具有普遍单调误差的普遍一致学习规则
A universally consistent learning rule with a universally monotone error
AI总结：
提出一种普遍一致且完全确定性的数据依赖划分学习规则，利用循环序和标签经验多样性划分，确保期望误差在任意数据分布下随样本量单调非增。
摘要：
我们提出了一种普遍一致的学习规则，其在任意数据分布下的期望误差随样本量单调非增。Devroye、Györfi和Lugosi于1996年提出了此类规则（称之为“smart”）的存在性问题。我们的规则是完全确定性的，是一种数据依赖的划分规则，使用循环序在任意域（标准Borel空间）中构建。其核心思想是仅在每一步划分那些表现出足够标签经验多样性的循环区间，从而避开误差函数为凸的区域。
英文摘要：
We present a universally consistent learning rule whose expected error is monotone non-increasing with the sample size under every data distribution. The question of existence of such rules was brought up in 1996 by Devroye, Györfi and Lugosi (who called them "smart"). Our rule is fully deterministic, a data-dependent partitioning rule constructed in an arbitrary domain (a standard Borel space) using a cyclic order. The central idea is to only partition at each step those cyclic intervals that exhibit a sufficient empirical diversity of labels, thus avoiding a region where the error function is convex.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
