Calibrated and Sharp Uncertainties in Deep Learning via Simple Density Estimation

Predictive uncertainties can be characterized by two properties--calibration and sharpness. This paper argues for reasoning about uncertainty in terms these properties and proposes simple algorithms for enforcing them in deep learning. Our methods focus on the strongest notion of calibration--distribution calibration--and enforce it by fitting a low-dimensional density or quantile function with a neural estimator. The resulting approach is much simpler and more broadly applicable than previous methods across both classification and regression. Empirically, we find that our methods improve predictive uncertainties on several tasks with minimal computational and implementation overhead. Our insights suggest simple and improved ways of training deep learning models that lead to accurate uncertainties that should be leveraged to improve performance across downstream applications.