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Validation of ML-UQ calibration statistics using simulated reference values: a sensitivity analysis (2403.00423v2)

Published 1 Mar 2024 in stat.ML, cs.LG, and physics.chem-ph

Abstract: Some popular Machine Learning Uncertainty Quantification (ML-UQ) calibration statistics do not have predefined reference values and are mostly used in comparative studies. In consequence, calibration is almost never validated and the diagnostic is left to the appreciation of the reader. Simulated reference values, based on synthetic calibrated datasets derived from actual uncertainties, have been proposed to palliate this problem. As the generative probability distribution for the simulation of synthetic errors is often not constrained, the sensitivity of simulated reference values to the choice of generative distribution might be problematic, shedding a doubt on the calibration diagnostic. This study explores various facets of this problem, and shows that some statistics are excessively sensitive to the choice of generative distribution to be used for validation when the generative distribution is unknown. This is the case, for instance, of the correlation coefficient between absolute errors and uncertainties (CC) and of the expected normalized calibration error (ENCE). A robust validation workflow to deal with simulated reference values is proposed.

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References (24)
  1. Pairwise difference regression: A machine learning meta-algorithm for improved prediction and uncertainty quantification in chemical search. J. Chem. Inf. Model., 61:3846–3857, 2021. PMID: 34347460.
  2. P. Pernot. Prediction uncertainty validation for computational chemists. J. Chem. Phys., 157:144103, 2022.
  3. Evaluating and Calibrating Uncertainty Prediction in Regression Tasks. Sensors, 22:5540, 2022.
  4. P. Pernot. Properties of the ENCE and other MAD-based calibration metrics. arXiv:2305.11905, May 2023.
  5. P. Pernot. Confidence curves for UQ validation: probabilistic reference vs. oracle. arXiv:2206.15272, June 2022.
  6. Uncertain of uncertainties? A comparison of uncertainty quantification metrics for chemical data sets. J. Cheminf., 15:1–17, December 2023.
  7. Methods for comparing uncertainty quantifications for material property predictions. Mach. Learn.: Sci. Technol., 1:025006, 2020.
  8. Evaluation of measurement data - Guide to the expression of uncertainty in measurement (GUM). Technical Report 100:2008, Joint Committee for Guides in Metrology, JCGM, 2008. URL: http://www.bipm.org/utils/common/documents/jcgm/JCGM_100_2008_F.pdf.
  9. Calibrated uncertainty for molecular property prediction using ensembles of message passing neural networks. Mach. Learn.: Sci. Technol., 3:015012, 2022.
  10. Deep Evidential Regression. arXiv:1910.02600, October 2019.
  11. Statistical Distributions. Wiley-Interscience, 3rd edition, 2000.
  12. P. Pernot. How to validate average calibration for machine learning regression tasks ? arXiv:2402.10043, February 2024. URL: https://arxiv.org/abs/2402.10043.
  13. P. Pernot. Calibration in machine learning uncertainty quantification: Beyond consistency to target adaptivity. APL Mach. Learn., 1:046121, 2023.
  14. P. Pernot. The long road to calibrated prediction uncertainty in computational chemistry. J. Chem. Phys., 156:114109, 2022.
  15. Graph neural network interatomic potential ensembles with calibrated aleatoric and epistemic uncertainty on energy and forces. Phys. Chem. Chem. Phys., 25:25828–25837, 2023.
  16. One step closer to unbiased aleatoric uncertainty estimation. arXiv:2312.10469, December 2023.
  17. Probabilistic forecasts, calibration and sharpness. J. R. Statist. Soc. B, 69:243–268, 2007.
  18. P. Pernot. Can bin-wise scaling improve consistency and adaptivity of prediction uncertainty for machine learning regression ? arXiv:2310.11978, October 2023.
  19. T. J. DiCiccio and B. Efron. Bootstrap confidence intervals. Statist. Sci., 11:189–212, 1996. URL: https://www.jstor.org/stable/2246110.
  20. Calibration after bootstrap for accurate uncertainty quantification in regression models. npj Comput. Mater., 8:115, 2022.
  21. R. A. Groeneveld and G. Meeden. Measuring skewness and kurtosis. The Statistician, 33:391–399, 1984. URL: http://www.jstor.org/stable/2987742.
  22. P. Pernot and A. Savin. Using the Gini coefficient to characterize the shape of computational chemistry error distributions. Theor. Chem. Acc., 140:24, 2021.
  23. Impact of non-normal error distributions on the benchmarking and ranking of Quantum Machine Learning models. Mach. Learn.: Sci. Technol., 1:035011, 2020.
  24. The variance of sample variance from a finite population. Int. J. Pure Appl. Math., 21:387–394, 2005. URL: http://www.ijpam.eu/contents/2005-21-3/10/10.pdf.

