# Out-of-distribution Generalization in the Presence of Nuisance-Induced Spurious Correlations

arXiv: https://arxiv.org/abs/2107.00520 · HTML: https://mlsanity.com/paper/2107.00520/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 51 references that are in the map.
- First posted on arXiv 29 Jun 2021.

## Builds on (most cited first, 30 of 39)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [CheXpert: A Large Chest Radiograph Dataset with Uncertainty Labels and Expert Comparison](https://mlsanity.com/paper/1901.07031/) (2019)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [Learning to Generalize: Meta-Learning for Domain Generalization](https://mlsanity.com/paper/1710.03463/) (2017)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [Mitigating Unwanted Biases with Adversarial Learning](https://mlsanity.com/paper/1801.07593/) (2018)
- [MIMIC-CXR-JPG, a large publicly available database of labeled chest radiographs](https://mlsanity.com/paper/1901.07042/) (2019)
- [Confounding variables can degrade generalization performance of radiological deep learning models](https://mlsanity.com/paper/1807.00431/) (2018)
- [An Investigation of Why Overparameterization Exacerbates Spurious Correlations](https://mlsanity.com/paper/2005.04345/) (2020)
- [Environment Inference for Invariant Learning](https://mlsanity.com/paper/2010.07249/) (2020)
- [A Brief Review of Domain Adaptation](https://mlsanity.com/paper/2010.03978/) (2020)
- [What is the Effect of Importance Weighting in Deep Learning?](https://mlsanity.com/paper/1812.03372/) (2018)
- [Fairness without Demographics through Adversarially Reweighted Learning](https://mlsanity.com/paper/2006.13114/) (2020)
- [Domain Generalization using Causal Matching](https://mlsanity.com/paper/2006.07500/) (2020)
- [Statistics of Robust Optimization: A Generalized Empirical Likelihood Approach](https://mlsanity.com/paper/1610.03425/) (2016)
- [On Calibration and Out-of-domain Generalization](https://mlsanity.com/paper/2102.10395/) (2021)
- [Invariant Rationalization](https://mlsanity.com/paper/2003.09772/) (2020)
- [Controllable Invariance through Adversarial Feature Learning](https://mlsanity.com/paper/1705.11122/) (2017)
- [Model Patching: Closing the Subgroup Performance Gap with Data Augmentation](https://mlsanity.com/paper/2008.06775/) (2020)
- [Counterfactual Invariance to Spurious Correlations: Why and How to Pass Stress Tests](https://mlsanity.com/paper/2106.00545/) (2021)
- [Can Subnetwork Structure be the Key to Out-of-Distribution Generalization?](https://mlsanity.com/paper/2106.02890/) (2021)
- [Robustness to Spurious Correlations in Text Classification via Automatically Generated Counterfactuals](https://mlsanity.com/paper/2012.10040/) (2020)

