论文标题
部分可观测时空混沌系统的无模型预测
Criterion for the resemblance between the mother and the model distribution
论文作者
论文摘要
如果概率分布模型旨在近似隐藏的母亲分布，则必须建立对母亲和模型分布之间相似之处的有用标准。 这项研究提出了一个标准，该标准可以测量两个分布的离散（量化）样本之间的距离。与信息标准（例如AIC）不同，此标准不需要模型分布的概率密度函数，而该模型分布无法明确获得复杂模型（例如深度学习机器）。其次，它可以在给定的阈值下得出积极的结论（即两个分布都足够接近），而统计假设检验，例如Kolmogorov-Smirnov检验，当接受假设时，无法真正导致积极的结论。 在这项研究中，我们为从贝叶斯错误率推论的标准建立了合理的阈值，并提出了标准估计量的渐近偏置。从这些结果中，建立了一个合理且易于使用的标准，可以直接从两个分布的两组样本中计算出来。
If the probability distribution model aims to approximate the hidden mother distribution, it is imperative to establish a useful criterion for the resemblance between the mother and the model distributions. This study proposes a criterion that measures the Hellinger distance between discretized (quantized) samples from both distributions. Unlike information criteria such as AIC, this criterion does not require the probability density function of the model distribution, which cannot be explicitly obtained for a complicated model such as a deep learning machine. Second, it can draw a positive conclusion (i.e., both distributions are sufficiently close) under a given threshold, whereas a statistical hypothesis test, such as the Kolmogorov-Smirnov test, cannot genuinely lead to a positive conclusion when the hypothesis is accepted. In this study, we establish a reasonable threshold for the criterion deduced from the Bayes error rate and also present the asymptotic bias of the estimator of the criterion. From these results, a reasonable and easy-to-use criterion is established that can be directly calculated from the two sets of samples from both distributions.
