A Measure of Dependence Between Discrete and Continuous Variables

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.