Nonparametric Universal Copula Modeling

TL;DR

This paper reviews the history and development of copula functions, emphasizing their growing importance in modeling dependence across various scientific fields over the past 60 years.

Contribution

It offers a comprehensive historical overview and a unified perspective on the evolution and current state of copula modeling techniques.

Findings

Copulas are widely used across disciplines for dependence modeling.

The paper provides a historical timeline of key developments.

It highlights the increasing relevance of copulas in data-driven sciences.

Abstract

To handle the ubiquitous problem of "dependence learning," copulas are quickly becoming a pervasive tool across a wide range of data-driven disciplines encompassing neuroscience, finance, econometrics, genomics, social science, machine learning, healthcare and many more. Copula (or connection) functions were invented in 1959 by Abe Sklar in response to a query of Maurice Frechet. After 60 years, where do we stand now? This article provides a history of the key developments and offers a unified perspective.