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

arXiv: https://arxiv.org/abs/2603.15158 · HTML: https://mlsanity.com/paper/2603.15158/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 30 references that are in the map.
- First posted on arXiv 16 Mar 2026.

## Builds on (most cited first, 18 of 18)

- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Detecting and Correcting for Label Shift with Black Box Predictors](https://mlsanity.com/paper/1802.03916/) (2018)
- [Measuring Catastrophic Forgetting in Neural Networks](https://mlsanity.com/paper/1708.02072/) (2017)
- [Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences](https://mlsanity.com/paper/1807.02582/) (2018)
- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [Few-Shot Adversarial Domain Adaptation](https://mlsanity.com/paper/1711.02536/) (2017)
- [Robustness to Spurious Correlations via Human Annotations](https://mlsanity.com/paper/2007.06661/) (2020)
- [Prediction-Oriented Bayesian Active Learning](https://mlsanity.com/paper/2304.08151/) (2023)
- [Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restriction](https://mlsanity.com/paper/2105.04544/) (2021)
- [Inference on Strongly Identified Functionals of Weakly Identified Functions](https://mlsanity.com/paper/2208.08291/) (2022)
- [Adapting to Latent Subgroup Shifts via Concepts and Proxies](https://mlsanity.com/paper/2212.11254/) (2022)
- [Quantifying Aleatoric Uncertainty of the Treatment Effect: A Novel Orthogonal Learner](https://mlsanity.com/paper/2411.03387/) (2024)
- [Partial Identification of Causal Effects Using Proxy Variables](https://mlsanity.com/paper/2304.04374/) (2023)
- [Proxy Methods for Domain Adaptation](https://mlsanity.com/paper/2403.07442/) (2024)
- [Scalable Out-of-distribution Robustness in the Presence of Unobserved Confounders](https://mlsanity.com/paper/2411.19923/) (2024)
- [Human-in-the-Loop Large-Scale Predictive Maintenance of Workstations](https://mlsanity.com/paper/2206.11574/) (2022)
- [Proxy-informed Bayesian transfer learning with unknown sources](https://mlsanity.com/paper/2411.03263/) (2024)

## Abstract (arXiv)

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.