Co-Information¶

The co-information [2] is one generalization of the mutual information to multiple variables. It is defined via an inclusion/exclusion sum:

\[\begin{split}\I[X_{0:n}] &= -\sum_{y \in \mathcal{P}(\{0..n\})} (-1)^{|y|} \H[X_y] \\ &= \sum_{x_{0:n} \in X_{0:n}} p(x_{0:n}) \log_2 \prod_{y \in \mathcal{P}(\{0..n\})} p(y)^{(-1)^{|y|}}\end{split}\]

$The co-information :math:`\I[X:Y]`$ $The co-information :math:`\I[X:Y:Z]`$

coinformation(dist, rvs=None, crvs=None, rv_names=None)[source]¶

Calculates the coinformation.

Parameters :	dist (Distribution) – The distribution from which the coinformation is calculated. rvs (list, None) – The indexes of the random variable used to calculate the coinformation between. If None, then the coinformation is calculated over all random variables. crvs (list, None) – The indexes of the random variables to condition on. If None, then no variables are condition on. rv_names (bool) – If True, then the elements of rvs are treated as random variable names. If False, then the elements of rvs are treated as random variable indexes. If None, then the value True is used if the distribution has specified names for its random variables.
Returns:	I (float) – The coinformation.
Raises :	`ditException` – Raised if dist is not a joint distribution.