# Modeling the Data-Generating Process is Necessary for Out-of-Distribution Generalization

arXiv: https://arxiv.org/abs/2206.07837 · HTML: https://mlsanity.com/paper/2206.07837/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 63 references that are in the map.
- First posted on arXiv 15 Jun 2022.

## Builds on (most cited first, 30 of 37)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [RandAugment: Practical automated data augmentation with a reduced search space](https://mlsanity.com/paper/1909.13719/) (2019)
- [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)
- [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)
- [Generalizing to Unseen Domains: A Survey on Domain Generalization](https://mlsanity.com/paper/2103.03097/) (2021)
- [Domain Generalization: A Survey](https://mlsanity.com/paper/2103.02503/) (2021)
- [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)
- [Domain Generalization via Invariant Feature Representation](https://mlsanity.com/paper/1301.2115/) (2013)
- [Self-Challenging Improves Cross-Domain Generalization](https://mlsanity.com/paper/2007.02454/) (2020)
- [Nuanced Metrics for Measuring Unintended Bias with Real Data for Text Classification](https://mlsanity.com/paper/1903.04561/) (2019)
- [The Pitfalls of Simplicity Bias in Neural Networks](https://mlsanity.com/paper/2006.07710/) (2020)
- [Functional Map of the World](https://mlsanity.com/paper/1711.07846/) (2017)
- [The Risks of Invariant Risk Minimization](https://mlsanity.com/paper/2010.05761/) (2020)
- [Domain Generalization for Object Recognition with Multi-task Autoencoders](https://mlsanity.com/paper/1508.07680/) (2015)
- [Weakly-Supervised Disentanglement Without Compromises](https://mlsanity.com/paper/2002.02886/) (2020)
- [Domain Generalization using Causal Matching](https://mlsanity.com/paper/2006.07500/) (2020)
- [Invariance Principle Meets Information Bottleneck for Out-of-Distribution Generalization](https://mlsanity.com/paper/2106.06607/) (2021)
- [Improving Out-of-Distribution Robustness via Selective Augmentation](https://mlsanity.com/paper/2201.00299/) (2022)
- [Improve Unsupervised Domain Adaptation with Mixup Training](https://mlsanity.com/paper/2001.00677/) (2020)
- [Quantifying the effects of data augmentation and stain color normalization in convolutional neural networks for computational pathology](https://mlsanity.com/paper/1902.06543/) (2019)
- [A Fine-Grained Analysis on Distribution Shift](https://mlsanity.com/paper/2110.11328/) (2021)
- [Reducing Gender Bias in Abusive Language Detection](https://mlsanity.com/paper/1808.07231/) (2018)
- [Domain Generalization via Conditional Invariant Representation](https://mlsanity.com/paper/1807.08479/) (2018)
- [Efficient Domain Generalization via Common-Specific Low-Rank Decomposition](https://mlsanity.com/paper/2003.12815/) (2020)
- [Generalizing to unseen domains via distribution matching](https://mlsanity.com/paper/1911.00804/) (2019)
- [Scatter Component Analysis: A Unified Framework for Domain Adaptation and Domain Generalization](https://mlsanity.com/paper/1510.04373/) (2015)

