论文标题
通过神经网络测试正态性
Testing for Normality with Neural Networks
论文作者
论文摘要
在本文中，我们将测试正态性的问题视为二进制分类问题，并构建了一个前馈神经网络，可以通过检查小样本来成功地检测正常分布。在不超过100个元素的小样本上进行的数值实验表明，我们训练的神经网络比正态性的最常用和最强大的标准测试更准确，更强大：Shapiro-Wilk，Shapiro-Wilk，Anderson-Darling，Lilliefors和Jarque-Berra，以及FortiT的核心测试。神经网络的AUROC分数将近1，与完美的二进制分类器相对应。此外，在一组具有250-1000个元素的较大样品中，网络的准确性高于96％。由于数据的正态性是多种用于分析和推理的技术的假设，因此在本研究中构建的神经网络在科学和行业的日常统计，数据分析和机器学习的日常实践中具有很高的潜力。
In this paper, we treat the problem of testing for normality as a binary classification problem and construct a feedforward neural network that can successfully detect normal distributions by inspecting small samples from them. The numerical experiments conducted on small samples with no more than 100 elements indicated that the neural network which we trained was more accurate and far more powerful than the most frequently used and most powerful standard tests of normality: Shapiro-Wilk, Anderson-Darling, Lilliefors and Jarque-Berra, as well as the kernel tests of goodness-of-fit. The neural network had the AUROC score of almost 1, which corresponds to the perfect binary classifier. Additionally, the network's accuracy was higher than 96% on a set of larger samples with 250-1000 elements. Since the normality of data is an assumption of numerous techniques for analysis and inference, the neural network constructed in this study has a very high potential for use in everyday practice of statistics, data analysis and machine learning in both science and industry.
