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

Pascal Pernot

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

Pascal Pernot

Machine Learning · Submitted 23 Aug 2024

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Overall, this method enables to test 20 $\%$ more datasets than ZMS testing.

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arXiv ID2408.13089 (version 2)

Pith IDWAEVOC4W, Pith's permanent record of this paper and its review

CitationPascal Pernot. "On the good reliability of an interval-based metric to validate prediction uncertainty for machine learning regression tasks." arXiv:2408.13089 (2024). https://pith.science/paper/WAEVOC4W

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.22 · human participants 0.02 · controlled comparison 0.55 · randomized assignment 0.02 · states quantitative result 0.97 · compares with prior results 0.91 · mentions code or data availability 0.03.

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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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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	This short study presents an opportunistic approach to a (more) reliable validation method for prediction uncertainty average calibration.	contribution 1.00	0.75	0.10	asserted 0.81
s1	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).	contribution 0.45	0.34	0.10	asserted 0.82
s2	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.	result 0.99	0.91	0.63	asserted 1.00
s3	Overall, this method enables to test 20 $\%$ more datasets than ZMS testing.	result 0.95	0.89	0.28	asserted 1.00
s4	Conditional calibration is also assessed using the PICP approach.	contribution 0.78	0.88	0.05	asserted 0.98

What kind of paper the classifier reports this is: method or tool 0.90 · evidence from analysis of existing data 0.81.

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Original 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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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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Contests 1 paper

For the latter, the post-hoc polynomial transformation used by Jacobs et al. [ref] has not been fully efficient to ensure calibration.

Machine Learning Materials Properties with Accurate Predictions, Uncertainty Estimates, Domain Guidance, and Persistent Online Accessibility · Conclusions · contest 0.79

Uses data or values from 1 paper

Jacobs et al. [ref] published an ensemble of 33 datasets of ML materials properties, with predictions by random forest models.

Machine Learning Materials Properties with Accurate Predictions, Uncertainty Estimates, Domain Guidance, and Persistent Online Accessibility · Application · 0.98

Compares with 1 paper

After checking the Student's distribution hypothesis for z-scores, the PICP analysis is performed and compared to the results for ZMS reported in the Appendix of Ref. [ref] .

Negative impact of heavy-tailed uncertainty and error distributions on the reliability of calibration statistics for machine learning regression tasks · Application · 0.91

Cites as background 1 paper

Assuming that $Z$ has a unit-variance Student's-$t$ distribution with $ν$ degrees of freedom ($Z∼t_s(ν)$), $Z^2$ has a unit-variance Fisher-Snedecor distribution [ref] with degrees of freedom $1$ and $ν$ ($Z^2∼F_s(1,ν)$) [ref] .

Negative impact of heavy-tailed uncertainty and error distributions on the reliability of calibration statistics for machine learning regression tasks · Shape of $Z$ distributions · 0.84

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