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

arXiv: https://arxiv.org/abs/2411.07957 · HTML: https://mlsanity.com/paper/2411.07957/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 22 references that are in the map.
- First posted on arXiv 12 Nov 2024.

## Builds on (most cited first, 1 of 1)

- [Hello Edge: Keyword Spotting on Microcontrollers](https://mlsanity.com/paper/1711.07128/) (2017)

## Abstract (arXiv)

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.