Copulas are a powerful tool for modeling multivariate distributions as they allow to separately estimate the univariate marginal distributions and the joint dependency structure. However, known parametric copulas offer limited flexibility especially in high dimensions, while commonly used non-parametric methods suffer from the curse of dimensionality. A popular remedy is to construct a tree-based hierarchy of conditional bivariate copulas. In this paper, we propose a flexible, yet conceptually simple alternative based on implicit generative neural networks. The key challenge is to ensure marginal uniformity of the estimated copula distribution. We achieve this by learning a multivariate latent distribution with unspecified marginals but the desired dependency structure. By applying the probability integral transform, we can then obtain samples from the high-dimensional copula distribution without relying on parametric assumptions or the need to find a suitable tree structure. Experiments on synthetic and real data from finance, physics, and image generation demonstrate the performance of this approach.
翻译:Copula是建模多变量分布的有力工具,因为这样可以分别估计单子边际分布和共同依赖结构。然而,已知的对数相形色体具有有限的灵活性,特别是在高维方面,而通常使用的非对数方法则受到维度的诅咒。一种流行的补救办法是建立一个基于树的有条件的双差相色体等级。在本文中,我们提出了一个基于隐性基因神经网络的灵活、但概念上简单的替代方案。关键的挑战是确保估计的 Cocula分布的边际统一性。我们通过学习与未指明的边际分布的多变量潜在分布,但需要的依附结构来实现这一点。通过应用概率整体变换,我们可以在不依赖参数假设或需要找到合适的树结构的情况下从高维相色的分布中获取样本。对来自金融、物理和图像生成的合成和真实数据进行实验,展示了这一方法的性能。