  Distributed Gaussian processes (DGPs) are prominent local approximation
methods to scale Gaussian processes (GPs) to large datasets. Instead of a
global estimation, they train local experts by dividing the training set into
subsets, thus reducing the time complexity. This strategy is based on the
conditional independence assumption, which basically means that there is a
perfect diversity between the local experts. In practice, however, this
assumption is often violated, and the aggregation of experts leads to
sub-optimal and inconsistent solutions. In this paper, we propose a novel
approach for aggregating the Gaussian experts by detecting strong violations of
conditional independence. The dependency between experts is determined by using
a Gaussian graphical model, which yields the precision matrix. The precision
matrix encodes conditional dependencies between experts and is used to detect
strongly dependent experts and construct an improved aggregation. Using both
synthetic and real datasets, our experimental evaluations illustrate that our
new method outperforms other state-of-the-art (SOTA) DGP approaches while being
substantially more time-efficient than SOTA approaches, which build on
independent experts.
