Calculate mutual information between groups of joint variates

This function calculates various entropic information measures of two variates (each variate may consist of joint variates): the mutual information, the conditional entropies, and the entropies.

Usage

mutualinfo(
  Y1names,
  Y2names,
  X = NULL,
  learnt,
  tails = NULL,
  n = NULL,
  unit = "Sh",
  parallel = NULL,
  silent = FALSE
)

Arguments

Y1names

Character vector: first group of joint variates

Y2names

Character vector or NULL: second group of joint variates

X

Matrix or data.frame or NULL: values of some variates conditional on which we want the probabilities.

learnt

Either a character with the name of a directory or full path for an 'learnt.rds' object, or such an object itself.

tails

Named vector or list, or NULL (default). The names must match some or all of the variates in arguments X. For variates in this list, the probability conditional is understood in an semi-open interval sense: X ≤ x or X ≥ x, an so on. See analogous argument in Pr().

n

Integer or NULL (default): number of samples from which to approximately calculate the mutual information. Default as many as Monte Carlo samples in learnt.

unit

Either one of 'Sh' for shannon (default), 'Hart' for hartley, 'nat' for natural unit, or a positive real indicating the base of the logarithms to be used.

parallel

Logical or positive integer or cluster object. TRUE: use roughly half of available cores; FALSE: use serial computation; integer: use this many cores. It can also be a cluster object previously created with parallel::makeCluster(); in this case the parallel computation will use this object.

silent

Logical: give warnings or updates in the computation?

Value

A list consisting of the elements MI, CondEn12, CondEn21, En1, En2, MI.rGauss, unit, Y1names, Y1names. All elements except unit, Y1names, Y2names are a vector of value and accuracy. Element MI is the mutual information between (joint) variates Y1names and (joint) variates Y2names. ElementCondEn12 is the conditional entropy of the first variate given the second, and vice versa for CondEn21. Elements En1 and En1 are the (differential) entropies of the first and second variates. Elements unit, Y1names, Y2names are identical to the same inputs. Element MI.rGauss is the absolute value of the Pearson correlation coefficient of a multivariate Gaussian distribution having mutual information MI (the two are related by MI = -log(1 - MI.rGauss^2)/2); it may provide a vague intuition for the MI value for people more familiar with Pearson's correlation, but should be taken with a grain of salt.