Unsupervised Domain Adaptation with an Unobservable Source Subpopulation

2025-09-24

AI Summary

This paper addresses unsupervised domain adaptation under unobserved subgroup structure in the source domain: the source is partitioned into four subgroups by binary label $Y$ and binary background variable $A$, with the subgroup $A=1,Y=1$ entirely missing. Ignoring this missingness induces prediction bias on the target domain. To address this, we propose a background-specific–global joint modeling framework—the first method enabling recoverable target-domain prediction under partial subgroup unobservability—accompanied by an upper bound on estimation error and asymptotic consistency guarantees. Our approach estimates latent subgroup proportions via distribution matching, without imposing strong assumptions on the missingness mechanism. Experiments on synthetic data and real-world medical and image datasets demonstrate that our method significantly outperforms naive baselines that ignore the missing structure, achieving higher accuracy and improved robustness on the target domain.

Technology Category

• Machine Learning: Transfer, Domain Adaptation, Multi-Task Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling for targeted and personalized online advertising
• Search and Retrieval-Augmented AI: Vertical and domain-specific search

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 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.

Problem

• Addresses unsupervised domain adaptation with missing source subpopulation data
• Recovers target domain predictions despite unobservable source subgroups
• Proposes distribution matching to estimate missing subpopulation proportions

Innovation

• Handles unobservable source subpopulation via distribution matching
• Derives background-specific and overall prediction models
• Provides theoretical guarantees and error bounds