Unsupervised Domain Adaptation for Binary Classification with an Unobservable Source Subpopulation

chao ying, Jun Jin, Haotian Zhang, Qinglong Tian, Yanyuan Ma, Sharon Li, Jiwei Zhao

Abstract: 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 predictive probabilities 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 benchmarks that do not account for this unobservable source subpopulation properly.

Submission Type: Long submission (more than 12 pages of main content)

Previous TMLR Submission Url: https://openreview.net/forum?id=9XmNbzTBXn&referrer=%5BAuthor%20Console%5D(%2Fgroup%3Fid%3DTMLR%2FAuthors%23your-submissions)

Changes Since Last Submission: We added the authors' information, broader impact statement, and the acknowledgment. This is our camera ready final version.

Assigned Action Editor: ~Sanghyuk_Chun1

Submission Number: 7026