AI 中文总结
本文将条件期望估计作为不适定逆问题，基于Vapnik定理的推广提出解决方案，推导了其样本误差的新上界。
AI 中文摘要
本文研究将条件期望估计作为不适定逆问题的问题，提出基于Vapnik定理（Hilbert空间中随机不适定问题的求解）推广的解决方案，作为应用推导了条件期望估计样本误差的新上界。
英文摘要
In this paper, we consider the problem of estimating conditional expectations as an ill-posed inverse problem. We propose a solution based on a generalization of Vapnik's theorem \cite[Theorem 7.2]{Vapnik1998} for solving stochastic ill-posed problems in Hilbert spaces. As an application, we derive a new upper bound for sample errors of conditional expectation estimation.
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