Towards a pretrained deep learning estimator of the Linfoot informational correlation

TL;DR

This paper introduces a supervised deep learning method to estimate the Linfoot informational correlation, a transformed version of mutual information, demonstrating improved bias and variance over existing estimators.

Contribution

The paper presents a novel deep learning estimator for the Linfoot informational correlation, leveraging ground truth labels from copulas, with better accuracy than traditional methods.

Findings

Lower bias compared to kernel density and k-NN estimators

Lower variance than neural estimators

Effective on Gaussian and Clayton copulas

Abstract

We develop a supervised deep-learning approach to estimate mutual information between two continuous random variables. As labels, we use the Linfoot informational correlation, a transformation of mutual information that has many important properties. Our method is based on ground truth labels for Gaussian and Clayton copulas. We compare our method with estimators based on kernel density, k-nearest neighbours and neural estimators. We show generally lower bias and lower variance. As a proof of principle, future research could look into training the model with a more diverse set of examples from other copulas for which ground truth labels are available.