  Recently, new methods for model assessment, based on subsampling and
posterior approximations, have been proposed for scaling leave-one-out
cross-validation (LOO) to large datasets. Although these methods work well for
estimating predictive performance for individual models, they are less powerful
in model comparison. We propose an efficient method for estimating differences
in predictive performance by combining fast approximate LOO surrogates with
exact LOO subsampling using the difference estimator and supply proofs with
regards to scaling characteristics. The resulting approach can be orders of
magnitude more efficient than previous approaches, as well as being better
suited to model comparison.
