  Many real-world regression problems demand a measure of the uncertainty
associated with each prediction. Standard decision forests deliver efficient
state-of-the-art predictive performance, but high-quality uncertainty estimates
are lacking. Gaussian processes (GPs) deliver uncertainty estimates, but
scaling GPs to large-scale data sets comes at the cost of approximating the
uncertainty estimates. We extend Mondrian forests, first proposed by
Lakshminarayanan et al. (2014) for classification problems, to the large-scale
non-parametric regression setting. Using a novel hierarchical Gaussian prior
that dovetails with the Mondrian forest framework, we obtain principled
uncertainty estimates, while still retaining the computational advantages of
decision forests. Through a combination of illustrative examples, real-world
large-scale datasets, and Bayesian optimization benchmarks, we demonstrate that
Mondrian forests outperform approximate GPs on large-scale regression tasks and
deliver better-calibrated uncertainty assessments than decision-forest-based
methods.
