  To use machine learning in high stakes applications (e.g. medicine), we need
tools for building confidence in the system and evaluating whether it is
reliable. Methods to improve model reliability often require new learning
algorithms (e.g. using Bayesian inference to obtain uncertainty estimates). An
alternative is to audit a model after it is trained. In this paper, we describe
resampling uncertainty estimation (RUE), an algorithm to audit the pointwise
reliability of predictions. Intuitively, RUE estimates the amount that a
prediction would change if the model had been fit on different training data.
The algorithm uses the gradient and Hessian of the model's loss function to
create an ensemble of predictions. Experimentally, we show that RUE more
effectively detects inaccurate predictions than existing tools for auditing
reliability subsequent to training. We also show that RUE can create predictive
distributions that are competitive with state-of-the-art methods like Monte
Carlo dropout, probabilistic backpropagation, and deep ensembles, but does not
depend on specific algorithms at train-time like these methods do.
