# Instrumental Variable-Driven Domain Generalization with Unobserved Confounders

arXiv: https://arxiv.org/abs/2110.01438 · HTML: https://mlsanity.com/paper/2110.01438/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 92 references that are in the map.
- First posted on arXiv 4 Oct 2021.

## Builds on (most cited first, 30 of 46)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Unsupervised Domain Adaptation by Backpropagation](https://mlsanity.com/paper/1409.7495/) (2014)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Moment Matching for Multi-Source Domain Adaptation](https://mlsanity.com/paper/1812.01754/) (2018)
- [Learning Transferable Features with Deep Adaptation Networks](https://mlsanity.com/paper/1502.02791/) (2015)
- [Deep Hashing Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1706.07522/) (2017)
- [Deeper, Broader and Artier Domain Generalization](https://mlsanity.com/paper/1710.03077/) (2017)
- [Do We Really Need to Access the Source Data? Source Hypothesis Transfer for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2002.08546/) (2020)
- [Learning to Generalize: Meta-Learning for Domain Generalization](https://mlsanity.com/paper/1710.03463/) (2017)
- [Maximum Classifier Discrepancy for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1712.02560/) (2017)
- [Deep Transfer Learning with Joint Adaptation Networks](https://mlsanity.com/paper/1605.06636/) (2016)
- [Domain Generalization with MixStyle](https://mlsanity.com/paper/2104.02008/) (2021)
- [Generalizing to Unseen Domains via Adversarial Data Augmentation](https://mlsanity.com/paper/1805.12018/) (2018)
- [Domain Generalization by Solving Jigsaw Puzzles](https://mlsanity.com/paper/1903.06864/) (2019)
- [Self-Challenging Improves Cross-Domain Generalization](https://mlsanity.com/paper/2007.02454/) (2020)
- [Domain Generalization via Model-Agnostic Learning of Semantic Features](https://mlsanity.com/paper/1910.13580/) (2019)
- [Bridging Theory and Algorithm for Domain Adaptation](https://mlsanity.com/paper/1904.05801/) (2019)
- [Learning to Learn Single Domain Generalization](https://mlsanity.com/paper/2003.13216/) (2020)
- [Learning to Generate Novel Domains for Domain Generalization](https://mlsanity.com/paper/2007.03304/) (2020)
- [Generalizing Across Domains via Cross-Gradient Training](https://mlsanity.com/paper/1804.10745/) (2018)
- [Learning Not to Learn: Training Deep Neural Networks with Biased Data](https://mlsanity.com/paper/1812.10352/) (2018)
- [Domain Generalization for Object Recognition with Multi-task Autoencoders](https://mlsanity.com/paper/1508.07680/) (2015)
- [Episodic Training for Domain Generalization](https://mlsanity.com/paper/1902.00113/) (2019)
- [Deep Domain-Adversarial Image Generation for Domain Generalisation](https://mlsanity.com/paper/2003.06054/) (2020)
- [Domain Generalization using Causal Matching](https://mlsanity.com/paper/2006.07500/) (2020)
- [Domain Generalization Using a Mixture of Multiple Latent Domains](https://mlsanity.com/paper/1911.07661/) (2019)
- [Learning to Optimize Domain Specific Normalization for Domain Generalization](https://mlsanity.com/paper/1907.04275/) (2019)
- [Deep Stable Learning for Out-Of-Distribution Generalization](https://mlsanity.com/paper/2104.07876/) (2021)
- [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)

## Built on by (most cited first, 7 of 7)

- [Universal Domain Adaptation via Compressive Attention Matching](https://mlsanity.com/paper/2304.11862/) (2023)
- [CausalMACE: Causality Empowered Multi-Agents in Minecraft Cooperative Tasks](https://mlsanity.com/paper/2508.18797/) (2025)
- [Generalized Universal Domain Adaptation with Generative Flow Networks](https://mlsanity.com/paper/2305.04466/) (2023)
- [Quantitatively Measuring and Contrastively Exploring Heterogeneity for Domain Generalization](https://mlsanity.com/paper/2305.15889/) (2023)
- [Domain Adversarial Active Learning for Domain Generalization Classification](https://mlsanity.com/paper/2403.06174/) (2024)
- [Dual Causal Inference: Integrating Backdoor Adjustment and Instrumental Variable Learning for Medical VQA](https://mlsanity.com/paper/2604.20306/) (2026)
- [Feature Matching Intervention: Leveraging Observational Data for Causal Representation Learning](https://mlsanity.com/paper/2503.03634/) (2025)

## Abstract (arXiv)

Domain generalization (DG) aims to learn from multiple source domains a model that can generalize well on unseen target domains. Existing DG methods mainly learn the representations with invariant marginal distribution of the input features, however, the invariance of the conditional distribution of the labels given the input features is more essential for unknown domain prediction. Meanwhile, the existing of unobserved confounders which affect the input features and labels simultaneously cause spurious correlation and hinder the learning of the invariant relationship contained in the conditional distribution. Interestingly, with a causal view on the data generating process, we find that the input features of one domain are valid instrumental variables for other domains. Inspired by this finding, we propose an instrumental variable-driven DG method (IV-DG) by removing the bias of the unobserved confounders with two-stage learning. In the first stage, it learns the conditional distribution of the input features of one domain given input features of another domain. In the second stage, it estimates the relationship by predicting labels with the learned conditional distribution. Theoretical analyses and simulation experiments show that it accurately captures the invariant relationship. Extensive experiments on real-world datasets demonstrate that IV-DG method yields state-of-the-art results.