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.

翻译：快速扩张的人工智能产业已催生出多样且强大的预测工具，每种工具都拥有独特的网络架构、训练策略、数据处理流程及特定领域的优势。这些工具为半监督推断创造了新机遇——在该场景下，标注数据稀缺且获取成本高昂，而未标注数据则丰富易得。针对一组预测器，我们将其视为专家混合模型（MOE），并基于预测驱动推断（PPI）原理，提出了一种MOE驱动的半监督推断框架。该框架受PPI中方差缩减原理启发，致力于寻找能实现最小化方差的专家混合模型。与标准PPI相比，MOE驱动的推断框架能自适应各预测器的未知性能，利用其集体预测能力，并具备最优专家保障。该框架具有灵活性，可适用于均值估计、线性回归、分位数估计及一般M估计。我们为MOE驱动的推断框架建立了非渐近理论，并给出了置信区间覆盖误差的上界。数值实验验证了MOE驱动推断的实践有效性，并佐证了理论分析结果。