## Built on by (most cited first, 30 of 34)

- [Compositional Abilities Emerge Multiplicatively: Exploring Diffusion Models on a Synthetic Task](https://mlsanity.com/paper/2310.09336/) (2023)
- [Mechanistic Mode Connectivity](https://mlsanity.com/paper/2211.08422/) (2022)
- [Emergence of Hidden Capabilities: Exploring Learning Dynamics in Concept Space](https://mlsanity.com/paper/2406.19370/) (2024)
- [Joint Learning of Label and Environment Causal Independence for Graph Out-of-Distribution Generalization](https://mlsanity.com/paper/2306.01103/) (2023)
- [A Survey on Evaluation of Out-of-Distribution Generalization](https://mlsanity.com/paper/2403.01874/) (2024)
- [Domain Generalization -- A Causal Perspective](https://mlsanity.com/paper/2209.15177/) (2022)
- [A Review of the Role of Causality in Developing Trustworthy AI Systems](https://mlsanity.com/paper/2302.06975/) (2023)
- [OOD-CV-v2: An extended Benchmark for Robustness to Out-of-Distribution Shifts of Individual Nuisances in Natural Images](https://mlsanity.com/paper/2304.10266/) (2023)
- [LCA-on-the-Line: Benchmarking Out-of-Distribution Generalization with Class Taxonomies](https://mlsanity.com/paper/2407.16067/) (2024)
- [Do causal predictors generalize better to new domains?](https://mlsanity.com/paper/2402.09891/) (2024)
- [Emerging Synergies in Causality and Deep Generative Models: A Survey](https://mlsanity.com/paper/2301.12351/) (2023)
- [Mind the Graph When Balancing Data for Fairness or Robustness](https://mlsanity.com/paper/2406.17433/) (2024)
- [Domain constraints improve risk prediction when outcome data is missing](https://mlsanity.com/paper/2312.03878/) (2023)
- [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)
- [A Markov Random Field model for Hypergraph-based Machine Learning](https://mlsanity.com/paper/2308.14172/) (2023)
- [Scalable Out-of-distribution Robustness in the Presence of Unobserved Confounders](https://mlsanity.com/paper/2411.19923/) (2024)
- [Mitigating Spurious Correlations in LLMs via Causality-Aware Post-Training](https://mlsanity.com/paper/2506.09433/) (2025)
- [Causally Inspired Regularization Enables Domain General Representations](https://mlsanity.com/paper/2404.16277/) (2024)
- [Emergence and Causality in Complex Systems: A Survey on Causal Emergence and Related Quantitative Studies](https://mlsanity.com/paper/2312.16815/) (2023)
- [Do regularization methods for shortcut mitigation work as intended?](https://mlsanity.com/paper/2503.17015/) (2025)
- [Heterogeneous Graph Structure Learning through the Lens of Data-generating Processes](https://mlsanity.com/paper/2503.08760/) (2025)
- [Test-Time Adaptation by Causal Trimming](https://mlsanity.com/paper/2510.11133/) (2025)
- [Causal Effect Regularization: Automated Detection and Removal of Spurious Attributes](https://mlsanity.com/paper/2306.11072/) (2023)
- [Domain Adaptation for Sustainable Soil Management using Causal and Contrastive Constraint Minimization](https://mlsanity.com/paper/2401.07175/) (2024)
- [A Unified Causal View of Instruction Tuning](https://mlsanity.com/paper/2402.06220/) (2024)
- [Self-Supervised Learning from Structural Invariance](https://mlsanity.com/paper/2602.02381/) (2026)
- [Does Your Neural Network Extrapolate? Feature Engineering as Identifiability Bias for OOD Generalization](https://mlsanity.com/paper/2605.07483/) (2026)
- [Structure-agnostic Causal Representation Learning](https://mlsanity.com/paper/2610.00968/) (2026)
- [Invariant Correlation of Representation with Label: Enhancing Domain Generalization in Noisy Environments](https://mlsanity.com/paper/2407.01749/) (2024)

## Abstract (arXiv)

Recent empirical studies on domain generalization (DG) have shown that DG algorithms that perform well on some distribution shifts fail on others, and no state-of-the-art DG algorithm performs consistently well on all shifts. Moreover, real-world data often has multiple distribution shifts over different attributes; hence we introduce multi-attribute distribution shift datasets and find that the accuracy of existing DG algorithms falls even further. To explain these results, we provide a formal characterization of generalization under multi-attribute shifts using a canonical causal graph. Based on the relationship between spurious attributes and the classification label, we obtain realizations of the canonical causal graph that characterize common distribution shifts and show that each shift entails different independence constraints over observed variables. As a result, we prove that any algorithm based on a single, fixed constraint cannot work well across all shifts, providing theoretical evidence for mixed empirical results on DG algorithms. Based on this insight, we develop Causally Adaptive Constraint Minimization (CACM), an algorithm that uses knowledge about the data-generating process to adaptively identify and apply the correct independence constraints for regularization. Results on fully synthetic, MNIST, small NORB, and Waterbirds datasets, covering binary and multi-valued attributes and labels, show that adaptive dataset-dependent constraints lead to the highest accuracy on unseen domains whereas incorrect constraints fail to do so. Our results demonstrate the importance of modeling the causal relationships inherent in the data-generating process.