# DARE-GRAM : Unsupervised Domain Adaptation Regression by Aligning Inverse Gram Matrices

arXiv: https://arxiv.org/abs/2303.13325 · HTML: https://mlsanity.com/paper/2303.13325/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 85 references that are in the map.
- First posted on arXiv 23 Mar 2023.

## Builds on (most cited first, 30 of 43)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Unsupervised Domain Adaptation by Backpropagation](https://mlsanity.com/paper/1409.7495/) (2014)
- [Learning Transferable Features with Deep Adaptation Networks](https://mlsanity.com/paper/1502.02791/) (2015)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [CyCADA: Cycle-Consistent Adversarial Domain Adaptation](https://mlsanity.com/paper/1711.03213/) (2017)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [Maximum Classifier Discrepancy for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1712.02560/) (2017)
- [ADVENT: Adversarial Entropy Minimization for Domain Adaptation in Semantic Segmentation](https://mlsanity.com/paper/1811.12833/) (2018)
- [Learning to Adapt Structured Output Space for Semantic Segmentation](https://mlsanity.com/paper/1802.10349/) (2018)
- [FDA: Fourier Domain Adaptation for Semantic Segmentation](https://mlsanity.com/paper/2004.05498/) (2020)
- [Continual Test-Time Domain Adaptation](https://mlsanity.com/paper/2203.13591/) (2022)
- [Contrastive Adaptation Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1901.00976/) (2019)
- [A Survey of Unsupervised Deep Domain Adaptation](https://mlsanity.com/paper/1812.02849/) (2018)
- [Unsupervised Pixel-Level Domain Adaptation with Generative Adversarial Networks](https://mlsanity.com/paper/1612.05424/) (2016)
- [Revisiting Batch Normalization For Practical Domain Adaptation](https://mlsanity.com/paper/1603.04779/) (2016)
- [Joint Distribution Optimal Transportation for Domain Adaptation](https://mlsanity.com/paper/1705.08848/) (2017)
- [3D Human Pose Estimation with Spatial and Temporal Transformers](https://mlsanity.com/paper/2103.10455/) (2021)
- [Prototypical Pseudo Label Denoising and Target Structure Learning for Domain Adaptive Semantic Segmentation](https://mlsanity.com/paper/2101.10979/) (2021)
- [HRDA: Context-Aware High-Resolution Domain-Adaptive Semantic Segmentation](https://mlsanity.com/paper/2204.13132/) (2022)
- [Demystifying Neural Style Transfer](https://mlsanity.com/paper/1701.01036/) (2017)
- [Domain Adaptation for Semantic Segmentation with Maximum Squares Loss](https://mlsanity.com/paper/1909.13589/) (2019)
- [A survey on domain adaptation theory: learning bounds and theoretical guarantees](https://mlsanity.com/paper/2004.11829/) (2020)
- [Constructing Self-motivated Pyramid Curriculums for Cross-Domain Semantic Segmentation: A Non-Adversarial Approach](https://mlsanity.com/paper/1908.09547/) (2019)
- [On the Transfer of Inductive Bias from Simulation to the Real World: a New Disentanglement Dataset](https://mlsanity.com/paper/1906.03292/) (2019)
- [Learning Probabilistic Ordinal Embeddings for Uncertainty-Aware Regression](https://mlsanity.com/paper/2103.13629/) (2021)
- [MetaAlign: Coordinating Domain Alignment and Classification for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2103.13575/) (2021)
- [DINE: Domain Adaptation from Single and Multiple Black-box Predictors](https://mlsanity.com/paper/2104.01539/) (2021)
- [From Synthetic to Real: Unsupervised Domain Adaptation for Animal Pose Estimation](https://mlsanity.com/paper/2103.14843/) (2021)
- [Regressive Domain Adaptation for Unsupervised Keypoint Detection](https://mlsanity.com/paper/2103.06175/) (2021)

