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arXiv · 2603.15158

Point-Identification of a Robust Predictor Under Latent Shift with Imperfect Proxies

Zahra Rahiminasab·Reza Soumi·Arto Klami·Samuel Kaski
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Abstract

Addressing the domain adaptation problem becomes more challenging when distribution shifts across domains stem from latent confounders that affect both covariates and outcomes. Existing proxy-based approaches that address latent shift rely on a strong completeness assumption to uniquely determine (point-identify) a robust predictor. Completeness requires that proxies have sufficient information about variations in latent confounders. For imperfect proxies the mapping from confounders to the space of proxy distributions is non-injective, and multiple latent confounder values can generate the same proxy distribution. This breaks the completeness assumption and observed data are consistent with multiple potential predictors (set-identified). To address this, we introduce latent equivalent classes (LECs). LECs are defined as groups of latent confounders that induce the same conditional proxy distribution. We show that point-identification for the robust predictor remains achievable as long as multiple domains differ sufficiently in how they mix proxy-induced LECs to form the robust predictor. This domain diversity condition is formalized as a cross-domain rank condition on the mixture weights, which is substantially weaker assumption than completeness. We introduce the Proximal Quasi-Bayesian Active learning (PQAL) framework, which actively queries a small, targeted set of diverse domains that satisfy this rank condition. PQAL can recover the point-identified predictor, demonstrates robustness to varying degrees of shift and outperforms previous methods on synthetic data and semi-synthetic dSprites, IHDP, ACS Folktables datasets.

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Zahra Rahiminasab, Reza Soumi, Arto Klami, Samuel Kaski. 2026-03-16. Point-Identification of a Robust Predictor Under Latent Shift with Imperfect Proxies. https://arxiv.org/abs/2603.15158

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