Privacy-preserving Meta-analysis through Low-Rank Basis Hunting

2026-04-26

AI Summary

This work addresses the challenge of predicting functional quantities—such as regression functions or conditional average treatment effects—in a target population when it differs from the studied populations in unknown ways. The authors propose MetaHunt, a novel meta-analysis framework that introduces a low-rank basis function structure: it assumes that the true underlying functions across studies lie within the convex hull of a small set of latent basis functions. By extending the Successive Projection Algorithm to function spaces and incorporating denoised basis extraction, MetaHunt links study-level covariates to mixing weights via semi- or non-parametric models. The method operates without individual-level data, accommodates heterogeneous machine learning algorithms, preserves privacy, and delivers asymptotically valid prediction intervals through conformal inference. Theoretical analysis establishes consistent recovery of the latent basis functions, while simulations and empirical applications demonstrate superior and robust predictive performance.

Technology Category

• Search and Optimization: Metareasoning and Metaheuristics
• Machine Learning: Other Foundations of Machine Learning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

A central challenge of meta-analysis is that the populations underlying existing studies often differ from the target population in unknown ways. We study the problem of predicting function-valued quantities, such as regression and conditional average treatment effect functions, for a new target population using only study-level covariates and estimates. We propose MetaHunt, a new meta-analysis methodology based on a shared low-rank structure, in which the true function from each study lies within the convex hull of a small set of latent basis functions. To recover these basis functions, we extend the Successive Projection Algorithm to the functional setting, incorporating a denoised basis-hunting step. We establish consistency of the recovered basis functions under mild regularity conditions. We then model the relationship between study-level covariates and the corresponding mixing weights using flexible semi-parametric or non-parametric methods. MetaHunt is privacy-preserving and enables meta-analytic prediction based on study-level information alone, even when individual-level data are unavailable to analysts. In addition, for each study, functions of interest can be estimated using possibly different machine learning algorithms. For uncertainty quantification, we construct prediction intervals via conformal prediction. We show that, under exchangeability and mild estimation-error conditions, these intervals achieve asymptotically valid marginal coverage. We demonstrate the effectiveness of MetaHunt through both simulation studies and empirical applications.

Problem

• meta-analysis
• function-valued prediction
• population shift
• privacy-preserving
• conditional average treatment effect

Innovation

• low-rank basis
• privacy-preserving meta-analysis
• functional data
• conformal prediction
• basis hunting