  Handling big data has largely been a major bottleneck in traditional
statistical models. Consequently, when accurate point prediction is the primary
target, machine learning models are often preferred over their statistical
counterparts for bigger problems. But full probabilistic statistical models
often outperform other models in quantifying uncertainties associated with
model predictions. We develop a data-driven statistical modeling framework that
combines the uncertainties from an ensemble of statistical models learned on
smaller subsets of data carefully chosen to account for imbalances in the input
space. We demonstrate this method on a photometric redshift estimation problem
in cosmology, which seeks to infer a distribution of the redshift -- the
stretching effect in observing the light of far-away galaxies -- given
multivariate color information observed for an object in the sky. Our proposed
method performs balanced partitioning, graph-based data subsampling across the
partitions, and training of an ensemble of Gaussian process models.
