# A Generalization Error Bound for Multi-class Domain Generalization

arXiv: https://arxiv.org/abs/1905.10392 · HTML: https://mlsanity.com/paper/1905.10392/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2019.

## Built on by (most cited first, 26 of 26)

- [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)
- [Towards Out-Of-Distribution Generalization: A Survey](https://mlsanity.com/paper/2108.13624/) (2021)
- [Model-Based Domain Generalization](https://mlsanity.com/paper/2102.11436/) (2021)
- [Towards a Theoretical Framework of Out-of-Distribution Generalization](https://mlsanity.com/paper/2106.04496/) (2021)
- [Domain-Adjusted Regression or: ERM May Already Learn Features Sufficient for Out-of-Distribution Generalization](https://mlsanity.com/paper/2202.06856/) (2022)
- [Adaptive Methods for Real-World Domain Generalization](https://mlsanity.com/paper/2103.15796/) (2021)
- [Probable Domain Generalization via Quantile Risk Minimization](https://mlsanity.com/paper/2207.09944/) (2022)
- [Credal Learning Theory](https://mlsanity.com/paper/2402.00957/) (2024)
- [An Online Learning Approach to Interpolation and Extrapolation in Domain Generalization](https://mlsanity.com/paper/2102.13128/) (2021)
- [Joint Learning of Label and Environment Causal Independence for Graph Out-of-Distribution Generalization](https://mlsanity.com/paper/2306.01103/) (2023)
- [Fairness and Accuracy under Domain Generalization](https://mlsanity.com/paper/2301.13323/) (2023)
- [MADG: Margin-based Adversarial Learning for Domain Generalization](https://mlsanity.com/paper/2311.08503/) (2023)
- [On the benefits of representation regularization in invariance based domain generalization](https://mlsanity.com/paper/2105.14529/) (2021)
- [On Learning Domain-Invariant Representations for Transfer Learning with Multiple Sources](https://mlsanity.com/paper/2111.13822/) (2021)
- [Graph Structure and Feature Extrapolation for Out-of-Distribution Generalization](https://mlsanity.com/paper/2306.08076/) (2023)
- [HMOE: Hypernetwork-based Mixture of Experts for Domain Generalization](https://mlsanity.com/paper/2211.08253/) (2022)
- [Epistemic Artificial Intelligence is Essential for Machine Learning Models to Truly 'Know When They Do Not Know'](https://mlsanity.com/paper/2505.04950/) (2025)
- [Fine-grained Generalization Analysis of Vector-valued Learning](https://mlsanity.com/paper/2104.14173/) (2021)
- [Generalization Properties of Retrieval-based Models](https://mlsanity.com/paper/2210.02617/) (2022)
- [Discriminative Domain-Invariant Adversarial Network for Deep Domain Generalization](https://mlsanity.com/paper/2108.08995/) (2021)
- [Explainability-aided Domain Generalization for Image Classification](https://mlsanity.com/paper/2104.01742/) (2021)
- [Offline RL With Resource Constrained Online Deployment](https://mlsanity.com/paper/2110.03165/) (2021)
- [Epistemic Errors of Imperfect Multitask Learners When Distributions Shift](https://mlsanity.com/paper/2505.23496/) (2025)
- [Counterfactual Supervision-based Information Bottleneck for Out-of-Distribution Generalization](https://mlsanity.com/paper/2208.07798/) (2022)
- [Structural State Translation: Condition Transfer between Civil Structures Using Domain-Generalization for Structural Health Monitoring](https://mlsanity.com/paper/2212.14048/) (2022)

## Abstract (arXiv)

Domain generalization is the problem of assigning labels to an unlabeled data set, given several similar data sets for which labels have been provided. Despite considerable interest in this problem over the last decade, there has been no theoretical analysis in the setting of multi-class classification. In this work, we study a kernel-based learning algorithm and establish a generalization error bound that scales logarithmically in the number of classes, matching state-of-the-art bounds for multi-class classification in the conventional learning setting. We also demonstrate empirically that the proposed algorithm achieves significant performance gains compared to a pooling strategy.