# Rethink Maximum Mean Discrepancy for Domain Adaptation

arXiv: https://arxiv.org/abs/2007.00689 · HTML: https://mlsanity.com/paper/2007.00689/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jul 2020.

## Built on by (most cited first, 11 of 11)

- [DARCNN: Domain Adaptive Region-based Convolutional Neural Network for Unsupervised Instance Segmentation in Biomedical Images](https://mlsanity.com/paper/2104.01325/) (2021)
- [Deep Learning for Cross-Domain Few-Shot Visual Recognition: A Survey](https://mlsanity.com/paper/2303.08557/) (2023)
- [Semi-supervised Domain Adaptive Structure Learning](https://mlsanity.com/paper/2112.06161/) (2021)
- [Approximate Domain Unlearning for Vision-Language Models](https://mlsanity.com/paper/2510.08132/) (2025)
- [Zero-Shot End-to-End Spoken Language Understanding via Cross-Modal Selective Self-Training](https://mlsanity.com/paper/2305.12793/) (2023)
- [ModSelect: Automatic Modality Selection for Synthetic-to-Real Domain Generalization](https://mlsanity.com/paper/2208.09414/) (2022)
- [Class Overwhelms: Mutual Conditional Blended-Target Domain Adaptation](https://mlsanity.com/paper/2302.01516/) (2023)
- [Towards Backwards-Compatible Data with Confounded Domain Adaptation](https://mlsanity.com/paper/2203.12720/) (2022)
- [Is Domain Adaptation Always Helpful? A Frozen-Backbone Study of Cross-Domain Sentiment Transfer](https://mlsanity.com/paper/2607.05937/) (2026)
- [E-ADDA: Unsupervised Adversarial Domain Adaptation Enhanced by a New Mahalanobis Distance Loss for Smart Computing](https://mlsanity.com/paper/2201.10001/) (2022)
- [Dual Domain-Adversarial Learning for Audio-Visual Saliency Prediction](https://mlsanity.com/paper/2208.05220/) (2022)

## Abstract (arXiv)

Existing domain adaptation methods aim to reduce the distributional difference between the source and target domains and respect their specific discriminative information, by establishing the Maximum Mean Discrepancy (MMD) and the discriminative distances. However, they usually accumulate to consider those statistics and deal with their relationships by estimating parameters blindly. This paper theoretically proves two essential facts: 1) minimizing the MMD equals to maximize the source and target intra-class distances respectively but jointly minimize their variance with some implicit weights, so that the feature discriminability degrades; 2) the relationship between the intra-class and inter-class distances is as one falls, another rises. Based on this, we propose a novel discriminative MMD. On one hand, we consider the intra-class and inter-class distances alone to remove a redundant parameter, and the revealed weights provide their approximate optimal ranges. On the other hand, we design two different strategies to boost the feature discriminability: 1) we directly impose a trade-off parameter on the implicit intra-class distance in MMD to regulate its change; 2) we impose the similar weights revealed in MMD on inter-class distance and maximize it, then a balanced factor could be introduced to quantitatively leverage the relative importance between the feature transferability and its discriminability. The experiments on several benchmark datasets not only prove the validity of theoretical results but also demonstrate that our approach could perform better than the comparative state-of-art methods substantially.