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.

本文提出了一种解决多输出高斯过程模型主类型和相关环境现象多种共存的主动学习问题的方法，该问题涉及选择最具信息量的采样位置和每个位置的测量类型，以在预算范围内最小化目标感兴趣的预测不确定性（即后验联合熵），为了解决优化时的问题，我们利用了稀疏 MOGP 模型的常见结构，推导出一种新的主动学习准则，并利用新准则的放松形式子模性质，设计了一种多项式时间近似算法，实证评估表明我们的方法优于 MOGP 和单输出 GP 模型的现有算法。