Accurate Uncertainties for Deep Learning Using Calibrated Regression

By Volodymyr Kuleshov, Nathan Fenner, Stefano Ermon. 2018

863 citations recorded by the source corpus.

Methods for reasoning under uncertainty are a key building block of accurate and reliable machine learning systems. Bayesian methods provide a general framework to quantify uncertainty. However, because of model misspecification and the use of approximate inference, Bayesian uncertainty estimates are often inaccurate -- for example, a 90% credible interval may not contain the true outcome 90% of the time. Here, we propose a simple procedure for calibrating any regression algorithm; when applied to Bayesian and probabilistic models, it is guaranteed to produce calibrated uncertainty estimates given enough data. Our procedure is inspired by Platt scaling and extends previous work on classification. We evaluate this approach on Bayesian linear regression, feedforward, and recurrent neural networks, and find that it consistently outputs well-calibrated credible intervals while improving performance on time series forecasting and model-based reinforcement learning tasks.

Subfields: Artificial Intelligence, Safety, Robustness & Interpretability

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Safety, Robustness & Interpretability

Citations in the corpus

Scalable agent alignment via reward modeling: a research direction (2018, methodology): “While Bayesian methods can help with calibration (Gal et al., 2017a), they are insufﬁcient in practice for deep neural networks (Kuleshov et al., 2018).”
Unsolved Problems in ML Safety (2021, background): “…express their domain of competence in a more representative and meaningful way, researchers could further improve model calibration on typical testing data [68, 133, 113, 109, 205, 107, 108, 124], though the greater challenge is calibration on testing data that is unlike the training data [137].”
A Simple Baseline for Bayesian Uncertainty in Deep Learning (2019, methodology): “[28] propose calibrated regression using a similar rescaling technique.”
BANANAS: Bayesian Optimization with Neural Architectures for Neural Architecture Search (2019, methodology): “[26] Volodymyr Kuleshov, Nathan Fenner, and Stefano Ermon.”
Verified Uncertainty Calibration (2019, methodology): “As most modern machine learning models, such as neural networks, do not output calibrated probabilities out of the box [9, 10, 11], reseachers use recalibration methods that take the output of an uncalibrated model, and transform it into a calibrated probability.”
Measuring Calibration in Deep Learning (2019, positive): “Kuleshov et al. (2018) extends ECE to the regression setting.”
MOPO: Model-based Offline Policy Optimization (2020, methodology): “Lastly, uncertainty estimation techniques, such as bootstrap ensembles, are well developed for supervised learning methods [39, 34, 59] and are known to perform poorly for value-based RL methods [70].”
Deep Evidential Regression (2019, methodology): “(C) Model uncertainty calibration [27]; (ideal: y = x).”
Long-tail learning via logit adjustment (2020, background): “, 2017), probabilistic sharpness (Gneiting et al., 2007; Kuleshov et al., 2018), or a proper scoring rule such as the log-loss or squared error (Gneiting & Raftery, 2007).”
Machine learning pipeline for battery state-of-health estimation (2021, methodology): “[59] Volodymyr Kuleshov, Nathan Fenner, and Stefano Ermon.”
Hands-On Bayesian Neural Networks—A Tutorial for Deep Learning Users (2020, methodology): “It also allows, to a certain extent, to recalibrate the model [47].”
Laplace Redux - Effortless Bayesian Deep Learning (2021, methodology): “We plot means ± standard errors of the NLL (top) and ECE (for classification) or regression calibration error [71] (bottom).”
Regression diagnostics meets forecast evaluation: conditional calibration, reliability diagrams, and coefficient of determination (2021, background): “…community, where the full conditional distribution of a response, given a feature vector, is of increasing interest, as exemplified by the work of Guo et al. (2017), Kuleshov et al. (2018), Song et al. (2019), Gupta et al. (2020), Zhao et al. (2020), Sahoo et al. (2021) and Roelofs et al. (2022).”
Rethinking drug design in the artificial intelligence era (2019, background): “Especially in conjunction with drug design and MOO, it is important to understand and address these issues of uncertainty calibration 100,101 .”
A Review and Comparative Study on Probabilistic Object Detection in Autonomous Driving (2020, methodology): “It has also been shown to produce miscalibrated probabilities in classiﬁcation [60], [69] and regression [70].”