论文标题
时间序列可预测性与贝叶斯错误率之间的等效性
Equivalence between Time Series Predictability and Bayes Error Rate
论文作者
论文摘要
可预测性是一个新兴的度量标准，它量化给定时间序列的最高预测准确性，广泛用于评估已知的预测算法并表征人类行为的内在规律性。最近，越来越多的批评旨在旨在由基于熵的方法引起的估计可预测性的不准确。在此简短的报告中，我们严格证明了时间序列可预测性等效于看似无关的度量的贝叶斯错误率，该指标探讨了分类中不可避免的最低错误率。该证明桥接两个独立发展的领域，因此每个领域都可以立即受益于另一个领域。例如，基于三个具有预测准确性的已知和可控上限的理论模型，我们表明基于贝叶斯错误率的估计可以在很大程度上解决可预测性的不准确问题。
Predictability is an emerging metric that quantifies the highest possible prediction accuracy for a given time series, being widely utilized in assessing known prediction algorithms and characterizing intrinsic regularities in human behaviors. Lately, increasing criticisms aim at the inaccuracy of the estimated predictability, caused by the original entropy-based method. In this brief report, we strictly prove that the time series predictability is equivalent to a seemingly unrelated metric called Bayes error rate that explores the lowest error rate unavoidable in classification. This proof bridges two independently developed fields, and thus each can immediately benefit from the other. For example, based on three theoretical models with known and controllable upper bounds of prediction accuracy, we show that the estimation based on Bayes error rate can largely solve the inaccuracy problem of predictability.
