母分布与模型分布相似性的判别准则
Criterion for the resemblance between the mother and the model distribution
AI总结：
针对概率分布模型逼近隐藏母分布的需求，提出一种基于量化样本Hellinger距离的相似性准则，无需模型概率密度函数，能在给定阈值下得出分布足够接近的肯定结论，并推导了合理阈值与估计量渐近偏差。
摘要：
若概率分布模型旨在逼近隐藏的母分布，则必须建立一个衡量母分布与模型分布相似性的有效准则。本研究提出一种准则，通过量化（离散化）两个分布的样本计算它们之间的Hellinger距离。与AIC等信息准则不同，该准则不需要模型分布的概率密度函数——对于深度学习模型这类复杂模型，其概率密度函数无法显式获取。其次，在给定阈值下，该准则可得出肯定结论（即两个分布足够接近）；而Kolmogorov-Smirnov检验等统计假设检验在接受原假设时无法真正得出肯定结论。本研究基于贝叶斯错误率推导了准则的合理阈值，并给出了准则估计量的渐近偏差。基于这些结果，建立了一个可直接从两个分布的样本集计算的合理且易用的准则。
英文摘要：
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.
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。
