Generative Archimedean Copulas
This work addresses the challenge of modeling complex dependencies in high-dimensional data for applications in statistics and machine learning, representing an incremental improvement with a novel method for a known bottleneck.
The paper tackled the problem of learning multidimensional cumulative distribution functions using copulas, specifically Archimedean and hierarchical Archimedean types, by proposing a generative modeling technique that represents them as mixture models with Laplace transforms from neural networks, resulting in demonstrated efficacy and computational efficiency compared to existing methods.
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.