Copula-based statistical dependence visualizations

TL;DR

This paper introduces copula-based visualizations for analyzing pairwise dependencies in data, offering richer insights than traditional correlation matrices or scatter plots by capturing the full dependency structure.

Contribution

It presents novel copula-based visualization methods and reviews their theoretical foundations, enhancing the detection of complex dependencies in continuous data.

Findings

Copula visualizations effectively reveal independence and dependency trends.

They outperform traditional methods in capturing dependency structures.

Color coding aids in identifying increasing or decreasing relationships.

Abstract

A frequent task in exploratory data analysis consists in examining pairwise dependencies between data variables. Popular approaches include visualizing correlation or scatter plot matrices. However, both methods can be misleading. The former is primarily limited because it reports a single value for a pair of random variables. Furthermore, scatter plots can fail to convey the dependency structure between variables properly. In this paper we discuss these shortcomings and present alternative and richer visualizations based on copula functions, which fully determine the dependency between continuous random variables. Since copulas seldom appear in the data visualization literature we first review essential theory, and propose alternative scatter plots and several heatmaps for assessing the statistical association between two continuous random variables. These visualizations not only allow users to detect independence, but also increasing and/or decreasing trends in the data through a color coding, which can also be applied in other methods such as parallel coordinates.