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

• URL: http://arxiv.org/abs/2603.15158v1
• Date: Mon, 16 Mar 2026 11:52:35 GMT
• Title: Point-Identification of a Robust Predictor Under Latent Shift with Imperfect Proxies
• Abstract summary: We introduce latent equivalent classes (LECs) that induce the same conditional proxy distribution.<n>LECs are defined as groups of latent confounders that induce the same conditional proxy distribution.<n>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.
• Score: 22.609134964894363
• License: http://creativecommons.org/licenses/by/4.0/
• 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 minimal set of diverse domains that satisfy this rank condition. PQAL can efficiently recover the point-identified predictor, demonstrates robustness to varying degrees of shift and outperforms previous methods on synthetic data and semi-synthetic dSprites dataset.

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