Tukey g-and-h neural network regression for non-Gaussian data

• URL: http://arxiv.org/abs/2411.07957v1
• Date: Tue, 12 Nov 2024 17:34:38 GMT
• Title: Tukey g-and-h neural network regression for non-Gaussian data
• Authors: Arthur P. Guillaumin, Natalia Efremova,
• Abstract summary: We consider the training of a neural network to predict the parameters of a Tukey g-and-h distribution in a regression framework. We show how we can carry out a goodness-of-fit analysis between the predicted distributions and the test data.
• Score: 0.0
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• Abstract: This paper addresses non-Gaussian regression with neural networks via the use of the Tukey g-and-h distribution.The Tukey g-and-h transform is a flexible parametric transform with two parameters $g$ and $h$ which, when applied to a standard normal random variable, introduces both skewness and kurtosis, resulting in a distribution commonly called the Tukey g-and-h distribution. Specific values of $g$ and $h$ produce good approximations to other families of distributions, such as the Cauchy and student-t distributions. The flexibility of the Tukey g-and-h distribution has driven its popularity in the statistical community, in applied sciences and finance. In this work we consider the training of a neural network to predict the parameters of a Tukey g-and-h distribution in a regression framework via the minimization of the corresponding negative log-likelihood, despite the latter having no closed-form expression. We demonstrate the efficiency of our procedure in simulated examples and apply our method to a real-world dataset of global crop yield for several types of crops. Finally, we show how we can carry out a goodness-of-fit analysis between the predicted distributions and the test data. A Pytorch implementation is made available on Github and as a Pypi package.

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