**************
Co-Information
**************

The co-information is one generalization of the mutual information to multiple
variables.

.. autofunction:: dit.algorithms.coinformation

***********************
Interaction Information
***********************

The interaction information is equal in magnitude to the co-information, but
has the opposite sign when taken over an odd number of variables:

.. math:: \operatorname{II}(X) = (-1)^{|X|} \cdot \operatorname{I}(X)

.. autofunction:: dit.algorithms.interaction_information

**************
Co-Information
**************

The co-information is one generalization of the mutual information to multiple
variables.

.. autofunction:: dit.algorithms.coinformation

***********************
Interaction Information
***********************

The interaction information is equal in magnitude to the co-information, but
has the opposite sign when taken over an odd number of variables:

.. math::

	\operatorname{II}(X_{0:n}) &= (-1)^{n} \cdot \operatorname{I}(X_{0:n})

Interaction information was first studied in the 3-variable case which, for
:math:`X_{0:3} = X_0X_1X_2`, takes the following form:

.. math::
   :nowrap:

   \operatorname{II}(X_0:X_1:X_2)
   	  = \operatorname{I}(X_0:X_1|X_2) - \operatorname{I}(X_0:X_1)

The extension to :math:`n>3` proceeds recursively. For example,

.. math::
   :nowrap:

   \begin{align*}
   \operatorname{II}(X_0:X_1:X_2:X_3)
   	  &= \operatorname{II}(X_0:X_1:X_2|X_3) - \operatorname{II}(X_0:X_1:X_2) \\
   	  &= I(X_0:X_1|X_2,X_3) - I(X_0:X_1|X_3) - I(X_0:X_1|X_2) + I(X_0:X_1)\\
   \end{align*}

.. autofunction:: dit.algorithms.interaction_information

Expand doc for interaction information a bit more.
Expand doc for interaction information a bit more.