Summary

  • The paper demonstrates that ML-UQ calibration statistics are highly sensitive to the choice of generative distribution.
  • The paper introduces a novel workflow using synthetic error generation to validate metrics like CC and ENCE.
  • The results underscore the necessity of sensitivity analysis for ensuring reliable calibration diagnostics in predictive models.

Validation of Machine Learning Uncertainty Quantification Through Simulated Reference Values

Introduction

The assessment and validation of uncertainty in predictions made by machine learning models are fundamental aspects that ensure their reliability and applicability in real-world scenarios. Among the various tools available, calibration statistics play a critical role in the quantification and understanding of uncertainty within machine learning predictions. However, the validation of these statistics often presents challenges, primarily due to the lack of predefined reference values. This obstacle limits our ability to comprehensively assess the calibration quality of predictive models. Addressing this issue, the paper presents an analytical exploration into the validation of Machine Learning Uncertainty Quantification (ML-UQ) calibration statistics using simulated reference values, with a focus on assessing sensitivity to the choice of generative distribution.

Key Concepts and Methodology

The paper dives into the intricacies of calibration statistics lacking predefined reference values and proposes the novel use of simulated reference values created from synthetic calibrated datasets. These datasets are derived from actual uncertainties, employing a generative probability distribution, referred to as DD, to simulate synthetic errors. The main thrust of the paper revolves around the sensitivity of these simulated reference values to the choice of DD, which is often unconstrained, casting doubt on calibration diagnostics.

The research specifically scrutinizes the correlation coefficient between absolute errors and uncertainties (CC), and the expected normalized calibration error (ENCE), along with their susceptibility to the choice of DD. A proposed workflow recommends practices for robust validation, including the consideration of alternative distributions for generating synthetic errors and assessing the impact on calibration statistics.

Findings and Implications

The findings point to a pronounced sensitivity of certain calibration statistics to the choice of DD, particularly for CC and ENCE. This sensitivity underscores the potential limitations in using these statistics for validation purposes when the generative distribution remains unknown. The research accentuates the necessity for a rigorous validation workflow, incorporating sensitivity analysis to ensure the reliability of simulated reference values.

The practical implications of this research are significant for practitioners in machine learning and AI. By establishing a robust framework for the validation of ML-UQ calibration statistics, the paper facilitates a deeper understanding and more accurate interpretation of uncertainty quantification metrics, ultimately contributing to the development of more reliable predictive models.

Future Directions in AI and Machine Learning

The paper instigates several avenues for future research, especially in developing methods to constrain the choice of generative distribution or in finding alternative approaches for validating calibration statistics without reliance on simulated reference values. Furthermore, the exploration of additional calibration statistics and their validation mechanisms could enrich the toolkit available for ML-UQ, enhancing the interpretability and trustworthiness of machine learning models across various domains.

Conclusion

This paper enriches the dialogue on Machine Learning Uncertainty Quantification by addressing a critical gap in the validation of calibration statistics. Through meticulous analysis and the introduction of a validated workflow, it paves the way for more rigorous and reliable practices in quantifying and validating uncertainty in machine learning predictions. As the field of AI continues to evolve, such foundational research will be paramount in harnessing the full potential of machine learning models, ensuring their applicability and trustworthiness in decision-making processes across industries.

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