PMI.measure: A comprehensive function for evaluating part mutual...
In Informeasure: R implementation of Information measures

Description Usage Arguments Details Value References Examples

The PMI.measure function is used to calculate the non-linearly direct dependencies between two variables conditioned on the third one form the joint count table.

PMI.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.

PMI.measure returns the part 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.

Zhao, J., Zhou, Y., Zhang, X., & Chen, L. (2016). Part mutual information for quantifying direct associations in networks. Proceedings of the National Academy of Sciences of the United States of America, 113(18), 5130-5135.

# 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 part mutual information
PMI.measure(XYZ)