# MSS Common Information¶

The Minimal Sufficient Statistic Common Information is the entropy of the join of the minimal sufficient statistic of each variable about the others:

$\M{X_{0:n}} = \H{ \join_i \left(X_i \mss X_\overline{\{i\}}\right) }$

The distribution that the MSS common information is the entroy of is also known “information trim” of the original distribution, and is accessable via dit.algorithms.minimal_sufficient_statistic.info_trim().

## API¶

mss_common_information(dist, rvs=None, crvs=None, rv_mode=None)[source]

Compute the minimal sufficient statistic common information, which is the entropy of the join of the minimal sufficent statistic of each variable about the others.

Parameters
• dist (Distribution) – The distribution for which the joint minimal sufficient statistic is computed.

• rvs (list, None) – The random variables to compute the joint minimal sufficient statistic of. If None, all random variables are used.

• crvs (list, None) – The random variables to condition the joint minimal sufficient statistic on. If None, then no random variables are conditioned on.

• rv_mode (str, None) – Specifies how to interpret rvs and crvs. Valid options are: {‘indices’, ‘names’}. If equal to ‘indices’, then the elements of crvs and rvs are interpreted as random variable indices. If equal to ‘names’, the the elements are interpreted as random variable names. If None, then the value of dist._rv_mode is consulted, which defaults to ‘indices’.