# Beyond H-Divergence: Domain Adaptation Theory With Jensen-Shannon Divergence

arXiv: https://arxiv.org/abs/2007.15567 · HTML: https://mlsanity.com/paper/2007.15567/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jul 2020.

## Built on by (most cited first, 15 of 15)

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- [Task-specific Inconsistency Alignment for Domain Adaptive Object Detection](https://mlsanity.com/paper/2203.15345/) (2022)
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- [Gap Minimization for Knowledge Sharing and Transfer](https://mlsanity.com/paper/2201.11231/) (2022)
- [Jacobian Norm for Unsupervised Source-Free Domain Adaptation](https://mlsanity.com/paper/2204.03467/) (2022)
- [User-Centric Federated Learning: Trading off Wireless Resources for Personalization](https://mlsanity.com/paper/2304.12930/) (2023)
- [Data-dependent and Oracle Bounds on Forgetting in Continual Learning](https://mlsanity.com/paper/2406.09370/) (2024)
- [Fairness Overfitting in Machine Learning: An Information-Theoretic Perspective](https://mlsanity.com/paper/2506.07861/) (2025)
- [Joint Semi-supervised 3D Super-Resolution and Segmentation with Mixed Adversarial Gaussian Domain Adaptation](https://mlsanity.com/paper/2107.07975/) (2021)
- [Class-wise Generalization Error: an Information-Theoretic Analysis](https://mlsanity.com/paper/2401.02904/) (2024)
- [Semi-Supervised Domain Adaptation by Similarity based Pseudo-label Injection](https://mlsanity.com/paper/2209.01881/) (2022)
- [Understanding Generalization in Role-Playing Models via Information Theory](https://mlsanity.com/paper/2512.17270/) (2025)

## Abstract (arXiv)

We reveal the incoherence between the widely-adopted empirical domain adversarial training and its generally-assumed theoretical counterpart based on H-divergence. Concretely, we find that H-divergence is not equivalent to Jensen-Shannon divergence, the optimization objective in domain adversarial training. To this end, we establish a new theoretical framework by directly proving the upper and lower target risk bounds based on joint distributional Jensen-Shannon divergence. We further derive bi-directional upper bounds for marginal and conditional shifts. Our framework exhibits inherent flexibilities for different transfer learning problems, which is usable for various scenarios where H-divergence-based theory fails to adapt. From an algorithmic perspective, our theory enables a generic guideline unifying principles of semantic conditional matching, feature marginal matching, and label marginal shift correction. We employ algorithms for each principle and empirically validate the benefits of our framework on real datasets.