A Measure of Dependence Between Discrete and Continuous Variables

TL;DR

This paper introduces a kernel density-based method to estimate mutual information between discrete and continuous variables, addressing a less-explored area with applications in sequence segmentation.

Contribution

It presents a novel approach for estimating mutual information between discrete and continuous data sets using kernel density approximation.

Findings

Effective MI estimation between discrete and continuous data.

Potential applications in sequence segmentation.

Addresses a gap in existing MI estimation methods.

Abstract

Mutual Information (MI) is an useful tool for the recognition of mutual dependence berween data sets. Differen methods for the estimation of MI have been developed when both data sets are discrete or when both data sets are continuous. The MI estimation between a discrete data set and a continuous data set has not received so much attention. We present here a method for the estimation of MI for this last case based on the kernel density approximation. The calculation may be of interest in diverse contexts. Since MI is closely related to Jensen Shannon divergence, the method here developed is of particular interest in the problem of sequence segmentation.