Neural Joint Entropy Estimation

TL;DR

This paper presents a neural network-based method for more accurate entropy estimation of discrete variables, especially with small samples, and extends this approach to related information measures like mutual information and transfer entropy.

Contribution

It introduces a novel neural estimation scheme that improves entropy and mutual information estimation accuracy and demonstrates strong consistency and superior performance across various applications.

Findings

Enhanced entropy estimation accuracy with neural networks.

Effective estimation of mutual information and transfer entropy.

Outperforms existing methods in diverse scenarios.

Abstract

Estimating the entropy of a discrete random variable is a fundamental problem in information theory and related fields. This problem has many applications in various domains, including machine learning, statistics and data compression. Over the years, a variety of estimation schemes have been suggested. However, despite significant progress, most methods still struggle when the sample is small, compared to the variable's alphabet size. In this work, we introduce a practical solution to this problem, which extends the work of McAllester and Statos (2020). The proposed scheme uses the generalization abilities of cross-entropy estimation in deep neural networks (DNNs) to introduce improved entropy estimation accuracy. Furthermore, we introduce a family of estimators for related information-theoretic measures, such as conditional entropy and mutual information. We show that these estimators are strongly consistent and demonstrate their performance in a variety of use-cases. First, we consider large alphabet entropy estimation. Then, we extend the scope to mutual information estimation. Next, we apply the proposed scheme to conditional mutual information estimation, as we focus on independence testing tasks. Finally, we study a transfer entropy estimation problem. The proposed estimators demonstrate improved performance compared to existing methods in all tested setups.