Implicit Generative Copulas
This addresses the problem of modeling complex dependencies in high-dimensional data for fields like finance and physics, offering a flexible alternative to tree-based methods, though it appears incremental as it builds on existing implicit generative techniques.
The paper tackles the limited flexibility of parametric copulas and the curse of dimensionality in non-parametric methods for high-dimensional multivariate distribution modeling by proposing an implicit generative neural network approach that ensures marginal uniformity through a latent distribution and probability integral transform, achieving performance demonstrated on synthetic and real data from finance, physics, and image generation.
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.