criterion. Then, we exploit a relaxed form of sub-modularity property of our new criterion for devising a polynomial-time approximation algorithm that guar-antees a constant-factor approximation of that achieved by the optimal set of selected observations. Empirical evaluation on real-world datasets shows that our pro-posed approach outperforms existing algorithms for ac-tive learning of MOGP and single-output GP models.