New Method Enables Robust Prediction Under Domain Shift with Imperfect Proxy Variables

A preprint posted to arXiv introduces the PQAL framework to address a fundamental challenge in domain adaptation: when distribution shifts between domains are driven by latent confounders that influence both covariates and outcomes, standard proxy-based methods require a completeness assumption that often fails in practice. The paper identifies the core problem as non-injectivity — when multiple latent confounder values produce identical proxy distributions, the completeness assumption breaks down and the robust predictor becomes only set-identified rather than point-identified. To resolve this, the authors define latent equivalent classes (LECs) as groups of latent confounders that induce the same conditional proxy distribution, and show that point-identification can still be achieved if multiple domains differ sufficiently in how they mix these LECs. This diversity requirement is formalized as a cross-domain rank condition on mixture weights, which the authors argue is substantially weaker than completeness. PQAL actively queries a small, targeted set of diverse domains satisfying this rank condition to recover the point-identified predictor. The framework is evaluated on synthetic data and semi-synthetic benchmarks including dSprites, IHDP, and ACS Folktables, where it demonstrates robustness to varying degrees of shift and outperforms prior methods.