## Built on by (most cited first, 30 of 41)

- [Change is Hard: A Closer Look at Subpopulation Shift](https://mlsanity.com/paper/2302.12254/) (2023)
- [Domain Generalization for Medical Image Analysis: A Review](https://mlsanity.com/paper/2310.08598/) (2023)
- [On the Challenges and Opportunities in Generative AI](https://mlsanity.com/paper/2403.00025/) (2024)
- [Don't blame Dataset Shift! Shortcut Learning due to Gradients and Cross Entropy](https://mlsanity.com/paper/2308.12553/) (2023)
- [Are All Spurious Features in Natural Language Alike? An Analysis through a Causal Lens](https://mlsanity.com/paper/2210.14011/) (2022)
- [Spurious Feature Diversification Improves Out-of-distribution Generalization](https://mlsanity.com/paper/2309.17230/) (2023)
- [Spuriosity Didn't Kill the Classifier: Using Invariant Predictions to Harness Spurious Features](https://mlsanity.com/paper/2307.09933/) (2023)
- [A Survey on Evaluation of Out-of-Distribution Generalization](https://mlsanity.com/paper/2403.01874/) (2024)
- [Causal Balancing for Domain Generalization](https://mlsanity.com/paper/2206.05263/) (2022)
- [Efficient Conditionally Invariant Representation Learning](https://mlsanity.com/paper/2212.08645/) (2022)
- [Nuisances via Negativa: Adjusting for Spurious Correlations via Data Augmentation](https://mlsanity.com/paper/2210.01302/) (2022)
- [When More is Less: Incorporating Additional Datasets Can Hurt Performance By Introducing Spurious Correlations](https://mlsanity.com/paper/2308.04431/) (2023)
- [Data Augmentations for Improved (Large) Language Model Generalization](https://mlsanity.com/paper/2310.12803/) (2023)
- [When accurate prediction models yield harmful self-fulfilling prophecies](https://mlsanity.com/paper/2312.01210/) (2023)
- [Beyond Distribution Shift: Spurious Features Through the Lens of Training Dynamics](https://mlsanity.com/paper/2302.09344/) (2023)
- [Evaluating Robustness to Dataset Shift via Parametric Robustness Sets](https://mlsanity.com/paper/2205.15947/) (2022)
- [To Use or not to Use Muon: How Simplicity Bias in Optimizers Matters](https://mlsanity.com/paper/2603.00742/) (2026)
- [SFP: Spurious Feature-targeted Pruning for Out-of-Distribution Generalization](https://mlsanity.com/paper/2305.11615/) (2023)
- [Mind the Graph When Balancing Data for Fairness or Robustness](https://mlsanity.com/paper/2406.17433/) (2024)
- [Beyond Invariance: Test-Time Label-Shift Adaptation for Distributions with "Spurious" Correlations](https://mlsanity.com/paper/2211.15646/) (2022)
- [Malign Overfitting: Interpolation Can Provably Preclude Invariance](https://mlsanity.com/paper/2211.15724/) (2022)
- [Are demographically invariant models and representations in medical imaging fair?](https://mlsanity.com/paper/2305.01397/) (2023)
- [Removing Spurious Concepts from Neural Network Representations via Joint Subspace Estimation](https://mlsanity.com/paper/2310.11991/) (2023)
- [Learning Invariant Representations with Missing Data](https://mlsanity.com/paper/2112.00881/) (2021)
- [Robustness to Spurious Correlations Improves Semantic Out-of-Distribution Detection](https://mlsanity.com/paper/2302.04132/) (2023)
- [A Causal Framework to Unify Common Domain Generalization Approaches](https://mlsanity.com/paper/2307.06825/) (2023)
- [Explanations that reveal all through the definition of encoding](https://mlsanity.com/paper/2411.02664/) (2024)
- [Boosted Control Functions: Distribution generalization and invariance in confounded models](https://mlsanity.com/paper/2310.05805/) (2023)
- [Bridging Distribution Shift and AI Safety: Conceptual and Methodological Synergies](https://mlsanity.com/paper/2505.22829/) (2025)
- [Superclass-Guided Representation Disentanglement for Spurious Correlation Mitigation](https://mlsanity.com/paper/2508.08570/) (2025)

## Abstract (arXiv)

In many prediction problems, spurious correlations are induced by a changing relationship between the label and a nuisance variable that is also correlated with the covariates. For example, in classifying animals in natural images, the background, which is a nuisance, can predict the type of animal. This nuisance-label relationship does not always hold, and the performance of a model trained under one such relationship may be poor on data with a different nuisance-label relationship. To build predictive models that perform well regardless of the nuisance-label relationship, we develop Nuisance-Randomized Distillation (NURD). We introduce the nuisance-randomized distribution, a distribution where the nuisance and the label are independent. Under this distribution, we define the set of representations such that conditioning on any member, the nuisance and the label remain independent. We prove that the representations in this set always perform better than chance, while representations outside of this set may not. NURD finds a representation from this set that is most informative of the label under the nuisance-randomized distribution, and we prove that this representation achieves the highest performance regardless of the nuisance-label relationship. We evaluate NURD on several tasks including chest X-ray classification where, using non-lung patches as the nuisance, NURD produces models that predict pneumonia under strong spurious correlations.