  A central problem in machine learning and statistics is to model joint
densities of random variables from data. Copulas are joint cumulative
distribution functions with uniform marginal distributions and are used to
capture interdependencies in isolation from marginals. Copulas are widely used
within statistics, but have not gained traction in the context of modern deep
learning. In this paper, we introduce ACNet, a novel differentiable neural
network architecture that enforces structural properties and enables one to
learn an important class of copulas--Archimedean Copulas. Unlike Generative
Adversarial Networks, Variational Autoencoders, or Normalizing Flow methods,
which learn either densities or the generative process directly, ACNet learns a
generator of the copula, which implicitly defines the cumulative distribution
function of a joint distribution. We give a probabilistic interpretation of the
network parameters of ACNet and use this to derive a simple but efficient
sampling algorithm for the learned copula. Our experiments show that ACNet is
able to both approximate common Archimedean Copulas and generate new copulas
which may provide better fits to data.
