Towards calibrated and scalable uncertainty representations for neural networks

For many applications it is critical to know the uncertainty of a neural network's predictions. While a variety of neural network parameter estimation methods have been proposed for uncertainty estimation, they have not been rigorously compared across uncertainty measures. We assess four of these parameter estimation methods to calibrate uncertainty estimation using four different uncertainty measures: entropy, mutual information, aleatoric uncertainty and epistemic uncertainty. We evaluate the calibration of these parameter estimation methods using expected calibration error. Additionally, we propose a novel method of neural network parameter estimation called RECAST, which combines cosine annealing with warm restarts with Stochastic Gradient Langevin Dynamics, capturing more diverse parameter distributions. When benchmarked against mutilated image data, we show that RECAST is well-calibrated and when combined with predictive entropy and epistemic uncertainty it offers the best calibrated measure of uncertainty when compared to recent methods.