Prediction-powered Inference by Mixture of Experts

arXiv stat.ML / 5/1/2026

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Key Points

The paper proposes a mixture-of-experts (MOE) framework for semi-supervised inference, aiming to improve prediction when labeled data are scarce but unlabeled data are plentiful.
Building on prediction-powered inference (PPI), the method selects experts to minimize variance, adapting to unknown performance across predictors while leveraging their combined strength.
The approach provides a “best-expert guarantee” and is shown to be flexible across tasks including mean estimation, linear regression, quantile estimation, and general M-estimation.
The authors develop non-asymptotic theoretical results and derive bounds on coverage error for confidence intervals produced by the framework.
Experiments indicate the proposed MOE-powered inference works well in practice and aligns with the theoretical coverage and error analyses.

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.