mi.plugin {entropy} R Documentation

## Plug-In Estimator of Mutual Information and of the Chi-Squared Statistic of Independence

### Description

`mi.plugin` computes the mutual information of two discrete random variables from the specified joint probability mass function.

`chi2indep.plugin` computes the chi-squared divergence of independence.

### Usage

```mi.plugin(freqs2d, unit=c("log", "log2", "log10"))
chi2indep.plugin(freqs2d, unit=c("log", "log2", "log10"))
```

### Arguments

 `freqs2d` matrix of joint bin frequencies (joint probability mass function). `unit` the unit in which entropy is measured. The default is "nats" (natural units). For computing entropy in "bits" set `unit="log2"`.

### Details

The mutual information of two random variables X and Y is the Kullback-Leibler divergence between the joint density/probability mass function and the product independence density of the marginals.

It can also defined using entropy as MI = H(X) + H(Y) - H(X, Y).

Similarly, the chi-squared divergence of independence is the chi-squared divergence between the joint density and the product density. It is a second-order approximation of twice the mutual information.

### Value

`mi.plugin` returns the mutual information.

`chi2indep.plugin` returns the chi-squared divergence of independence.

### Author(s)

Korbinian Strimmer (http://www.strimmerlab.org).

`mi.Dirichlet`, `mi.shrink`, `mi.empirical`, `KL.plugin`, `discretize2d`.

### Examples

```# load entropy library
library("entropy")

# joint distribution of two discrete variables
freqs2d = rbind( c(0.2, 0.1, 0.15), c(0.1, 0.2, 0.25) )

# corresponding mutual information
mi.plugin(freqs2d)

# MI computed via entropy
H1 = entropy.plugin(rowSums(freqs2d))
H2 = entropy.plugin(colSums(freqs2d))
H12 = entropy.plugin(freqs2d)
H1+H2-H12

# and corresponding (half) chi-squared divergence of independence
0.5*chi2indep.plugin(freqs2d)

```

[Package entropy version 1.3.0 Index]