Generative Archimedean Copulas

TL;DR

This paper introduces a novel generative modeling approach for multidimensional copulas, leveraging neural networks to improve efficiency and sampling in high-dimensional settings.

Contribution

It presents a new neural network-based representation of Archimedean copulas as mixture models, enabling efficient learning and sampling of complex multidimensional distributions.

Findings

Demonstrates improved computational efficiency over existing methods

Shows effective learning of multidimensional CDFs with neural networks

Provides scalable sampling techniques for high-dimensional copulas

Abstract

We propose a new generative modeling technique for learning multidimensional cumulative distribution functions (CDFs) in the form of copulas. Specifically, we consider certain classes of copulas known as Archimedean and hierarchical Archimedean copulas, popular for their parsimonious representation and ability to model different tail dependencies. We consider their representation as mixture models with Laplace transforms of latent random variables from generative neural networks. This alternative representation allows for computational efficiencies and easy sampling, especially in high dimensions. We describe multiple methods for optimizing the network parameters. Finally, we present empirical results that demonstrate the efficacy of our proposed method in learning multidimensional CDFs and its computational efficiency compared to existing methods.