# Continuously Indexed Domain Adaptation

arXiv: https://arxiv.org/abs/2007.01807 · HTML: https://mlsanity.com/paper/2007.01807/

## Key facts

- Cited by 75 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jul 2020.

## Built on by (most cited first, 30 of 75)

- [Generalizing to Unseen Domains: A Survey on Domain Generalization](https://mlsanity.com/paper/2103.03097/) (2021)
- [Delving into Deep Imbalanced Regression](https://mlsanity.com/paper/2102.09554/) (2021)
- [Domain Adaptation for Time Series Forecasting via Attention Sharing](https://mlsanity.com/paper/2102.06828/) (2021)
- [AdaNPC: Exploring Non-Parametric Classifier for Test-Time Adaptation](https://mlsanity.com/paper/2304.12566/) (2023)
- [Temporal Domain Generalization with Drift-Aware Dynamic Neural Networks](https://mlsanity.com/paper/2205.10664/) (2022)
- [Free Lunch for Domain Adversarial Training: Environment Label Smoothing](https://mlsanity.com/paper/2302.00194/) (2023)
- [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)
- [Understanding Gradual Domain Adaptation: Improved Analysis, Optimal Path and Beyond](https://mlsanity.com/paper/2204.08200/) (2022)
- [Out-of-Distribution Representation Learning for Time Series Classification](https://mlsanity.com/paper/2209.07027/) (2022)
- [When Age-Invariant Face Recognition Meets Face Age Synthesis: A Multi-Task Learning Framework](https://mlsanity.com/paper/2103.01520/) (2021)
- [Self-Adversarial Disentangling for Specific Domain Adaptation](https://mlsanity.com/paper/2108.03553/) (2021)
- [Training for the Future: A Simple Gradient Interpolation Loss to Generalize Along Time](https://mlsanity.com/paper/2108.06721/) (2021)
- [Curriculum Reinforcement Learning using Optimal Transport via Gradual Domain Adaptation](https://mlsanity.com/paper/2210.10195/) (2022)
- [Learngene: From Open-World to Your Learning Task](https://mlsanity.com/paper/2106.06788/) (2021)
- [Exploring Transformer Backbones for Heterogeneous Treatment Effect Estimation](https://mlsanity.com/paper/2202.01336/) (2022)
- [Drift-Resilient TabPFN: In-Context Learning Temporal Distribution Shifts on Tabular Data](https://mlsanity.com/paper/2411.10634/) (2024)
- [DIVERSIFY: A General Framework for Time Series Out-of-distribution Detection and Generalization](https://mlsanity.com/paper/2308.02282/) (2023)
- [ManyDG: Many-domain Generalization for Healthcare Applications](https://mlsanity.com/paper/2301.08834/) (2023)
- [On Calibration of LLM-based Guard Models for Reliable Content Moderation](https://mlsanity.com/paper/2410.10414/) (2024)
- [Domain Generalization via Frequency-domain-based Feature Disentanglement and Interaction](https://mlsanity.com/paper/2201.08029/) (2022)
- [Domain-Indexing Variational Bayes: Interpretable Domain Index for Domain Adaptation](https://mlsanity.com/paper/2302.02561/) (2023)
- [Graph-Relational Domain Adaptation](https://mlsanity.com/paper/2202.03628/) (2022)
- [Generalizing to Evolving Domains with Latent Structure-Aware Sequential Autoencoder](https://mlsanity.com/paper/2205.07649/) (2022)
- [Gradual Domain Adaptation: Theory and Algorithms](https://mlsanity.com/paper/2310.13852/) (2023)
- [CF-GODE: Continuous-Time Causal Inference for Multi-Agent Dynamical Systems](https://mlsanity.com/paper/2306.11216/) (2023)
- [Continuous Temporal Domain Generalization](https://mlsanity.com/paper/2405.16075/) (2024)
- [Learning Robust Spectral Dynamics for Temporal Domain Generalization](https://mlsanity.com/paper/2505.12585/) (2025)
- [Generalizing across Temporal Domains with Koopman Operators](https://mlsanity.com/paper/2402.07834/) (2024)
- [Gradual Domain Adaptation via Normalizing Flows](https://mlsanity.com/paper/2206.11492/) (2022)

## Abstract (arXiv)

Existing domain adaptation focuses on transferring knowledge between domains with categorical indices (e.g., between datasets A and B). However, many tasks involve continuously indexed domains. For example, in medical applications, one often needs to transfer disease analysis and prediction across patients of different ages, where age acts as a continuous domain index. Such tasks are challenging for prior domain adaptation methods since they ignore the underlying relation among domains. In this paper, we propose the first method for continuously indexed domain adaptation. Our approach combines traditional adversarial adaptation with a novel discriminator that models the encoding-conditioned domain index distribution. Our theoretical analysis demonstrates the value of leveraging the domain index to generate invariant features across a continuous range of domains. Our empirical results show that our approach outperforms the state-of-the-art domain adaption methods on both synthetic and real-world medical datasets.