论文标题
神经副群：一个统一的框架，用于估计通用高维副函数
Neural Copula: A unified framework for estimating generic high-dimensional Copula functions
论文作者
论文摘要
该副群被广泛用于描述边际分布与随机变量的关节分布之间的关系。高维副群的估计很困难，大多数现有的解决方案都依赖于简化的假设或复杂的递归分解。因此，人们仍然希望获得具有普遍性和简单性的通用Copula估计方法。为了实现这一目标，本文提出了一种基于神经网络的新方法（名为神经副群）。在这种方法中，构建了分层无监督的神经网络，以通过求解微分方程来估计边缘分布函数和copula函数。在培训计划中，对神经网络及其衍生物都施加了各种限制。通过所提出的方法估计的副物是平滑的，具有分析表达。在现实世界数据集和复杂的数值模拟上评估了所提出方法的有效性。实验结果表明，神经副群在复杂分布中的拟合质量比经典方法要好得多。实验的相关代码可在GitHub上获得。 （我们鼓励读者运行该程序，以更好地理解所提出的方法）。
The Copula is widely used to describe the relationship between the marginal distribution and joint distribution of random variables. The estimation of high-dimensional Copula is difficult, and most existing solutions rely either on simplified assumptions or on complicating recursive decompositions. Therefore, people still hope to obtain a generic Copula estimation method with both universality and simplicity. To reach this goal, a novel neural network-based method (named Neural Copula) is proposed in this paper. In this method, a hierarchical unsupervised neural network is constructed to estimate the marginal distribution function and the Copula function by solving differential equations. In the training program, various constraints are imposed on both the neural network and its derivatives. The Copula estimated by the proposed method is smooth and has an analytic expression. The effectiveness of the proposed method is evaluated on both real-world datasets and complex numerical simulations. Experimental results show that Neural Copula's fitting quality for complex distributions is much better than classical methods. The relevant code for the experiments is available on GitHub. (We encourage the reader to run the program for a better understanding of the proposed method).
