Uncertainty quantification

Taxonomy
DUQ networks
Bayes
Physical model setting
Conformal prediction
Chaos expansions
Uncertainty Quantification 360
References

Using machine learning to make predictions, with a measure of the confidence of those predictions.

Taxonomy

Should clarify. TBD. Here is a recent reference on the theme: Kendall and Gal (2017) This extricates aleatoric and epistemic uncertainty. Also to mention, model uncertainty.

DUQ networks

Amersfoort et al. (2020); Kendall and Gal (2017)

Bayes

Bayes methods have some ideas of uncertainty baked in. You can get some way with e.g., e.g. Gaussian process regression, or probabilistic NNs.

Physical model setting

PEST, PEST++, and pyemu are some integrated systems for uncertainty quantification that use some weird terminology, such a FOSM (First-order-second-moment) models, which at first glance resemble LIME-style local regression model interpretations. The common thread is that these models have complicated physical dynamics which are hard to handle directly, but a surrogate model might be more tractable.

Conformal prediction

See conformal prediction.

Chaos expansions

See chaos expansions.

Uncertainty Quantification 360

IBM’s Uncertainty Quantification 360 toolkit is both a handy software library and a summary of popular generic methods:

Auxiliary Interval Predictor
Use an auxiliary model to improve the calibration of UQ generated by the original model.
Blackbox Metamodel Classification
Extract confidence scores from trained black-box classification models using a meta-model.
Blackbox Metamodel Regression
Extract prediction intervals from trained black-box regression models using a meta-model.
Classification Calibration
Post-hoc calibration of classification models using Isotonic Regression and Platt Scaling.
Heteroscedastic Regression
Train regression models that capture data uncertainty, assuming the targets are noisy and the amount of noise varies between data points.
Homoscedastic Gaussian Process Regression
Train Gaussian Process Regression models with homoscedastic noise that capture data and model uncertainty.
Horseshoe BNN classification
Train Bayesian neural networks classifiers with Gaussian and Horseshoe priors that capture data and model uncertainty.
Horseshoe BNN regression
Train BNNs regression models with Gaussian and Horseshoe priors that capture data and model uncertainty.
Infinitesimal Jackknife
Extract uncertainty from trained models by approximating the effect of training data perturbations on the model’s predictions.
Quantile Regression
Train Quantile Regression models that capture data uncertainty, by learning two separate models for the upper and lower quantile to obtain the prediction intervals.
UCC Recalibration
Recalibrate UQ of a regression model to specified operating point using Uncertainty Characteristics Curve

They provide guidance on method selection in the manual:

Source: UQ360

References

Amersfoort, Joost Van, Lewis Smith, Yee Whye Teh, and Yarin Gal. 2020. “Uncertainty Estimation Using a Single Deep Deterministic Neural Network.” In International Conference on Machine Learning, 9690–700. PMLR.

Bhatt, Umang, Javier Antorán, Yunfeng Zhang, Q. Vera Liao, Prasanna Sattigeri, Riccardo Fogliato, Gabrielle Gauthier Melançon, et al. 2021. “Uncertainty as a Form of Transparency: Measuring, Communicating, and Using Uncertainty.” arXiv:2011.07586 [Cs], May.

Bishop, Christopher. 1994. “Mixture Density Networks.” Microsoft Research, January.

Burrows, Wesley, and John Doherty. 2015. “Efficient Calibration/Uncertainty Analysis Using Paired Complex/Surrogate Models.” Groundwater 53 (4): 531–41.

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Chipman, Hugh A, Edward I George, and Robert E Mcculloch. 2006. “Bayesian Ensemble Learning.” In, 8.

Daxberger, Erik, Agustinus Kristiadi, Alexander Immer, Runa Eschenhagen, Matthias Bauer, and Philipp Hennig. 2021. “Laplace Redux – Effortless Bayesian Deep Learning.” In arXiv:2106.14806 [Cs, Stat].

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Gal, Yarin, and Zoubin Ghahramani. 2015. “Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning.” In Proceedings of the 33rd International Conference on Machine Learning (ICML-16).

———. 2016. “Dropout as a Bayesian Approximation: Appendix.” arXiv:1506.02157 [Stat], May.

Ghosh, Soumya, Q. Vera Liao, Karthikeyan Natesan Ramamurthy, Jiri Navratil, Prasanna Sattigeri, Kush R. Varshney, and Yunfeng Zhang. 2021. “Uncertainty Quantification 360: A Holistic Toolkit for Quantifying and Communicating the Uncertainty of AI.” arXiv:2106.01410 [Cs], June.

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Higdon, Dave, James Gattiker, Brian Williams, and Maria Rightley. 2008. “Computer Model Calibration Using High-Dimensional Output.” Journal of the American Statistical Association 103 (482): 570–83.

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Jarvenpaa, Marko, Aki Vehtari, and Pekka Marttinen. 2020. “Batch Simulations and Uncertainty Quantification in Gaussian Process Surrogate Approximate Bayesian Computation.” In Conference on Uncertainty in Artificial Intelligence, 779–88. PMLR.

Kasim, M. F., D. Watson-Parris, L. Deaconu, S. Oliver, P. Hatfield, D. H. Froula, G. Gregori, et al. 2020. “Up to Two Billion Times Acceleration of Scientific Simulations with Deep Neural Architecture Search.” arXiv:2001.08055 [Physics, Stat], January.

Kendall, Alex, and Yarin Gal. 2017. “What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?” March.

Kingma, Diederik P., Tim Salimans, and Max Welling. 2015. “Variational Dropout and the Local Reparameterization Trick.” In Proceedings of the 28th International Conference on Neural Information Processing Systems - Volume 2, 2575–83. NIPS’15. Cambridge, MA, USA: MIT Press.

Kristiadi, Agustinus, Matthias Hein, and Philipp Hennig. 2021. “Learnable Uncertainty Under Laplace Approximations.” In Uncertainty in Artificial Intelligence.

Lakshminarayanan, Balaji, Alexander Pritzel, and Charles Blundell. 2017. “Simple and Scalable Predictive Uncertainty Estimation Using Deep Ensembles.” In Proceedings of the 31st International Conference on Neural Information Processing Systems, 6405–16. NIPS’17. Red Hook, NY, USA: Curran Associates Inc.

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Mukhoti, Jishnu, Andreas Kirsch, Joost van Amersfoort, Philip H. S. Torr, and Yarin Gal. 2021. “Deterministic Neural Networks with Inductive Biases Capture Epistemic and Aleatoric Uncertainty,” February.

O’Hagan, Anthony. 2013. “Polynomial Chaos: A Tutorial and Critique from a Statistician’s Perspective,” 20.

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———. 2016b. “A Python Framework for Environmental Model Uncertainty Analysis.” Environmental Modelling & Software 85 (November): 217–28.

Zeni, Gianluca, Matteo Fontana, and Simone Vantini. 2020. “Conformal Prediction: A Unified Review of Theory and New Challenges.” arXiv:2005.07972 [Cs, Econ, Stat], May.

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