Copulas and deep learning: a review

In the last two decades, there has been a surge in the research on neural networks, and particularly on deep learning. At the same time, copulas as a statistical modeling tool for multivariate distributions became more and more popular. We survey how copulas are used in neural networks and deep learning and vice versa how neural networks and deep learning are used in the copula domain. For example, we highlight that copulas can be constructed from generative deep learning models and that neural networks can help in goodness-of-fit assessment of copulas. Moreover, we discuss how copulas amplify specific deep learning models and how copulas are harnessed to combine neural network outputs.