# Conditional Bures Metric for Domain Adaptation

arXiv: https://arxiv.org/abs/2108.00302 · HTML: https://mlsanity.com/paper/2108.00302/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 47 references that are in the map.
- First posted on arXiv 31 Jul 2021.

## Builds on (most cited first, 17 of 17)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Learning Transferable Features with Deep Adaptation Networks](https://mlsanity.com/paper/1502.02791/) (2015)
- [Deep Hashing Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1706.07522/) (2017)
- [CyCADA: Cycle-Consistent Adversarial Domain Adaptation](https://mlsanity.com/paper/1711.03213/) (2017)
- [Deep Transfer Learning with Joint Adaptation Networks](https://mlsanity.com/paper/1605.06636/) (2016)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Return of Frustratingly Easy Domain Adaptation](https://mlsanity.com/paper/1511.05547/) (2015)
- [Joint Distribution Optimal Transportation for Domain Adaptation](https://mlsanity.com/paper/1705.08848/) (2017)
- [DeepJDOT: Deep Joint Distribution Optimal Transport for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1803.10081/) (2018)
- [Deep Subdomain Adaptation Network for Image Classification](https://mlsanity.com/paper/2106.09388/) (2021)
- [Maximum Density Divergence for Domain Adaptation](https://mlsanity.com/paper/2004.12615/) (2020)
- [Discriminative Adversarial Domain Adaptation](https://mlsanity.com/paper/1911.12036/) (2019)
- [Unsupervised Multi-Class Domain Adaptation: Theory, Algorithms, and Practice](https://mlsanity.com/paper/2002.08681/) (2020)
- [Unsupervised Domain Adaptation via Discriminative Manifold Propagation](https://mlsanity.com/paper/2008.10030/) (2020)
- [A Rigorous Theory of Conditional Mean Embeddings](https://mlsanity.com/paper/1912.00671/) (2019)

## Built on by (most cited first, 25 of 25)

- [Reusing the Task-specific Classifier as a Discriminator: Discriminator-free Adversarial Domain Adaptation](https://mlsanity.com/paper/2204.03838/) (2022)
- [Patch-Mix Transformer for Unsupervised Domain Adaptation: A Game Perspective](https://mlsanity.com/paper/2303.13434/) (2023)
- [Divide to Adapt: Mitigating Confirmation Bias for Domain Adaptation of Black-Box Predictors](https://mlsanity.com/paper/2205.14467/) (2022)
- [Undoing the Damage of Label Shift for Cross-domain Semantic Segmentation](https://mlsanity.com/paper/2204.05546/) (2022)
- [Learning Unbiased Transferability for Domain Adaptation by Uncertainty Modeling](https://mlsanity.com/paper/2206.01319/) (2022)
- [Towards Unsupervised Domain Adaptation via Domain-Transformer](https://mlsanity.com/paper/2202.13777/) (2022)
- [Dynamic Instance Domain Adaptation](https://mlsanity.com/paper/2203.05028/) (2022)
- [Consistent Optimal Transport with Empirical Conditional Measures](https://mlsanity.com/paper/2305.15901/) (2023)
- [Domain Adaptation with Cauchy-Schwarz Divergence](https://mlsanity.com/paper/2405.19978/) (2024)
- [Pseudo-keypoint RKHS Learning for Self-supervised 6DoF Pose Estimation](https://mlsanity.com/paper/2311.09500/) (2023)
- [COD: Learning Conditional Invariant Representation for Domain Adaptation Regression](https://mlsanity.com/paper/2408.06638/) (2024)
- [Generalized Label Shift Correction via Minimum Uncertainty Principle: Theory and Algorithm](https://mlsanity.com/paper/2202.13043/) (2022)
- [Discriminative Radial Domain Adaptation](https://mlsanity.com/paper/2301.00383/) (2023)
- [Uncertainty-Guided Alignment for Unsupervised Domain Adaptation in Regression](https://mlsanity.com/paper/2401.13721/) (2024)
- [SPNet: A novel deep neural network for retinal vessel segmentation based on shared decoder and pyramid-like loss](https://mlsanity.com/paper/2202.09515/) (2022)
- [Maximizing Conditional Independence for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2203.03212/) (2022)
- [When Invariant Representation Learning Meets Label Shift: Insufficiency and Theoretical Insights](https://mlsanity.com/paper/2406.16608/) (2024)
- [Geometric Understanding of Discriminability and Transferability for Visual Domain Adaptation](https://mlsanity.com/paper/2407.09524/) (2024)
- [Partial Domain Adaptation via Importance Sampling-based Shift Correction](https://mlsanity.com/paper/2507.20191/) (2025)
- [Geometry-Aware Unsupervised Domain Adaptation](https://mlsanity.com/paper/2112.11041/) (2021)
- [Bures Joint Distribution Alignment with Dynamic Margin for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2203.06836/) (2022)
- [OT Score: An OT based Confidence Score for Prototype-Assisted Source Free Unsupervised Domain Adaptation](https://mlsanity.com/paper/2505.11669/) (2025)
- [A Generalized Label Shift Perspective for Cross-Domain Gaze Estimation](https://mlsanity.com/paper/2505.13043/) (2025)
- [Bi-level Unbalanced Optimal Transport for Partial Domain Adaptation](https://mlsanity.com/paper/2506.08020/) (2025)
- [Locality-aware Private Class Identification for Domain Adaptation with Extreme Label Shift](https://mlsanity.com/paper/2605.05567/) (2026)

## Abstract (arXiv)

As a vital problem in classification-oriented transfer, unsupervised domain adaptation (UDA) has attracted widespread attention in recent years. Previous UDA methods assume the marginal distributions of different domains are shifted while ignoring the discriminant information in the label distributions. This leads to classification performance degeneration in real applications. In this work, we focus on the conditional distribution shift problem which is of great concern to current conditional invariant models. We aim to seek a kernel covariance embedding for conditional distribution which remains yet unexplored. Theoretically, we propose the Conditional Kernel Bures (CKB) metric for characterizing conditional distribution discrepancy, and derive an empirical estimation for the CKB metric without introducing the implicit kernel feature map. It provides an interpretable approach to understand the knowledge transfer mechanism. The established consistency theory of the empirical estimation provides a theoretical guarantee for convergence. A conditional distribution matching network is proposed to learn the conditional invariant and discriminative features for UDA. Extensive experiments and analysis show the superiority of our proposed model.