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

Predicting with competence: the best machine learning idea you never heard of:

The essential idea is that a “conformity function” exists. Effectively you are constructing a sort of multivariate cumulative distribution function for your machine learning gizmo using the conformity function. Such CDFs exist for classical stuff like ARIMA and linear regression under the correct circumstances; CP brings the idea to machine learning in general, and to models like ARIMA when the standard parametric confidence intervals won’t work.

Hmm. Perhaps see (“Predicting With Confidence: Using Conformal Prediction in Drug Discovery” 2021; Shafer and Vovk 2008; Zeni, Fontana, and Vantini 2020). Question: how well does this work under dataset shift? (Tibshirani et al. 2019).

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.

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Doherty, John. 2015. Calibration and uncertainty analysis for complex environmental models.

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).

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

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

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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.

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