  Local approximations are popular methods to scale Gaussian processes (GPs) to
big data. Local approximations reduce time complexity by dividing the original
dataset into subsets and training a local expert on each subset. Aggregating
the experts' prediction is done assuming either conditional dependence or
independence between the experts. Imposing the \emph{conditional independence
assumption} (CI) between the experts renders the aggregation of different
expert predictions time efficient at the cost of poor uncertainty
quantification. On the other hand, modeling dependent experts can provide
precise predictions and uncertainty quantification at the expense of
impractically high computational costs. By eliminating weak experts via a
theory-guided expert selection step, we substantially reduce the computational
cost of aggregating dependent experts while ensuring calibrated uncertainty
quantification. We leverage techniques from the literature on undirected
graphical models, using sparse precision matrices that encode conditional
dependencies between experts to select the most important experts. Moreov