## Built on by (most cited first, 28 of 28)

- [Gramian Multimodal Representation Learning and Alignment](https://mlsanity.com/paper/2412.11959/) (2024)
- [Advances in Multimodal Adaptation and Generalization: From Traditional Approaches to Foundation Models](https://mlsanity.com/paper/2501.18592/) (2025)
- [Unsupervised Domain Adaptation via Domain-Adaptive Diffusion](https://mlsanity.com/paper/2308.13893/) (2023)
- [Test-time Adaptation for Regression by Subspace Alignment](https://mlsanity.com/paper/2410.03263/) (2024)
- [Multi-Granularity Class Prototype Topology Distillation for Class-Incremental Source-Free Unsupervised Domain Adaptation](https://mlsanity.com/paper/2411.16064/) (2024)
- [MOS: Model Synergy for Test-Time Adaptation on LiDAR-Based 3D Object Detection](https://mlsanity.com/paper/2406.14878/) (2024)
- [VT-FSL: Bridging Vision and Text with LLMs for Few-Shot Learning](https://mlsanity.com/paper/2509.25033/) (2025)
- [Recall and Refine: A Simple but Effective Source-free Open-set Domain Adaptation Framework](https://mlsanity.com/paper/2411.12558/) (2024)
- [COD: Learning Conditional Invariant Representation for Domain Adaptation Regression](https://mlsanity.com/paper/2408.06638/) (2024)
- [Domain-Adaptive Full-Face Gaze Estimation via Novel-View-Synthesis and Feature Disentanglement](https://mlsanity.com/paper/2305.16140/) (2023)
- [Uncertainty-Guided Alignment for Unsupervised Domain Adaptation in Regression](https://mlsanity.com/paper/2401.13721/) (2024)
- [Out of the Ordinary: Spectrally Adapting Regression for Covariate Shift](https://mlsanity.com/paper/2312.17463/) (2023)
- [Sim2Real in Reconstructive Spectroscopy: Deep Learning with Augmented Device-Informed Data Simulation](https://mlsanity.com/paper/2403.12354/) (2024)
- [Get Your Embedding Space in Order: Domain-Adaptive Regression for Forest Monitoring](https://mlsanity.com/paper/2405.00514/) (2024)
- [Efficient Unsupervised Domain Adaptation Regression for Spatial-Temporal Sensor Fusion](https://mlsanity.com/paper/2411.06917/) (2024)
- [ConDo: Continual Domain Expansion for Absolute Pose Regression](https://mlsanity.com/paper/2412.13452/) (2024)
- [A Physics-preserved Transfer Learning Method for Differential Equations](https://mlsanity.com/paper/2505.01281/) (2025)
- [Target-specific Adaptation and Consistent Degradation Alignment for Cross-Domain Remaining Useful Life Prediction](https://mlsanity.com/paper/2512.02610/) (2025)
- [CoRe-DA: Contrastive Regression for Unsupervised Domain Adaptation in Surgical Skill Assessment](https://mlsanity.com/paper/2603.29666/) (2026)
- [Rapidly deploying on-device eye tracking by distilling visual foundation models](https://mlsanity.com/paper/2604.02509/) (2026)
- [Towards Trustworthy Unsupervised Domain Adaptation: A Representation Learning Perspective for Enhancing Robustness, Discrimination, and Generalization](https://mlsanity.com/paper/2406.13180/) (2024)
- [A Generalized Label Shift Perspective for Cross-Domain Gaze Estimation](https://mlsanity.com/paper/2505.13043/) (2025)
- [Hybrid-Domain Adaptative Representation Learning for Gaze Estimation](https://mlsanity.com/paper/2511.13222/) (2025)
- [Backpropagation-Free Test-Time Adaptation for Lightweight EEG-Based Brain-Computer Interfaces](https://mlsanity.com/paper/2601.07556/) (2026)
- [MUSDA: Multi-source Multi-modality Unsupervised Domain Adaptive 3D Object Detection for Autonomous Driving](https://mlsanity.com/paper/2605.10026/) (2026)
- [XPASS-Vis: A Dataset for Cross-Domain Personalized Image Aesthetic Assessment](https://mlsanity.com/paper/2606.15629/) (2026)
- [SemMSA: Latent Semantic-Aided Robust Multimodal Sentiment Analysis with Incomplete Data](https://mlsanity.com/paper/2609.30238/) (2026)
- [WhiteCon: Semi-Supervised Domain Adaptation Regression Through Whitening Transform and Dual Consistency](https://mlsanity.com/paper/2609.34078/) (2026)

## Abstract (arXiv)

Unsupervised Domain Adaptation Regression (DAR) aims to bridge the domain gap between a labeled source dataset and an unlabelled target dataset for regression problems. Recent works mostly focus on learning a deep feature encoder by minimizing the discrepancy between source and target features. In this work, we present a different perspective for the DAR problem by analyzing the closed-form ordinary least square~(OLS) solution to the linear regressor in the deep domain adaptation context. Rather than aligning the original feature embedding space, we propose to align the inverse Gram matrix of the features, which is motivated by its presence in the OLS solution and the Gram matrix's ability to capture the feature correlations. Specifically, we propose a simple yet effective DAR method which leverages the pseudo-inverse low-rank property to align the scale and angle in a selected subspace generated by the pseudo-inverse Gram matrix of the two domains. We evaluate our method on three domain adaptation regression benchmarks. Experimental results demonstrate that our method achieves state-of-the-art performance. Our code is available at https://github.com/ismailnejjar/DARE-GRAM.