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

• URL: http://arxiv.org/abs/2408.13089v2
• Date: Mon, 26 Aug 2024 06:40:07 GMT
• Title: On the good reliability of an interval-based metric to validate prediction uncertainty for machine learning regression tasks
• Authors: Pascal Pernot,
• Abstract summary: This study presents an opportunistic approach to a (more) reliable validation method for prediction uncertainty average calibration. Considering that variance-based calibration metrics 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) The resulting PICPs are more quickly and reliably tested than variance-based calibration metrics.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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