  This paper considers the generation of prediction intervals (PIs) by neural
networks for quantifying uncertainty in regression tasks. It is axiomatic that
high-quality PIs should be as narrow as possible, whilst capturing a specified
portion of data. We derive a loss function directly from this axiom that
requires no distributional assumption. We show how its form derives from a
likelihood principle, that it can be used with gradient descent, and that model
uncertainty is accounted for in ensembled form. Benchmark experiments show the
method outperforms current state-of-the-art uncertainty quantification methods,
reducing average PI width by over 10%.
