# On Calibration and Out-of-domain Generalization

arXiv: https://arxiv.org/abs/2102.10395 · HTML: https://mlsanity.com/paper/2102.10395/

## Key facts

- Cited by 134 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 78 references that are in the map.
- First posted on arXiv 20 Feb 2021.

## Builds on (most cited first, 30 of 35)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Measuring Calibration in Deep Learning](https://mlsanity.com/paper/1904.01685/) (2019)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [On Fairness and Calibration](https://mlsanity.com/paper/1709.02012/) (2017)
- [Nuanced Metrics for Measuring Unintended Bias with Real Data for Text Classification](https://mlsanity.com/paper/1903.04561/) (2019)
- [Confounding variables can degrade generalization performance of radiological deep learning models](https://mlsanity.com/paper/1807.00431/) (2018)
- [Calibrating Deep Neural Networks using Focal Loss](https://mlsanity.com/paper/2002.09437/) (2020)
- [Functional Map of the World](https://mlsanity.com/paper/1711.07846/) (2017)
- [Calibration of Pre-trained Transformers](https://mlsanity.com/paper/2003.07892/) (2020)
- [The Risks of Invariant Risk Minimization](https://mlsanity.com/paper/2010.05761/) (2020)
- [Learning Not to Learn: Training Deep Neural Networks with Biased Data](https://mlsanity.com/paper/1812.10352/) (2018)
- [Evaluating model calibration in classification](https://mlsanity.com/paper/1902.06977/) (2019)
- [Invariant Causal Prediction for Nonlinear Models](https://mlsanity.com/paper/1706.08576/) (2017)
- [Domain Adaptation by Using Causal Inference to Predict Invariant Conditional Distributions](https://mlsanity.com/paper/1707.06422/) (2017)
- [Anchor regression: heterogeneous data meets causality](https://mlsanity.com/paper/1801.06229/) (2018)
- [Does Invariant Risk Minimization Capture Invariance?](https://mlsanity.com/paper/2101.01134/) (2021)
- [Distribution-free binary classification: prediction sets, confidence intervals and calibration](https://mlsanity.com/paper/2006.10564/) (2020)

## Built on by (most cited first, 30 of 134)

- [Generalizing to Unseen Domains: A Survey on Domain Generalization](https://mlsanity.com/paper/2103.03097/) (2021)
- [Fishr: Invariant Gradient Variances for Out-of-Distribution Generalization](https://mlsanity.com/paper/2109.02934/) (2021)
- [Causal Inference in Natural Language Processing: Estimation, Prediction, Interpretation and Beyond](https://mlsanity.com/paper/2109.00725/) (2021)
- [WARM: On the Benefits of Weight Averaged Reward Models](https://mlsanity.com/paper/2401.12187/) (2024)
- [Nonparametric Identifiability of Causal Representations from Unknown Interventions](https://mlsanity.com/paper/2306.00542/) (2023)
- [Uncertainty Quantification with Pre-trained Language Models: A Large-Scale Empirical Analysis](https://mlsanity.com/paper/2210.04714/) (2022)
- [On the Paradox of Learning to Reason from Data](https://mlsanity.com/paper/2205.11502/) (2022)
- [Evading the Simplicity Bias: Training a Diverse Set of Models Discovers Solutions with Superior OOD Generalization](https://mlsanity.com/paper/2105.05612/) (2021)
- [Domain-Adjusted Regression or: ERM May Already Learn Features Sufficient for Out-of-Distribution Generalization](https://mlsanity.com/paper/2202.06856/) (2022)
- [Trustworthy clinical AI solutions: a unified review of uncertainty quantification in deep learning models for medical image analysis](https://mlsanity.com/paper/2210.03736/) (2022)
- [PADA: Example-based Prompt Learning for on-the-fly Adaptation to Unseen Domains](https://mlsanity.com/paper/2102.12206/) (2021)
- [Assaying Out-Of-Distribution Generalization in Transfer Learning](https://mlsanity.com/paper/2207.09239/) (2022)
- [Energy-Based Open-World Uncertainty Modeling for Confidence Calibration](https://mlsanity.com/paper/2107.12628/) (2021)
- [Out-of-distribution Generalization in the Presence of Nuisance-Induced Spurious Correlations](https://mlsanity.com/paper/2107.00520/) (2021)
- [The Clever Hans Mirage: A Comprehensive Survey on Spurious Correlations in Machine Learning](https://mlsanity.com/paper/2402.12715/) (2024)
- [Robust Calibration with Multi-domain Temperature Scaling](https://mlsanity.com/paper/2206.02757/) (2022)
- [Pareto Invariant Risk Minimization: Towards Mitigating the Optimization Dilemma in Out-of-Distribution Generalization](https://mlsanity.com/paper/2206.07766/) (2022)
- [Invariant and Transportable Representations for Anti-Causal Domain Shifts](https://mlsanity.com/paper/2207.01603/) (2022)
- [Towards Understanding and Boosting Adversarial Transferability from a Distribution Perspective](https://mlsanity.com/paper/2210.04213/) (2022)
- [Understanding and Improving Feature Learning for Out-of-Distribution Generalization](https://mlsanity.com/paper/2304.11327/) (2023)
- [Rich Feature Construction for the Optimization-Generalization Dilemma](https://mlsanity.com/paper/2203.15516/) (2022)
- [Calibrated ensembles can mitigate accuracy tradeoffs under distribution shift](https://mlsanity.com/paper/2207.08977/) (2022)
- [Calibrated Selective Classification](https://mlsanity.com/paper/2208.12084/) (2022)
- [Don't blame Dataset Shift! Shortcut Learning due to Gradients and Cross Entropy](https://mlsanity.com/paper/2308.12553/) (2023)
- [Sample-Efficient Reinforcement Learning in the Presence of Exogenous Information](https://mlsanity.com/paper/2206.04282/) (2022)
- [Predicting is not Understanding: Recognizing and Addressing Underspecification in Machine Learning](https://mlsanity.com/paper/2207.02598/) (2022)
- [Discovering environments with XRM](https://mlsanity.com/paper/2309.16748/) (2023)
- [Exploring Predictive Uncertainty and Calibration in NLP: A Study on the Impact of Method & Data Scarcity](https://mlsanity.com/paper/2210.15452/) (2022)
- [Improving Generalization of Alignment with Human Preferences through Group Invariant Learning](https://mlsanity.com/paper/2310.11971/) (2023)
- [Distribution Shift Inversion for Out-of-Distribution Prediction](https://mlsanity.com/paper/2306.08328/) (2023)

## Abstract (arXiv)

Out-of-domain (OOD) generalization is a significant challenge for machine learning models. Many techniques have been proposed to overcome this challenge, often focused on learning models with certain invariance properties. In this work, we draw a link between OOD performance and model calibration, arguing that calibration across multiple domains can be viewed as a special case of an invariant representation leading to better OOD generalization. Specifically, we show that under certain conditions, models which achieve multi-domain calibration are provably free of spurious correlations. This leads us to propose multi-domain calibration as a measurable and trainable surrogate for the OOD performance of a classifier. We therefore introduce methods that are easy to apply and allow practitioners to improve multi-domain calibration by training or modifying an existing model, leading to better performance on unseen domains. Using four datasets from the recently proposed WILDS OOD benchmark, as well as the Colored MNIST dataset, we demonstrate that training or tuning models so they are calibrated across multiple domains leads to significantly improved performance on unseen test domains. We believe this intriguing connection between calibration and OOD generalization is promising from both a practical and theoretical point of view.