# A Unified Joint Maximum Mean Discrepancy for Domain Adaptation

arXiv: https://arxiv.org/abs/2101.09979 · HTML: https://mlsanity.com/paper/2101.09979/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 56 references that are in the map.
- First posted on arXiv 25 Jan 2021.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Features with Deep Adaptation Networks](https://mlsanity.com/paper/1502.02791/) (2015)
- [Deep Transfer Learning with Joint Adaptation Networks](https://mlsanity.com/paper/1605.06636/) (2016)
- [Deep Domain Confusion: Maximizing for Domain Invariance](https://mlsanity.com/paper/1412.3474/) (2014)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Contrastive Adaptation Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1901.00976/) (2019)
- [Joint Distribution Optimal Transportation for Domain Adaptation](https://mlsanity.com/paper/1705.08848/) (2017)
- [Generative Moment Matching Networks](https://mlsanity.com/paper/1502.02761/) (2015)
- [Universal Source-Free Domain Adaptation](https://mlsanity.com/paper/2004.04393/) (2020)
- [DeepJDOT: Deep Joint Distribution Optimal Transport for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1803.10081/) (2018)
- [Mind the Class Weight Bias: Weighted Maximum Mean Discrepancy for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1705.00609/) (2017)
- [Rethinking Class-Balanced Methods for Long-Tailed Visual Recognition from a Domain Adaptation Perspective](https://mlsanity.com/paper/2003.10780/) (2020)
- [Gradually Vanishing Bridge for Adversarial Domain Adaptation](https://mlsanity.com/paper/2003.13183/) (2020)
- [InfoVAE: Information Maximizing Variational Autoencoders](https://mlsanity.com/paper/1706.02262/) (2017)
- [Visual Domain Adaptation with Manifold Embedded Distribution Alignment](https://mlsanity.com/paper/1807.07258/) (2018)
- [Open Compound Domain Adaptation](https://mlsanity.com/paper/1909.03403/) (2019)
- [Unsupervised Domain Adaptation via Structured Prediction Based Selective Pseudo-Labeling](https://mlsanity.com/paper/1911.07982/) (2019)
- [Domain Adaptive Neural Networks for Object Recognition](https://mlsanity.com/paper/1409.6041/) (2014)
- [Joint Geometrical and Statistical Alignment for Visual Domain Adaptation](https://mlsanity.com/paper/1705.05498/) (2017)
- [A Linear-Time Kernel Goodness-of-Fit Test](https://mlsanity.com/paper/1705.07673/) (2017)
- [Transfer Learning with Dynamic Distribution Adaptation](https://mlsanity.com/paper/1909.08531/) (2019)
- [Balanced Distribution Adaptation for Transfer Learning](https://mlsanity.com/paper/1807.00516/) (2018)
- [Wasserstein Discriminant Analysis](https://mlsanity.com/paper/1608.08063/) (2016)
- [Locality Preserving Joint Transfer for Domain Adaptation](https://mlsanity.com/paper/1906.07441/) (2019)
- [Easy Transfer Learning By Exploiting Intra-domain Structures](https://mlsanity.com/paper/1904.01376/) (2019)
- [Learning Domain-Invariant Subspace using Domain Features and Independence Maximization](https://mlsanity.com/paper/1603.04535/) (2016)
- [Mining Label Distribution Drift in Unsupervised Domain Adaptation](https://mlsanity.com/paper/2006.09565/) (2020)

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

- [Bridging Contrastive Learning and Domain Adaptation: Theoretical Perspective and Practical Application](https://mlsanity.com/paper/2502.00052/) (2025)

## Abstract (arXiv)

Domain adaptation has received a lot of attention in recent years, and many algorithms have been proposed with impressive progress. However, it is still not fully explored concerning the joint probability distribution (P(X, Y)) distance for this problem, since its empirical estimation derived from the maximum mean discrepancy (joint maximum mean discrepancy, JMMD) will involve complex tensor-product operator that is hard to manipulate. To solve this issue, this paper theoretically derives a unified form of JMMD that is easy to optimize, and proves that the marginal, class conditional and weighted class conditional probability distribution distances are our special cases with different label kernels, among which the weighted class conditional one not only can realize feature alignment across domains in the category level, but also deal with imbalance dataset using the class prior probabilities. From the revealed unified JMMD, we illustrate that JMMD degrades the feature-label dependence (discriminability) that benefits to classification, and it is sensitive to the label distribution shift when the label kernel is the weighted class conditional one. Therefore, we leverage Hilbert Schmidt independence criterion and propose a novel MMD matrix to promote the dependence, and devise a novel label kernel that is robust to label distribution shift. Finally, we conduct extensive experiments on several cross-domain datasets to demonstrate the validity and effectiveness of the revealed theoretical results.