Source code for dit.multivariate.common_informations.gk_common_information

Compute the Gacs-Korner common information

from ...algorithms import insert_meet
from ...helpers import normalize_rvs, parse_rvs
from ...npdist import Distribution
from ...shannon import conditional_entropy as H
from ...utils import unitful

[docs]@unitful def gk_common_information(dist, rvs=None, crvs=None, rv_mode=None): """ Calculates the Gacs-Korner common information K[X1:X2...] over the random variables in `rvs`. Parameters ---------- dist : Distribution The distribution from which the common information is calculated. rvs : list, None The indexes of the random variables for which the Gacs-Korner common information is to be computed. If None, then the common information is calculated over all random variables. crvs : list, None The indexes of the random variables to condition the common information by. If none, than there is no conditioning. 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'. Returns ------- K : float The Gacs-Korner common information of the distribution. Raises ------ ditException Raised if `rvs` or `crvs` contain non-existant random variables. """ rvs, crvs, rv_mode = normalize_rvs(dist, rvs, crvs, rv_mode) crvs = parse_rvs(dist, crvs, rv_mode)[1] outcomes, pmf = zip(*dist.zipped(mode='patoms')) # The GK-common information is sensitive to zeros in the sample space. # Here, we make sure to remove them. d = Distribution(outcomes, pmf, sample_space=outcomes) d.set_rv_names(dist.get_rv_names()) d2 = insert_meet(d, -1, rvs, rv_mode=rv_mode) common = [d2.outcome_length() - 1] K = H(d2, common, crvs) return K