Abstract
Mutual information (MI) is a powerful method for detecting relationships between data sets. There are accurate methods for estimating MI that avoid problems with “binning” when both data sets are discrete or when both data sets are continuous. We present an accurate, non-binning MI estimator for the case of one discrete data set and one continuous data set. This case applies when measuring, for example, the relationship between base sequence and gene expression level, or the effect of a cancer drug on patient survival time. We also show how our method can be adapted to calculate the Jensen–Shannon divergence of two or more data sets.
Highlights
Mutual information (MI) [1] is in several ways a perfect statistic for measuring the degree of relatedness between data sets
MI will detect any sort of relationship between data sets whatsoever, whether it involves the mean values or the variances or higher moments
MI has a straightforward interpretation as the amount of shared information between data sets; other statistics such as rankordering are harder to interpret
Summary
Mutual information (MI) [1] is in several ways a perfect statistic for measuring the degree of relatedness between data sets. We can apply our method to estimate the weighted JS divergence, by storing samples from each distribution to be compared in the continuous data set Y , and using the discrete data set X to identify which distribution each sample was drawn from.
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