Function information::cmi::conditional_mutual_information

pub fn conditional_mutual_information(p_xyz: &Array3<f64>) -> f64

Conditional Mutual Information

https://en.wikipedia.org/wiki/Conditional_mutual_information

Calculates the expected value of the mutual information of two random variables given a third.

The conditional mutual information I(X;Y|Z) is calculated as follows:

I(X;Y|Z) = Σ Σ Σ p(x,y,z) * ln [ (p(z) * p(x,y,z)) / (p(x,z) * p(y,z))]
           z y x

Usage

use ndarray::Array1;
use ndarray_rand::{RandomExt, rand_distr::Uniform};
use information::{prob3d, conditional_mutual_information};

let x = Array1::random(1000, Uniform::new(0, 2));
let y = Array1::random(1000, Uniform::new(0, 2));
let z = Array1::random(1000, Uniform::new(0, 2));
let xyz = prob3d(&x, &y, &z, 2, 2, 2).unwrap();
 
let cmi = conditional_mutual_information(&xyz);
 
// Measures: I(X;Y|Z) >= 0
assert!(cmi >= 0.0);