  This paper addresses the problem of active learning of a multi-output
Gaussian process (MOGP) model representing multiple types of coexisting
correlated environmental 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 criterion 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 learning criterion. Then, we exploit a relaxed form
of submodularity property of our new criterion for devising a polynomial-time
approximation algorithm that guarantees a constant-factor approximation of that
achieved by the optimal set of selected observations. Empirical evaluation on
real-world datasets shows that our proposed approach outperforms existing
algorithms for active learning of MOGP and single-output GP models.
