MI.z {EntropyEstimation}

MI.z

Description

Returns the Z estimator of Mutual Information. This estimator has exponentially decaying bias. See Zhang and Zheng (2014) for details.

Usage

MI.z(x)

Arguments

x

Matrix of counts. Must be integer valued. Each entry represents the number of observations of a distinct combination of letters from the two alphabets.

Author(s)

Lijuan Cao and Michael Grabchak

References

Z. Zhang and L. Zheng (2014). A Mutual Information Estimator with Exponentially Decaying Bias.

Examples

x = matrix(c(0, 0, 0, 1, 1, 0, 0, 0, 0, 0,
       0, 0, 0, 1, 0, 0, 1, 1, 0, 1,
       0, 0, 0, 2, 1, 0, 1, 0, 0, 1,
       0, 0, 0, 1, 1, 2, 0, 0, 0, 0,
       0, 0, 0, 3, 6, 2, 2, 0, 0, 0,
       2, 0, 2, 5, 6, 5, 1, 0, 0, 0,
       0, 0, 4, 6, 11, 5, 1, 1, 0, 1,
       0, 0, 5, 10, 21, 7, 5, 1, 0, 1,
       0, 0, 7, 11, 9, 6, 3, 0, 0, 1,
       0, 0, 4, 10, 6, 5, 1, 0, 0, 0),10,10,byrow=TRUE)
MI.z(x)       


x = rbinom(100,20,.5)
y = rbinom(100,20,.5)
MI.z(table(x,y))