  We are concerned with obtaining well-calibrated output distributions from
regression models. Such distributions allow us to quantify the uncertainty that
the model has regarding the predicted target value. We introduce the novel
concept of distribution calibration, and demonstrate its advantages over the
existing definition of quantile calibration. We further propose a post-hoc
approach to improving the predictions from previously trained regression
models, using multi-output Gaussian Processes with a novel Beta link function.
The proposed method is experimentally verified on a set of common regression
models and shows improvements for both distribution-level and quantile-level
calibration.
