Multi-source Learning for Target Population by High-dimensional Calibration

2025-12-03

AI Summary

This paper addresses parameter estimation under nonresponse in the target population when integrating multiple heterogeneous data sources. We propose the High-dimensional Debiased Calibration (HDC) framework and its multi-source extension, the Multi-source HDC (MHDC) estimator. MHDC achieves high-dimensional covariate balance in an augmented covariate space, ensuring Neyman orthogonality, circumventing inverse probability weighting, and accommodating flexible modeling of density ratios and outcome regressions—while retaining multiple robustness. We further develop a formal transferability test to rigorously assess the validity of cross-dataset knowledge transfer. Theoretically, MHDC is shown to be asymptotically efficient, outperforming existing doubly robust estimators. Simulation studies corroborate its finite-sample efficiency and robustness. Empirical analysis on meteorological data demonstrates its practical effectiveness and stability in real-world settings.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Multi-source learning is an emerging area of research in statistics, where information from multiple datasets with heterogeneous distributions is combined to estimate the parameter of interest for a target population without observed responses. We propose a high-dimensional debiased calibration (HDC) method and a multi-source HDC (MHDC) estimator for general estimating equations. The HDC method uses a novel approach to achieve Neyman orthogonality for the target parameter via high-dimensional covariate balancing on an augmented set of covariates. It avoids the augmented inverse probability weighting formulation and leads to an easier optimization algorithm for the target parameter in estimating equations and M-estimation. The proposed MHDC estimator integrates multi-source data while supporting flexible specifications for both density ratio and outcome regression models, achieving multiple robustness against model misspecification. Its asymptotic normality is established, and a specification test is proposed to examine the transferability condition for the multi-source data. Compared to the linear combination of single-source HDC estimators, the MHDC estimator improves efficiency by jointly utilizing all data sources. Through simulation studies, we show that the MHDC estimator accommodates multiple sources and multiple working models effectively and performs better than the existing doubly robust estimators for multi-source learning. An empirical analysis of a meteorological dataset demonstrates the utility of the proposed method in practice.

Problem

• Estimates target population parameters from heterogeneous multi-source data
• Achieves robustness against model misspecification in density and outcome models
• Improves efficiency by jointly utilizing all available data sources

Innovation

• High-dimensional debiased calibration with covariate balancing
• Multi-source estimator integrating flexible density ratio and outcome models
• Achieves multiple robustness and efficiency via joint data utilization