# COD: Learning Conditional Invariant Representation for Domain Adaptation Regression

arXiv: https://arxiv.org/abs/2408.06638 · HTML: https://mlsanity.com/paper/2408.06638/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 62 references that are in the map.
- First posted on arXiv 13 Aug 2024.

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

- [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)
- [CyCADA: Cycle-Consistent Adversarial Domain Adaptation](https://mlsanity.com/paper/1711.03213/) (2017)
- [Maximum Classifier Discrepancy for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1712.02560/) (2017)
- [Deep Transfer Learning with Joint Adaptation Networks](https://mlsanity.com/paper/1605.06636/) (2016)
- [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)
- [Sliced Wasserstein Discrepancy for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1903.04064/) (2019)
- [DeepJDOT: Deep Joint Distribution Optimal Transport for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1803.10081/) (2018)
- [Multi-Adversarial Domain Adaptation](https://mlsanity.com/paper/1809.02176/) (2018)
- [Classes Matter: A Fine-grained Adversarial Approach to Cross-domain Semantic Segmentation](https://mlsanity.com/paper/2007.09222/) (2020)
- [Domain Adaptation with Conditional Distribution Matching and Generalized Label Shift](https://mlsanity.com/paper/2003.04475/) (2020)
- [On the Transfer of Inductive Bias from Simulation to the Real World: a New Disentanglement Dataset](https://mlsanity.com/paper/1906.03292/) (2019)
- [Deep transfer operator learning for partial differential equations under conditional shift](https://mlsanity.com/paper/2204.09810/) (2022)
- [Rethinking Depth Estimation for Multi-View Stereo: A Unified Representation](https://mlsanity.com/paper/2201.01501/) (2022)
- [Conditional Learning of Fair Representations](https://mlsanity.com/paper/1910.07162/) (2019)
- [Discriminative Adversarial Domain Adaptation](https://mlsanity.com/paper/1911.12036/) (2019)
- [Learning Invariant Representations and Risks for Semi-supervised Domain Adaptation](https://mlsanity.com/paper/2010.04647/) (2020)
- [Reusing the Task-specific Classifier as a Discriminator: Discriminator-free Adversarial Domain Adaptation](https://mlsanity.com/paper/2204.03838/) (2022)
- [Few-shot Domain Adaptation by Causal Mechanism Transfer](https://mlsanity.com/paper/2002.03497/) (2020)
- [Poseur: Direct Human Pose Regression with Transformers](https://mlsanity.com/paper/2201.07412/) (2022)
- [Fundamental Limits and Tradeoffs in Invariant Representation Learning](https://mlsanity.com/paper/2012.10713/) (2020)
- [Regressive Domain Adaptation for Unsupervised Keypoint Detection](https://mlsanity.com/paper/2103.06175/) (2021)
- [Unsupervised Domain Adaptation via Discriminative Manifold Propagation](https://mlsanity.com/paper/2008.10030/) (2020)
- [DARE-GRAM : Unsupervised Domain Adaptation Regression by Aligning Inverse Gram Matrices](https://mlsanity.com/paper/2303.13325/) (2023)
- [Conditional Bures Metric for Domain Adaptation](https://mlsanity.com/paper/2108.00302/) (2021)
- [Adversarial Weighting for Domain Adaptation in Regression](https://mlsanity.com/paper/2006.08251/) (2020)
- [Mapping conditional distributions for domain adaptation under generalized target shift](https://mlsanity.com/paper/2110.15057/) (2021)
- [Learning Unbiased Transferability for Domain Adaptation by Uncertainty Modeling](https://mlsanity.com/paper/2206.01319/) (2022)

## Built on by (most cited first, 4 of 4)

- [QD-PCQA: Quality-Aware Domain Adaptation for Point Cloud Quality Assessment](https://mlsanity.com/paper/2603.03726/) (2026)
- [A Physics-preserved Transfer Learning Method for Differential Equations](https://mlsanity.com/paper/2505.01281/) (2025)
- [A Generalized Label Shift Perspective for Cross-Domain Gaze Estimation](https://mlsanity.com/paper/2505.13043/) (2025)
- [Unsupervised Domain Adaptation for Sim-to-Real Object Pose Estimation with Contrastive Alignment and Pseudo-Label Refinement](https://mlsanity.com/paper/2606.21287/) (2026)

## Abstract (arXiv)

Aiming to generalize the label knowledge from a source domain with continuous outputs to an unlabeled target domain, Domain Adaptation Regression (DAR) is developed for complex practical learning problems. However, due to the continuity problem in regression, existing conditional distribution alignment theory and methods with discrete prior, which are proven to be effective in classification settings, are no longer applicable. In this work, focusing on the feasibility problems in DAR, we establish the sufficiency theory for the regression model, which shows the generalization error can be sufficiently dominated by the cross-domain conditional discrepancy. Further, to characterize conditional discrepancy with continuous conditioning variable, a novel Conditional Operator Discrepancy (COD) is proposed, which admits the metric property on conditional distributions via the kernel embedding theory. Finally, to minimize the discrepancy, a COD-based conditional invariant representation learning model is proposed, and the reformulation is derived to show that reasonable modifications on moment statistics can further improve the discriminability of the adaptation model. Extensive experiments on standard DAR datasets verify the validity of theoretical results and the superiority over SOTA DAR methods.