用泰克g-and-h分布改进神经网络非高斯回归，提升对偏态厚尾数据的建模能力。
Tukey g-and-h neural network regression for non-Gaussian data
- 用神经网络预测泰克g-and-h分布参数，通过最小化负对数似然训练。
- 在模拟和真实全球作物产量数据上均表现良好，能有效捕捉偏度与峰度。
- 适合处理金融、农业等存在极端值的非高斯回归任务，代码开源可用。
本文通过使用泰克g-and-h分布解决神经网络在非高斯回归中的问题。该分布具有两个参数g和h，对标准正态变量进行变换可引入偏度与峰度，形成广义的泰克g-and-h分布，其特定取值可逼近柯西分布、t分布等。该分布因灵活性强，在统计学、应用科学和金融领域广泛应用。本文提出训练神经网络以预测泰克g-and-h分布参数，基于负对数似然优化，尽管该似然无闭式表达。我们在模拟实验中验证了方法的有效性，并将其应用于多种作物的全球产量真实数据集。最后，展示了预测分布与测试数据间的拟合优度分析。代码已通过PyTorch实现，并发布于GitHub和Pypi。
原文摘要 · Abstract (English)
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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