# Domain-Indexing Variational Bayes: Interpretable Domain Index for Domain Adaptation

arXiv: https://arxiv.org/abs/2302.02561 · HTML: https://mlsanity.com/paper/2302.02561/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 47 references that are in the map.
- First posted on arXiv 6 Feb 2023.

## Builds on (most cited first, 30 of 32)

- [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)
- [Big Self-Supervised Models are Strong Semi-Supervised Learners](https://mlsanity.com/paper/2006.10029/) (2020)
- [Moment Matching for Multi-Source Domain Adaptation](https://mlsanity.com/paper/1812.01754/) (2018)
- [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)
- [Maximum Classifier Discrepancy for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1712.02560/) (2017)
- [Deep Domain Confusion: Maximizing for Domain Invariance](https://mlsanity.com/paper/1412.3474/) (2014)
- [Learning multiple visual domains with residual adapters](https://mlsanity.com/paper/1705.08045/) (2017)
- [Bridging Theory and Algorithm for Domain Adaptation](https://mlsanity.com/paper/1904.05801/) (2019)
- [Generate To Adapt: Aligning Domains using Generative Adversarial Networks](https://mlsanity.com/paper/1704.01705/) (2017)
- [Domain Generalization Using a Mixture of Multiple Latent Domains](https://mlsanity.com/paper/1911.07661/) (2019)
- [Understanding Self-Training for Gradual Domain Adaptation](https://mlsanity.com/paper/2002.11361/) (2020)
- [Neural Unsupervised Domain Adaptation in NLP---A Survey](https://mlsanity.com/paper/2006.00632/) (2020)
- [A Large-Scale Car Dataset for Fine-Grained Categorization and Verification](https://mlsanity.com/paper/1506.08959/) (2015)
- [AdaRNN: Adaptive Learning and Forecasting of Time Series](https://mlsanity.com/paper/2108.04443/) (2021)
- [Collaborative Deep Learning for Recommender Systems](https://mlsanity.com/paper/1409.2944/) (2014)
- [SENTRY: Selective Entropy Optimization via Committee Consistency for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2012.11460/) (2020)
- [AutoDIAL: Automatic DomaIn Alignment Layers](https://mlsanity.com/paper/1704.08082/) (2017)
- [Continuously Indexed Domain Adaptation](https://mlsanity.com/paper/2007.01807/) (2020)
- [Towards Bayesian Deep Learning: A Framework and Some Existing Methods](https://mlsanity.com/paper/1608.06884/) (2016)
- [Unsupervised Multi-Target Domain Adaptation Through Knowledge Distillation](https://mlsanity.com/paper/2007.07077/) (2020)
- [Blending-target Domain Adaptation by Adversarial Meta-Adaptation Networks](https://mlsanity.com/paper/1907.03389/) (2019)
- [DARec: Deep Domain Adaptation for Cross-Domain Recommendation via Transferring Rating Patterns](https://mlsanity.com/paper/1905.10760/) (2019)
- [AdaGraph: Unifying Predictive and Continuous Domain Adaptation through Graphs](https://mlsanity.com/paper/1903.07062/) (2019)
- [A Bit More Bayesian: Domain-Invariant Learning with Uncertainty](https://mlsanity.com/paper/2105.04030/) (2021)
- [Gradual Domain Adaptation without Indexed Intermediate Domains](https://mlsanity.com/paper/2207.04587/) (2022)
- [Domain2Vec: Domain Embedding for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2007.09257/) (2020)
- [StandardGAN: Multi-source Domain Adaptation for Semantic Segmentation of Very High Resolution Satellite Images by Data Standardization](https://mlsanity.com/paper/2004.06402/) (2020)

## Built on by (most cited first, 20 of 20)

- [A Unified Approach to Domain Incremental Learning with Memory: Theory and Algorithm](https://mlsanity.com/paper/2310.12244/) (2023)
- [Energy-Based Concept Bottleneck Models: Unifying Prediction, Concept Intervention, and Probabilistic Interpretations](https://mlsanity.com/paper/2401.14142/) (2024)
- [DIVERSIFY: A General Framework for Time Series Out-of-distribution Detection and Generalization](https://mlsanity.com/paper/2308.02282/) (2023)
- [Continuous Temporal Domain Generalization](https://mlsanity.com/paper/2405.16075/) (2024)
- [Taxonomy-Structured Domain Adaptation](https://mlsanity.com/paper/2306.07874/) (2023)
- [Continuous Invariance Learning](https://mlsanity.com/paper/2310.05348/) (2023)
- [Probabilistic Conceptual Explainers: Trustworthy Conceptual Explanations for Vision Foundation Models](https://mlsanity.com/paper/2406.12649/) (2024)
- [Concept-Based Unsupervised Domain Adaptation](https://mlsanity.com/paper/2505.05195/) (2025)
- [Pre-trained Recommender Systems: A Causal Debiasing Perspective](https://mlsanity.com/paper/2310.19251/) (2023)
- [PoGDiff: Product-of-Gaussians Diffusion Models for Imbalanced Text-to-Image Generation](https://mlsanity.com/paper/2502.08106/) (2025)
- [Continuous Domain Generalization](https://mlsanity.com/paper/2505.13519/) (2025)
- [Towards Domain Adaptive Neural Contextual Bandits](https://mlsanity.com/paper/2406.09564/) (2024)
- [Variational Language Concepts for Interpreting Foundation Language Models](https://mlsanity.com/paper/2410.03964/) (2024)
- [Beyond Batch Learning: Global Awareness Enhanced Domain Adaptation](https://mlsanity.com/paper/2502.06272/) (2025)
- [Noise Optimized Conditional Diffusion for Domain Adaptation](https://mlsanity.com/paper/2505.07548/) (2025)
- [Client2Vec: Improving Federated Learning by Distribution Shifts Aware Client Indexing](https://mlsanity.com/paper/2405.16233/) (2024)
- [Global Variational Inference Enhanced Robust Domain Adaptation](https://mlsanity.com/paper/2507.03291/) (2025)
- [Probabilistic Geometric Alignment via Bayesian Latent Transport for Domain-Adaptive Foundation Models](https://mlsanity.com/paper/2603.23783/) (2026)
- [Probabilistic Residual Learning for Online Recommendations](https://mlsanity.com/paper/2607.20863/) (2026)
- [When Debate Helps: Proposal Supply and Verification-Aware Readout in Multi-Agent Reasoning](https://mlsanity.com/paper/2610.04686/) (2026)

## Abstract (arXiv)

Previous studies have shown that leveraging domain index can significantly boost domain adaptation performance (arXiv:2007.01807, arXiv:2202.03628). However, such domain indices are not always available. To address this challenge, we first provide a formal definition of domain index from the probabilistic perspective, and then propose an adversarial variational Bayesian framework that infers domain indices from multi-domain data, thereby providing additional insight on domain relations and improving domain adaptation performance. Our theoretical analysis shows that our adversarial variational Bayesian framework finds the optimal domain index at equilibrium. Empirical results on both synthetic and real data verify that our model can produce interpretable domain indices which enable us to achieve superior performance compared to state-of-the-art domain adaptation methods. Code is available at https://github.com/Wang-ML-Lab/VDI.