From Risk to Uncertainty: Generating Predictive Uncertainty Measures via Bayesian Estimation
Nikita Kotelevskii Vladimir Kondratyev Martin Takáč Eric Moulines Maxim Panov
There are various measures of predictive uncertainty in the literature, but their relationships to each other remain unclear. This paper uses a decomposition of statistical pointwise risk into components associated with different sources of predictive uncertainty: namely, aleatoric uncertainty (inherent data variability) and epistemic uncertainty (model-related uncertainty). Together with Bayesian methods applied as approximations, we build a framework that allows one to generate different predictive uncertainty measures.

We validate measures, derived from our framework on image datasets by evaluating its performance in detecting out-of-distribution and misclassified instances using the AUROC metric. The experimental results confirm that the measures derived from our framework are useful for the considered downstream tasks.
Uncertainty quantification, Bayesian methods, Statistics
We show, how one can get predictive uncertainty measures using Bayesian approximations of statistical risk.