Binding Information¶

The binding information [1], or dual total correlation, is yet another generalization of the mutual information. It is defined as:

\[\begin{split}\B[X_{0:n}] &= \H[X_{0:n}] - \sum \H[X_i | X_{\{0..n\}/i}] \\ &= - \sum_{x_{0:n} \in X_{0:n}} p(x_{0:n}) \log_2 \frac{p(x_{0:n})}{\prod p(x_i|x_{\{0:n\}/i})}\end{split}\]

$The binding information :math:`\B[X:Y]`$ $The binding information :math:`\B[X:Y:Z]`$

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

Parameters :	dist (Distribution) – The distribution from which the binding information is calculated. rvs (list, None) – The indexes of the random variable used to calculate the binding information. If None, then the binding information 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:	B (float) – The binding information
Raises :	`ditException` – Raised if dist is not a joint distribution.