On the good reliability of an interval-based metric to validate prediction uncertainty for machine learning regression tasks

TL;DR

This paper proposes an interval-based metric, PICP, for more reliable validation of prediction uncertainty in machine learning regression, especially in heavy-tailed distributions, outperforming variance-based metrics in speed and reliability.

Contribution

It introduces the PICP metric as a more robust alternative to variance-based calibration metrics for prediction uncertainty validation.

Findings

Student's-t distribution models z-scores well

Simple 2-sigma rule estimates 95% intervals for ν>3

PICP tests more datasets than ZMS

Abstract

This short study presents an opportunistic approach to a (more) reliable validation method for prediction uncertainty average calibration. Considering that variance-based calibration metrics (ZMS, NLL, RCE...) are quite sensitive to the presence of heavy tails in the uncertainty and error distributions, a shift is proposed to an interval-based metric, the Prediction Interval Coverage Probability (PICP). It is shown on a large ensemble of molecular properties datasets that (1) sets of z-scores are well represented by Student's-$t(\nu)$ distributions, $\nu$ being the number of degrees of freedom; (2) accurate estimation of 95 $\%$ prediction intervals can be obtained by the simple $2\sigma$ rule for $\nu>3$; and (3) the resulting PICPs are more quickly and reliably tested than variance-based calibration metrics. Overall, this method enables to test 20 $\%$ more datasets than ZMS testing. Conditional calibration is also assessed using the PICP approach.