CMI.measure: A comprehensive function for estimating conditional mutual...
In Informeasure: R implementation of Information measures

Description Usage Arguments Details Value References Examples

The CMI.measure function is used to calculate the expected mutual information between two random variables conditioned on the third one from the joint count table.

CMI.measure(
  XYZ,
  method = c("ML", "Jeffreys", "Laplace", "SG", "minimax", "shrink"),
  lambda.probs,
  unit = c("log", "log2", "log10"),
  verbose = TRUE
)

`XYZ`	a joint count distribution table of three random variables.
`method`	six probability estimation algorithms are available, "ML" is the default.
`lambda.probs`	the shrinkage intensity, only called when the probability estimator is "shrink".
`unit`	the base of the logarithm. The default is natural logarithm, which is "log". For evaluating entropy in bits, it is suggested to set the unit to "log2".
`verbose`	a logic variable. if verbose is true, report the shrinkage intensity.

Six probability estimation methods are available to evaluate the underlying bin probability from observed counts:
method = "ML": maximum likelihood estimator, also referred to empirical probability,
method = "Jeffreys": Dirichlet distribution estimator with prior a = 0.5,
method = "Laplace": Dirichlet distribution estimator with prior a = 1,
method = "SG": Dirichlet distribution estimator with prior a = 1/length(XY),
method = "minimax": Dirichlet distribution estimator with prior a = sqrt(sum(XY))/length(XY),
method = "shrink": shrinkage estimator.

CMI.measure returns the conditional mutual information.

#' Hausser, J., & Strimmer, K. (2009). Entropy Inference and the James-Stein Estimator, with Application to Nonlinear Gene Association Networks. Journal of Machine Learning Research, 1469-1484.

# three numeric vectors corresponding to three continuous random variables
x <- c(0.0, 0.2, 0.2, 0.7, 0.9, 0.9, 0.9, 0.9, 1.0)
y <- c(1.0, 2.0,  12, 8.0, 1.0, 9.0, 0.0, 3.0, 9.0)
z <- c(3.0, 7.0, 2.0,  11,  10,  10,  14, 2.0,  11)

# corresponding joint count table estimated by "uniform width" algorithm
XYZ <- discretize3D(x, y, z, "uniform_width")

# corresponding conditional mutual information
CMI.measure(XYZ)