How robustly can you predict the future?
How robustly can you predict the future?
复制标题
您对未来的预测有多可靠？
DOI：
10.4153/s0008414x22000402
复制
发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Matthew Elpers
中科院分区：
文献类型：
--
作者：
Sean D. Cox;Matthew Elpers
抽象的哈丁和泰勒证明了实数上的任何函数--即使是一个不连续的函数--都可以仅仅基于它过去的行为，在几乎每一个时间点上正确地预测出来。他们表明，人们甚至可以安排预报器对简单的时间转移保持稳健，并询问它们是否可以对其他更复杂的时间扭曲保持稳健。Bajpai和Velleman部分回答了这个问题，他们提供了上界和下界(在子群格子中
$\mathrm{homeo}^+(\mathbb{R})$
)关于预报器可能的健壮性。我们改进了这两个边界，其中一些最终归结为Hölder定理的结果(即每个阿基米德群都是阿贝尔的)。
Abstract Hardin and Taylor proved that any function on the reals—even a nowhere continuous one—can be correctly predicted, based solely on its past behavior, at almost every point in time. They showed that one could even arrange for the predictors to be robust with respect to simple time shifts, and asked whether they could be robust with respect to other, more complicated time distortions. This question was partially answered by Bajpai and Velleman, who provided upper and lower frontiers (in the subgroup lattice of
$\mathrm{Homeo}^+(\mathbb {R})$
) on how robust a predictor can possibly be. We improve both frontiers, some of which reduce ultimately to consequences of Hölder’s Theorem (that every Archimedean group is abelian).