# Mapping conditional distributions for domain adaptation under generalized target shift

arXiv: https://arxiv.org/abs/2110.15057 · HTML: https://mlsanity.com/paper/2110.15057/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 48 references that are in the map.
- First posted on arXiv 26 Oct 2021.

## Builds on (most cited first, 22 of 22)

- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Learning Transferable Features with Deep Adaptation Networks](https://mlsanity.com/paper/1502.02791/) (2015)
- [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)
- [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)
- [Detecting and Correcting for Label Shift with Black Box Predictors](https://mlsanity.com/paper/1802.03916/) (2018)
- [Joint Distribution Optimal Transportation for Domain Adaptation](https://mlsanity.com/paper/1705.08848/) (2017)
- [DeepJDOT: Deep Joint Distribution Optimal Transport for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1803.10081/) (2018)
- [Domain Adaptation with Conditional Distribution Matching and Generalized Label Shift](https://mlsanity.com/paper/2003.04475/) (2020)
- [A Unified View of Label Shift Estimation](https://mlsanity.com/paper/2003.07554/) (2020)
- [Optimal Transport for Multi-source Domain Adaptation under Target Shift](https://mlsanity.com/paper/1803.04899/) (2018)
- [Domain Adaptation with Asymmetrically-Relaxed Distribution Alignment](https://mlsanity.com/paper/1903.01689/) (2019)
- [Regularized Discrete Optimal Transport](https://mlsanity.com/paper/1307.5551/) (2013)
- [Aggregating From Multiple Target-Shifted Sources](https://mlsanity.com/paper/2105.04051/) (2021)
- [Optimal Transport for Conditional Domain Matching and Label Shift](https://mlsanity.com/paper/2006.08161/) (2020)
- [A Principle of Least Action for the Training of Neural Networks](https://mlsanity.com/paper/2009.08372/) (2020)
- [LASS: a simple assignment model with Laplacian smoothing](https://mlsanity.com/paper/1405.5960/) (2014)
- [Unsupervised domain adaptation with non-stochastic missing data](https://mlsanity.com/paper/2109.09505/) (2021)

## Built on by (most cited first, 18 of 18)

- [Partial Identifiability for Domain Adaptation](https://mlsanity.com/paper/2306.06510/) (2023)
- [Mixture Domain Adaptation to Improve Semantic Segmentation in Real-World Surveillance](https://mlsanity.com/paper/2211.10119/) (2022)
- [Generalized Universal Domain Adaptation with Generative Flow Networks](https://mlsanity.com/paper/2305.04466/) (2023)
- [Domain Adaptation and Entanglement: an Optimal Transport Perspective](https://mlsanity.com/paper/2503.08155/) (2025)
- [Sparse joint shift in multinomial classification](https://mlsanity.com/paper/2303.16971/) (2023)
- [Invariance assumptions for class distribution estimation](https://mlsanity.com/paper/2311.17225/) (2023)
- [COD: Learning Conditional Invariant Representation for Domain Adaptation Regression](https://mlsanity.com/paper/2408.06638/) (2024)
- [CASUAL: Conditional Support Alignment for Domain Adaptation with Label Shift](https://mlsanity.com/paper/2305.18458/) (2023)
- [Gradual Domain Adaptation via Manifold-Constrained Distributionally Robust Optimization](https://mlsanity.com/paper/2410.14061/) (2024)
- [Connecting sufficient conditions for domain adaptation: source-guided uncertainty, relaxed divergences and discrepancy localization](https://mlsanity.com/paper/2203.05076/) (2022)
- [Learning representations that are closed-form Monge mapping optimal with application to domain adaptation](https://mlsanity.com/paper/2305.07500/) (2023)
- [When Invariant Representation Learning Meets Label Shift: Insufficiency and Theoretical Insights](https://mlsanity.com/paper/2406.16608/) (2024)
- [Geometric Understanding of Discriminability and Transferability for Visual Domain Adaptation](https://mlsanity.com/paper/2407.09524/) (2024)
- [Partial Domain Adaptation via Importance Sampling-based Shift Correction](https://mlsanity.com/paper/2507.20191/) (2025)
- [Source-free Domain Adaptation Requires Penalized Diversity](https://mlsanity.com/paper/2304.02798/) (2023)
- [Theory-inspired Label Shift Adaptation via Aligned Distribution Mixture](https://mlsanity.com/paper/2411.02047/) (2024)
- [A Generalized Label Shift Perspective for Cross-Domain Gaze Estimation](https://mlsanity.com/paper/2505.13043/) (2025)
- [Towards Conditional Feature Alignment for Cross-Domain Counting](https://mlsanity.com/paper/2506.17137/) (2025)

## Abstract (arXiv)

We consider the problem of unsupervised domain adaptation (UDA) between a source and a target domain under conditional and label shift a.k.a Generalized Target Shift (GeTarS). Unlike simpler UDA settings, few works have addressed this challenging problem. Recent approaches learn domain-invariant representations, yet they have practical limitations and rely on strong assumptions that may not hold in practice. In this paper, we explore a novel and general approach to align pretrained representations, which circumvents existing drawbacks. Instead of constraining representation invariance, it learns an optimal transport map, implemented as a NN, which maps source representations onto target ones. Our approach is flexible and scalable, it preserves the problem's structure and it has strong theoretical guarantees under mild assumptions. In particular, our solution is unique, matches conditional distributions across domains, recovers target proportions and explicitly controls the target generalization risk. Through an exhaustive comparison on several datasets, we challenge the state-of-the-art in GeTarS.