On mutual information estimation for mixed-pair random variables

TL;DR

This paper introduces a kernel-based method for estimating mutual information between mixed discrete-continuous random variables, providing theoretical guarantees and validation through simulations.

Contribution

It presents a novel kernel estimation technique for mixed-pair mutual information with proven asymptotic properties and empirical validation.

Findings

Establishes a central limit theorem for the estimator.

Demonstrates the estimator's effectiveness via simulations.

Provides theoretical insights into mutual information estimation for mixed variables.

Abstract

We study the mutual information estimation for mixed-pair random variables. One random variable is discrete and the other one is continuous. We develop a kernel method to estimate the mutual information between the two random variables. The estimates enjoy a central limit theorem under some regular conditions on the distributions. The theoretical results are demonstrated by simulation study.