# Unsupervised Domain Adaptation for Binary Classification with an Unobservable Source Subpopulation

arXiv: https://arxiv.org/abs/2509.20587 · HTML: https://mlsanity.com/paper/2509.20587/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 40 of its 58 references that are in the map.
- First posted on arXiv 24 Sep 2025.

## Builds on (most cited first, 30 of 40)

- [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)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Learning Transferable Features with Deep Adaptation Networks](https://mlsanity.com/paper/1502.02791/) (2015)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Adversarial Discriminative Domain Adaptation](https://mlsanity.com/paper/1702.05464/) (2017)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Deep Domain Confusion: Maximizing for Domain Invariance](https://mlsanity.com/paper/1412.3474/) (2014)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Towards Out-Of-Distribution Generalization: A Survey](https://mlsanity.com/paper/2108.13624/) (2021)
- [Last Layer Re-Training is Sufficient for Robustness to Spurious Correlations](https://mlsanity.com/paper/2204.02937/) (2022)
- [Detecting and Correcting for Label Shift with Black Box Predictors](https://mlsanity.com/paper/1802.03916/) (2018)
- [Rethinking Spatial Dimensions of Vision Transformers](https://mlsanity.com/paper/2103.16302/) (2021)
- [An Investigation of Why Overparameterization Exacerbates Spurious Correlations](https://mlsanity.com/paper/2005.04345/) (2020)
- [Exploring the Limits of Out-of-Distribution Detection](https://mlsanity.com/paper/2106.03004/) (2021)
- [No Subclass Left Behind: Fine-Grained Robustness in Coarse-Grained Classification Problems](https://mlsanity.com/paper/2011.12945/) (2020)
- [Learning De-biased Representations with Biased Representations](https://mlsanity.com/paper/1910.02806/) (2019)
- [Deep Reconstruction-Classification Networks for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1607.03516/) (2016)
- [A review of domain adaptation without target labels](https://mlsanity.com/paper/1901.05335/) (2019)
- [On Feature Learning in the Presence of Spurious Correlations](https://mlsanity.com/paper/2210.11369/) (2022)
- [A Unified View of Label Shift Estimation](https://mlsanity.com/paper/2003.07554/) (2020)
- [HoMM: Higher-order Moment Matching for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1912.11976/) (2019)
- [Extending the WILDS Benchmark for Unsupervised Adaptation](https://mlsanity.com/paper/2112.05090/) (2021)
- [Discover and Cure: Concept-aware Mitigation of Spurious Correlation](https://mlsanity.com/paper/2305.00650/) (2023)
- [On the Impact of Spurious Correlation for Out-of-distribution Detection](https://mlsanity.com/paper/2109.05642/) (2021)
- [Mixture Proportion Estimation via Kernel Embedding of Distributions](https://mlsanity.com/paper/1603.02501/) (2016)
- [Identifying Spurious Correlations for Robust Text Classification](https://mlsanity.com/paper/2010.02458/) (2020)

## Abstract (arXiv)

We study an unsupervised domain adaptation problem where the source domain consists of subpopulations defined by the binary label Y and a binary background (or environment) A. We focus on a challenging setting in which one such subpopulation in the source domain is unobservable. Naively ignoring this unobserved group can result in biased estimates and degraded predictive performance. Despite this structured missingness, we show that the prediction in the target domain can still be recovered. Specifically, we rigorously derive both background-specific and overall prediction models for the target domain. For practical implementation, we propose the distribution matching method to estimate the subpopulation proportions. We provide theoretical guarantees for the asymptotic behavior of our estimator, and establish an upper bound on the prediction error. Experiments on both synthetic and real-world datasets show that our method outperforms the naive benchmark that does not account for this unobservable source subpopulation.