Prediction-powered Inference by Mixture of Experts

2026-04-30

AI Summary

This work proposes the first semi-supervised inference framework that integrates Mixture-of-Experts (MoE) with Prediction-Powered Inference (PPI) for settings where labeled data are scarce but unlabeled data are abundant. The approach treats multiple heterogeneous predictors as experts and adaptively combines their predictions via a variance-minimization criterion, achieving optimal ensemble performance without requiring prior knowledge of individual expert accuracy. Grounded in non-asymptotic statistical theory and M-estimation, the framework significantly enhances inference accuracy across tasks such as mean estimation, linear regression, and quantile estimation. Theoretical analysis provides rigorous error upper bounds, while empirical experiments demonstrate the method’s effectiveness and robustness.

Abstract

The rapidly expanding artificial intelligence (AI) industry has produced diverse yet powerful prediction tools, each with its own network architecture, training strategy, data-processing pipeline, and domain-specific strengths. These tools create new opportunities for semi-supervised inference, in which labeled data are limited and expensive to obtain, whereas unlabeled data are abundant and widely available. Given a collection of predictors, we treat them as a mixture of experts (MOE) and introduce an MOE-powered semi-supervised inference framework built upon prediction-powered inference (PPI). Motivated by the variance reduction principle underlying PPI, the proposed framework seeks the mixture of experts that achieves the smallest possible variance. Compared with standard PPI, the MOE-powered inference framework adapts to the unknown performance of individual predictors, benefits from their collective predictive power, and enjoys a best-expert guarantee. The framework is flexible and applies to mean estimation, linear regression, quantile estimation, and general M-estimation. We develop non-asymptotic theory for the MOE-powered inference framework and establish upper bounds on the coverage error of the resulting confidence intervals. Numerical experiments demonstrate the practical effectiveness of MOE-powered inference and corroborate our theoretical findings.

Problem

• semi-supervised inference
• mixture of experts
• prediction-powered inference
• variance reduction
• confidence intervals

Innovation

• Mixture of Experts
• Prediction-Powered Inference
• Semi-supervised Inference
• Variance Reduction
• Non-asymptotic Theory