On the good reliability of an interval-based metric to validate prediction uncertainty for machine learning regression tasks
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910576166305792 |
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| author | Pernot, Pascal |
| author_facet | Pernot, Pascal |
| contents | 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-$t(ν)$ distributions, $ν$ being the number of degrees of freedom; (2) accurate estimation of 95 $\%$ prediction intervals can be obtained by the simple $2σ$ rule for $ν>3$; 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13089 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the good reliability of an interval-based metric to validate prediction uncertainty for machine learning regression tasks Pernot, Pascal Machine Learning 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-$t(ν)$ distributions, $ν$ being the number of degrees of freedom; (2) accurate estimation of 95 $\%$ prediction intervals can be obtained by the simple $2σ$ rule for $ν>3$; 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. |
| title | On the good reliability of an interval-based metric to validate prediction uncertainty for machine learning regression tasks |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2408.13089 |