# Domain Generalization via Conditional Invariant Representation

arXiv: https://arxiv.org/abs/1807.08479 · HTML: https://mlsanity.com/paper/1807.08479/

## Key facts

- Cited by 146 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jul 2018.

## Built on by (most cited first, 30 of 146)

- [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)
- [SWAD: Domain Generalization by Seeking Flat Minima](https://mlsanity.com/paper/2102.08604/) (2021)
- [Towards Causal Representation Learning](https://mlsanity.com/paper/2102.11107/) (2021)
- [Fishr: Invariant Gradient Variances for Out-of-Distribution Generalization](https://mlsanity.com/paper/2109.02934/) (2021)
- [Domain Generalization by Mutual-Information Regularization with Pre-trained Models](https://mlsanity.com/paper/2203.10789/) (2022)
- [Sharpness-Aware Gradient Matching for Domain Generalization](https://mlsanity.com/paper/2303.10353/) (2023)
- [OoD-Bench: Quantifying and Understanding Two Dimensions of Out-of-Distribution Generalization](https://mlsanity.com/paper/2106.03721/) (2021)
- [Exploiting Domain-Specific Features to Enhance Domain Generalization](https://mlsanity.com/paper/2110.09410/) (2021)
- [Adaptive Methods for Real-World Domain Generalization](https://mlsanity.com/paper/2103.15796/) (2021)
- [MixStyle Neural Networks for Domain Generalization and Adaptation](https://mlsanity.com/paper/2107.02053/) (2021)
- [Domain Invariant Representation Learning with Domain Density Transformations](https://mlsanity.com/paper/2102.05082/) (2021)
- [Mechanistic Mode Connectivity](https://mlsanity.com/paper/2211.08422/) (2022)
- [Out-of-distribution Generalization with Causal Invariant Transformations](https://mlsanity.com/paper/2203.11528/) (2022)
- [Leveraging Vision-Language Models for Improving Domain Generalization in Image Classification](https://mlsanity.com/paper/2310.08255/) (2023)
- [Modeling the Data-Generating Process is Necessary for Out-of-Distribution Generalization](https://mlsanity.com/paper/2206.07837/) (2022)
- [Domain-invariant Feature Exploration for Domain Generalization](https://mlsanity.com/paper/2207.12020/) (2022)
- [DiPrompT: Disentangled Prompt Tuning for Multiple Latent Domain Generalization in Federated Learning](https://mlsanity.com/paper/2403.08506/) (2024)
- [Domain Generalization in Computational Pathology: Survey and Guidelines](https://mlsanity.com/paper/2310.19656/) (2023)
- [Flatness-Aware Minimization for Domain Generalization](https://mlsanity.com/paper/2307.11108/) (2023)
- [On Multi-Domain Long-Tailed Recognition, Imbalanced Domain Generalization and Beyond](https://mlsanity.com/paper/2203.09513/) (2022)
- [Learning to Generalize across Domains on Single Test Samples](https://mlsanity.com/paper/2202.08045/) (2022)
- [Fairness and Accuracy under Domain Generalization](https://mlsanity.com/paper/2301.13323/) (2023)
- [Supervised Algorithmic Fairness in Distribution Shifts: A Survey](https://mlsanity.com/paper/2402.01327/) (2024)
- [Rethinking Multi-domain Generalization with A General Learning Objective](https://mlsanity.com/paper/2402.18853/) (2024)
- [Style-Hallucinated Dual Consistency Learning: A Unified Framework for Visual Domain Generalization](https://mlsanity.com/paper/2212.09068/) (2022)
- [Invariant Learning via Probability of Sufficient and Necessary Causes](https://mlsanity.com/paper/2309.12559/) (2023)
- [StableFDG: Style and Attention Based Learning for Federated Domain Generalization](https://mlsanity.com/paper/2311.00227/) (2023)
- [DART: Diversify-Aggregate-Repeat Training Improves Generalization of Neural Networks](https://mlsanity.com/paper/2302.14685/) (2023)
- [Rethinking the Evaluation Protocol of Domain Generalization](https://mlsanity.com/paper/2305.15253/) (2023)

## Abstract (arXiv)

Domain generalization aims to apply knowledge gained from multiple labeled source domains to unseen target domains. The main difficulty comes from the dataset bias: training data and test data have different distributions, and the training set contains heterogeneous samples from different distributions. Let X denote the features, and Y be the class labels. Existing domain generalization methods address the dataset bias problem by learning a domain-invariant representation h(X) that has the same marginal distribution mathbbP(h(X)) across multiple source domains. The functional relationship encoded in mathbbP(Y|X) is usually assumed to be stable across domains such that mathbbP(Y|h(X)) is also invariant. However, it is unclear whether this assumption holds in practical problems. In this paper, we consider the general situation where both mathbbP(X) and mathbbP(Y|X) can change across all domains. We propose to learn a feature representation which has domain-invariant class conditional distributions mathbbP(h(X)|Y). With the conditional invariant representation, the invariance of the joint distribution mathbbP(h(X),Y) can be guaranteed if the class prior mathbbP(Y) does not change across training and test domains. Extensive experiments on both synthetic and real data demonstrate the effectiveness of the proposed method.