# Reducing the Covariate Shift by Mirror Samples in Cross Domain Alignment

arXiv: https://arxiv.org/abs/2110.06448 · HTML: https://mlsanity.com/paper/2110.06448/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 68 references that are in the map.
- First posted on arXiv 13 Oct 2021.

## Builds on (most cited first, 30 of 44)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [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)
- [Adversarial Discriminative Domain Adaptation](https://mlsanity.com/paper/1702.05464/) (2017)
- [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)
- [CyCADA: Cycle-Consistent Adversarial Domain Adaptation](https://mlsanity.com/paper/1711.03213/) (2017)
- [Do We Really Need to Access the Source Data? Source Hypothesis Transfer for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2002.08546/) (2020)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Maximum Classifier Discrepancy for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1712.02560/) (2017)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [VisDA: The Visual Domain Adaptation Challenge](https://mlsanity.com/paper/1710.06924/) (2017)
- [Contrastive Adaptation Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1901.00976/) (2019)
- [Bridging Theory and Algorithm for Domain Adaptation](https://mlsanity.com/paper/1904.05801/) (2019)
- [Unsupervised Pixel-Level Domain Adaptation with Generative Adversarial Networks](https://mlsanity.com/paper/1612.05424/) (2016)
- [Joint Distribution Optimal Transportation for Domain Adaptation](https://mlsanity.com/paper/1705.08848/) (2017)
- [Adversarial Domain Adaptation with Domain Mixup](https://mlsanity.com/paper/1912.01805/) (2019)
- [Coupled Generative Adversarial Networks](https://mlsanity.com/paper/1606.07536/) (2016)
- [DeepJDOT: Deep Joint Distribution Optimal Transport for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1803.10081/) (2018)
- [Central Moment Discrepancy (CMD) for Domain-Invariant Representation Learning](https://mlsanity.com/paper/1702.08811/) (2017)
- [Transferrable Prototypical Networks for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1904.11227/) (2019)
- [Unsupervised Domain Adaptation via Structurally Regularized Deep Clustering](https://mlsanity.com/paper/2003.08607/) (2020)
- [Gradually Vanishing Bridge for Adversarial Domain Adaptation](https://mlsanity.com/paper/2003.13183/) (2020)
- [Domain Adaptation with Conditional Distribution Matching and Generalized Label Shift](https://mlsanity.com/paper/2003.04475/) (2020)
- [FixBi: Bridging Domain Spaces for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2011.09230/) (2020)
- [Domain-Symmetric Networks for Adversarial Domain Adaptation](https://mlsanity.com/paper/1904.04663/) (2019)
- [CrDoCo: Pixel-level Domain Transfer with Cross-Domain Consistency](https://mlsanity.com/paper/2001.03182/) (2020)
- [Visual Domain Adaptation with Manifold Embedded Distribution Alignment](https://mlsanity.com/paper/1807.07258/) (2018)
- [HoMM: Higher-order Moment Matching for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1912.11976/) (2019)

## Built on by (most cited first, 10 of 10)

- [Semi-Supervised Domain Adaptation with Source Label Adaptation](https://mlsanity.com/paper/2302.02335/) (2023)
- [JAWS: Auditing Predictive Uncertainty Under Covariate Shift](https://mlsanity.com/paper/2207.10716/) (2022)
- [CARLANE: A Lane Detection Benchmark for Unsupervised Domain Adaptation from Simulation to multiple Real-World Domains](https://mlsanity.com/paper/2206.08083/) (2022)
- [Exploiting Inter-Sample Affinity for Knowability-Aware Universal Domain Adaptation](https://mlsanity.com/paper/2207.09280/) (2022)
- [Relating tSNE and UMAP to Classical Dimensionality Reduction](https://mlsanity.com/paper/2306.11898/) (2023)
- [Geometric Moment Alignment for Domain Adaptation via Siegel Embeddings](https://mlsanity.com/paper/2510.14666/) (2025)
- [DATTA: Domain Diversity Aware Test-Time Adaptation for Dynamic Domain Shift Data Streams](https://mlsanity.com/paper/2408.08056/) (2024)
- [Towards Unsupervised Representation Learning: Learning, Evaluating and Transferring Visual Representations](https://mlsanity.com/paper/2312.00101/) (2023)
- [A Multi-View Consistency Framework with Semi-Supervised Domain Adaptation](https://mlsanity.com/paper/2601.19266/) (2026)
- [Retrieval-guided Twin Fusion with Similarity-aware Contrast for Molecule-Text Alignment](https://mlsanity.com/paper/2608.16005/) (2026)

## Abstract (arXiv)

Eliminating the covariate shift cross domains is one of the common methods to deal with the issue of domain shift in visual unsupervised domain adaptation. However, current alignment methods, especially the prototype based or sample-level based methods neglect the structural properties of the underlying distribution and even break the condition of covariate shift. To relieve the limitations and conflicts, we introduce a novel concept named (virtual) mirror, which represents the equivalent sample in another domain. The equivalent sample pairs, named mirror pairs reflect the natural correspondence of the empirical distributions. Then a mirror loss, which aligns the mirror pairs cross domains, is constructed to enhance the alignment of the domains. The proposed method does not distort the internal structure of the underlying distribution. We also provide theoretical proof that the mirror samples and mirror loss have better asymptotic properties in reducing the domain shift. By applying the virtual mirror and mirror loss to the generic unsupervised domain adaptation model, we achieved consistent superior performance on several mainstream benchmarks. Code is available at https://github.com/CTI-VISION/Mirror-Sample