A Bayesian Nonparametric Estimation of Mutual Information

TL;DR

This paper introduces an efficient Bayesian nonparametric estimator for mutual information, demonstrating superior performance over existing methods through empirical comparisons in various applications.

Contribution

It proposes a novel Bayesian nonparametric estimator for mutual information, improving accuracy and efficiency compared to traditional frequentist approaches.

Findings

Estimator has smaller mean squared error.

Performs well across diverse examples.

Outperforms frequentist methods in accuracy.

Abstract

Mutual information is a widely-used information theoretic measure to quantify the amount of association between variables. It is used extensively in many applications such as image registration, diagnosis of failures in electrical machines, pattern recognition, data mining and tests of independence. The main goal of this paper is to provide an efficient estimator of the mutual information based on the approach of Al Labadi et. al. (2021). The estimator is explored through various examples and is compared to its frequentist counterpart due to Berrett et al. (2019). The results show the good performance of the procedure by having a smaller mean squared error.