.. functional_common_information.rst
.. py:module:: dit.multivariate.common_informations.functional_common_information

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Functional Common Information
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The functional common information captures the minimum amount of information neccessary to capture all of a distribution's share information using a function of that information. In other words:

.. math::

   \F{X_{0:n} \mid Y_{0:m}} = \min_{\substack{\ind X_{0:n} \mid Y_{0:m}, W \\ W = f(X_{0:n}, Y_{0:m})}} \H{W}

Relationship To Other Measures of Common Information
====================================================

Since this is an additional constraint on the Exact common information, it is generally larger than it, and since its constraint is weaker than that of the :doc:`mss_common_information`, it is generally less than it:

.. math::

   \G{X_{0:n}} \leq \F{X_{0:n}} \leq \M{X_{0:n}}

API
===

.. autofunction:: functional_common_information