Source code for dit.multivariate.caekl_mutual_information

The CAEKL mutual information, as define [Chan, Chung, et al. "Multivariate Mutual Information Inspired by Secret-Key Agreement." Proceedings of the IEEE 103.10 (2015): 1883-1913].

from __future__ import division

from ..helpers import normalize_rvs
from ..utils import partitions, unitful
from .entropy import entropy

__all__ = [

[docs]@unitful def caekl_mutual_information(dist, rvs=None, crvs=None, rv_mode=None): """ Calculates the Chan-AlBashabsheh-Ebrahimi-Kaced-Liu mutual information. Parameters ---------- dist : Distribution The distribution from which the CAEKL mutual information is calculated. rvs : list, None A list of lists. Each inner list specifies the indexes of the random variables used to calculate the total correlation. If None, then the total correlation is calculated over all random variables, which is equivalent to passing `rvs=dist.rvs`. crvs : list, None A single list of indexes specifying the random variables to condition on. If None, then no 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'. Returns ------- J : float The CAEKL mutual information. Examples -------- >>> d = dit.example_dists.Xor() >>> dit.multivariate.caekl_mutual_information(d) 0.5 >>> dit.multivariate.caekl_mutual_information(d, rvs=[[0], [1]]) 0.0 Raises ------ ditException Raised if `dist` is not a joint distribution or if `rvs` or `crvs` contain non-existant random variables. """ rvs, crvs, rv_mode = normalize_rvs(dist, rvs, crvs, rv_mode) H = entropy(dist, rvs, crvs, rv_mode) def I_P(part): a = sum(entropy(dist, rvs=p, crvs=crvs, rv_mode=rv_mode) for p in part) return (a - H)/(len(part) - 1) J = min(I_P(p) for p in partitions(map(tuple, rvs)) if len(p) > 1) return J