# Scalable Out-of-distribution Robustness in the Presence of Unobserved Confounders

arXiv: https://arxiv.org/abs/2411.19923 · HTML: https://mlsanity.com/paper/2411.19923/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 57 references that are in the map.
- First posted on arXiv 29 Nov 2024.

## Builds on (most cited first, 30 of 36)

- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [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)
- [Just Train Twice: Improving Group Robustness without Training Group Information](https://mlsanity.com/paper/2107.09044/) (2021)
- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [Towards Stable Test-Time Adaptation in Dynamic Wild World](https://mlsanity.com/paper/2302.12400/) (2023)
- [Last Layer Re-Training is Sufficient for Robustness to Spurious Correlations](https://mlsanity.com/paper/2204.02937/) (2022)
- [Detecting and Correcting for Label Shift with Black Box Predictors](https://mlsanity.com/paper/1802.03916/) (2018)
- [Environment Inference for Invariant Learning](https://mlsanity.com/paper/2010.07249/) (2020)
- [The Risks of Invariant Risk Minimization](https://mlsanity.com/paper/2010.05761/) (2020)
- [Domain Generalization using Causal Matching](https://mlsanity.com/paper/2006.07500/) (2020)
- [Adaptive Risk Minimization: Learning to Adapt to Domain Shift](https://mlsanity.com/paper/2007.02931/) (2020)
- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [An Introduction to Proximal Causal Learning](https://mlsanity.com/paper/2009.10982/) (2020)
- [Heterogeneous Risk Minimization](https://mlsanity.com/paper/2105.03818/) (2021)
- [Spread Spurious Attribute: Improving Worst-group Accuracy with Spurious Attribute Estimation](https://mlsanity.com/paper/2204.02070/) (2022)
- [A causal framework for distribution generalization](https://mlsanity.com/paper/2006.07433/) (2020)
- [ZIN: When and How to Learn Invariance Without Environment Partition?](https://mlsanity.com/paper/2203.05818/) (2022)
- [Diagnosing failures of fairness transfer across distribution shift in real-world medical settings](https://mlsanity.com/paper/2202.01034/) (2022)
- [Out-of-distribution Generalization with Causal Invariant Transformations](https://mlsanity.com/paper/2203.11528/) (2022)
- [Harnessing Out-Of-Distribution Examples via Augmenting Content and Style](https://mlsanity.com/paper/2207.03162/) (2022)
- [Rao-Blackwellizing the Straight-Through Gumbel-Softmax Gradient Estimator](https://mlsanity.com/paper/2010.04838/) (2020)
- [Modeling the Data-Generating Process is Necessary for Out-of-Distribution Generalization](https://mlsanity.com/paper/2206.07837/) (2022)
- [RLSbench: Domain Adaptation Under Relaxed Label Shift](https://mlsanity.com/paper/2302.03020/) (2023)
- [Spuriosity Didn't Kill the Classifier: Using Invariant Predictions to Harness Spurious Features](https://mlsanity.com/paper/2307.09933/) (2023)
- [Causal Balancing for Domain Generalization](https://mlsanity.com/paper/2206.05263/) (2022)
- [Robust Causal Graph Representation Learning against Confounding Effects](https://mlsanity.com/paper/2208.08584/) (2022)

## Built on by (most cited first, 5 of 5)

- [When Shift Happens - Confounding Is to Blame](https://mlsanity.com/paper/2505.21422/) (2025)
- [Counterfactual Residual Data Augmentation for Regression](https://mlsanity.com/paper/2606.28460/) (2026)
- [Should Bias be Eliminated? A General Framework to Use Bias for OOD Generalization](https://mlsanity.com/paper/2507.17001/) (2025)
- [Transferring Causal Effects using Proxies](https://mlsanity.com/paper/2510.25924/) (2025)
- [Point-Identification of a Robust Predictor Under Latent Shift with Imperfect Proxies](https://mlsanity.com/paper/2603.15158/) (2026)

## Abstract (arXiv)

We consider the task of out-of-distribution (OOD) generalization, where the distribution shift is due to an unobserved confounder (Z) affecting both the covariates (X) and the labels (Y). This confounding introduces heterogeneity in the predictor, i.e., P(Y | X) = EP(Z | X)[P(Y | X,Z)], making traditional covariate and label shift assumptions unsuitable. OOD generalization differs from traditional domain adaptation in that it does not assume access to the covariate distribution (Xte) of the test samples during training. These conditions create a challenging scenario for OOD robustness: (a) Ztr is an unobserved confounder during training, (b) Pte(Z) neq Ptr(Z), (c) Xte is unavailable during training, and (d) the predictive distribution depends on Pte(Z). While prior work has developed complex predictors requiring multiple additional variables for identifiability of the latent distribution, we explore a set of identifiability assumptions that yield a surprisingly simple predictor using only a single additional variable. Our approach demonstrates superior empirical performance on several benchmark tasks.