Testing for Normality with Neural Networks
This provides a more accurate tool for testing normality, which is a critical assumption in many statistical and machine learning methods, potentially benefiting everyday practice in science and industry.
The authors tackled the problem of testing for normality by framing it as a binary classification task and training a feedforward neural network to detect normal distributions from small samples. The neural network achieved near-perfect performance with an AUROC score of almost 1, outperforming standard tests like Shapiro-Wilk and others, and maintained over 96% accuracy on larger samples.
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.