# Barycentric-alignment and reconstruction loss minimization for domain generalization

arXiv: https://arxiv.org/abs/2109.01902 · HTML: https://mlsanity.com/paper/2109.01902/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 55 references that are in the map.
- First posted on arXiv 4 Sep 2021.

## Builds on (most cited first, 27 of 27)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (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)
- [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)
- [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)
- [SWAD: Domain Generalization by Seeking Flat Minima](https://mlsanity.com/paper/2102.08604/) (2021)
- [Domain Generalization via Model-Agnostic Learning of Semantic Features](https://mlsanity.com/paper/1910.13580/) (2019)
- [Fast Computation of Wasserstein Barycenters](https://mlsanity.com/paper/1310.4375/) (2013)
- [Adaptive Risk Minimization: Learning to Adapt to Domain Shift](https://mlsanity.com/paper/2007.02931/) (2020)
- [Domain Generalization by Marginal Transfer Learning](https://mlsanity.com/paper/1711.07910/) (2017)
- [Generalizing to unseen domains via distribution matching](https://mlsanity.com/paper/1911.00804/) (2019)
- [Theoretical Analysis of Domain Adaptation with Optimal Transport](https://mlsanity.com/paper/1610.04420/) (2016)
- [Learning to Learn with Variational Information Bottleneck for Domain Generalization](https://mlsanity.com/paper/2007.07645/) (2020)
- [Support and Invertibility in Domain-Invariant Representations](https://mlsanity.com/paper/1903.03448/) (2019)
- [Domain Adaptation with Asymmetrically-Relaxed Distribution Alignment](https://mlsanity.com/paper/1903.01689/) (2019)
- [Scalable Computations of Wasserstein Barycenter via Input Convex Neural Networks](https://mlsanity.com/paper/2007.04462/) (2020)
- [Domain Generalization via Optimal Transport with Metric Similarity Learning](https://mlsanity.com/paper/2007.10573/) (2020)
- [Rethinking Domain Generalization Baselines](https://mlsanity.com/paper/2101.09060/) (2021)
- [EEG-Based Driver Drowsiness Estimation Using Feature Weighted Episodic Training](https://mlsanity.com/paper/1909.11456/) (2019)
- [Domain Adaptation for Robust Workload Level Alignment Between Sessions and Subjects using fNIRS](https://mlsanity.com/paper/2007.06706/) (2020)

## Built on by (most cited first, 1 of 1)

- [A principled approach to model validation in domain generalization](https://mlsanity.com/paper/2304.00629/) (2023)

## Abstract (arXiv)

This paper advances the theory and practice of Domain Generalization (DG) in machine learning. We consider the typical DG setting where the hypothesis is composed of a representation mapping followed by a labeling function. Within this setting, the majority of popular DG methods aim to jointly learn the representation and the labeling functions by minimizing a well-known upper bound for the classification risk in the unseen domain. In practice, however, methods based on this theoretical upper bound ignore a term that cannot be directly optimized due to its dual dependence on both the representation mapping and the unknown optimal labeling function in the unseen domain. To bridge this gap between theory and practice, we introduce a new upper bound that is free of terms having such dual dependence, resulting in a fully optimizable risk upper bound for the unseen domain. Our derivation leverages classical and recent transport inequalities that link optimal transport metrics with information-theoretic measures. Compared to previous bounds, our bound introduces two new terms: (i) the Wasserstein-2 barycenter term that aligns distributions between domains, and (ii) the reconstruction loss term that assesses the quality of representation in reconstructing the original data. Based on this new upper bound, we propose a novel DG algorithm named Wasserstein Barycenter Auto-Encoder (WBAE) that simultaneously minimizes the classification loss, the barycenter loss, and the reconstruction loss. Numerical results demonstrate that the proposed method outperforms current state-of-the-art DG algorithms on several datasets.