# Domain Generalisation via Risk Distribution Matching

arXiv: https://arxiv.org/abs/2310.18598 · HTML: https://mlsanity.com/paper/2310.18598/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 64 references that are in the map.
- First posted on arXiv 28 Oct 2023.

## Builds on (most cited first, 30 of 38)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Moment Matching for Multi-Source Domain Adaptation](https://mlsanity.com/paper/1812.01754/) (2018)
- [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)
- [Deep Hashing Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1706.07522/) (2017)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [Deeper, Broader and Artier Domain Generalization](https://mlsanity.com/paper/1710.03077/) (2017)
- [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)
- [Recognition in Terra Incognita](https://mlsanity.com/paper/1807.04975/) (2018)
- [Domain Generalization via Invariant Feature Representation](https://mlsanity.com/paper/1301.2115/) (2013)
- [Domain Generalization with MixStyle](https://mlsanity.com/paper/2104.02008/) (2021)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Unified Deep Supervised Domain Adaptation and Generalization](https://mlsanity.com/paper/1709.10190/) (2017)
- [Gradient Matching for Domain Generalization](https://mlsanity.com/paper/2104.09937/) (2021)
- [Generative Moment Matching Networks](https://mlsanity.com/paper/1502.02761/) (2015)
- [MMD GAN: Towards Deeper Understanding of Moment Matching Network](https://mlsanity.com/paper/1705.08584/) (2017)
- [Domain Generalization using Causal Matching](https://mlsanity.com/paper/2006.07500/) (2020)
- [Fishr: Invariant Gradient Variances for Out-of-Distribution Generalization](https://mlsanity.com/paper/2109.02934/) (2021)
- [Progressive Feature Alignment for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1811.08585/) (2018)
- [Domain Generalization via Conditional Invariant Representation](https://mlsanity.com/paper/1807.08479/) (2018)
- [Invariance, Causality and Robustness](https://mlsanity.com/paper/1812.08233/) (2018)
- [Exact Feature Distribution Matching for Arbitrary Style Transfer and Domain Generalization](https://mlsanity.com/paper/2203.07740/) (2022)
- [Generalizing to unseen domains via distribution matching](https://mlsanity.com/paper/1911.00804/) (2019)
- [Domain Agnostic Learning with Disentangled Representations](https://mlsanity.com/paper/1904.12347/) (2019)

## Built on by (most cited first, 14 of 14)

- [Bridging Domain Generalization to Multimodal Domain Generalization via Unified Representations](https://mlsanity.com/paper/2507.03304/) (2025)
- [Domain Generalization via Pareto Optimal Gradient Matching](https://mlsanity.com/paper/2507.14227/) (2025)
- [Distribution Shift Is Key to Learning Invariant Prediction](https://mlsanity.com/paper/2601.12296/) (2026)
- [DICS: Find Domain-Invariant and Class-Specific Features for Out-of-Distribution Generalization](https://mlsanity.com/paper/2409.08557/) (2024)
- [GNN-based Unified Deep Learning](https://mlsanity.com/paper/2508.10583/) (2025)
- [CPCANet: Deep Unfolding Common Principal Component Analysis for Domain Generalization](https://mlsanity.com/paper/2605.05136/) (2026)
- [Guidance Not Obstruction: A Conjugate Consistent Enhanced Strategy for Domain Generalization](https://mlsanity.com/paper/2412.10089/) (2024)
- [Should Bias be Eliminated? A General Framework to Use Bias for OOD Generalization](https://mlsanity.com/paper/2507.17001/) (2025)
- [CFL: On the Use of Characteristic Function Loss for Domain Alignment in Machine Learning](https://mlsanity.com/paper/2511.02148/) (2025)
- [SemAlign: Language Guided Semi-supervised Domain Generalization](https://mlsanity.com/paper/2601.11724/) (2026)
- [Negatives-Dominant Contrastive Learning for Generalization in Imbalanced Domains](https://mlsanity.com/paper/2601.21999/) (2026)
- [Environment-Conditioned Tail Reweighting for Invariant Learning under Mixed Shifts](https://mlsanity.com/paper/2601.22944/) (2026)
- [Projection Pursuit CPCANet for Domain Generalization](https://mlsanity.com/paper/2607.22117/) (2026)
- [Domain Generalization for Smartphone-Based Human Activity Recognition: A Systematic Analysis of Components and Interactions](https://mlsanity.com/paper/2609.14863/) (2026)

## Abstract (arXiv)

We propose a novel approach for domain generalisation (DG) leveraging risk distributions to characterise domains, thereby achieving domain invariance. In our findings, risk distributions effectively highlight differences between training domains and reveal their inherent complexities. In testing, we may observe similar, or potentially intensifying in magnitude, divergences between risk distributions. Hence, we propose a compelling proposition: Minimising the divergences between risk distributions across training domains leads to robust invariance for DG. The key rationale behind this concept is that a model, trained on domain-invariant or stable features, may consistently produce similar risk distributions across various domains. Building upon this idea, we propose Risk Distribution Matching (RDM). Using the maximum mean discrepancy (MMD) distance, RDM aims to minimise the variance of risk distributions across training domains. However, when the number of domains increases, the direct optimisation of variance leads to linear growth in MMD computations, resulting in inefficiency. Instead, we propose an approximation that requires only one MMD computation, by aligning just two distributions: that of the worst-case domain and the aggregated distribution from all domains. Notably, this method empirically outperforms optimising distributional variance while being computationally more efficient. Unlike conventional DG matching algorithms, RDM stands out for its enhanced efficacy by concentrating on scalar risk distributions, sidestepping the pitfalls of high-dimensional challenges seen in feature or gradient matching. Our extensive experiments on standard benchmark datasets demonstrate that RDM shows superior generalisation capability over state-of-the-art DG methods.