Source code for dit.other.lautum_information

The lautum (mutual backwards) information, as defined by Palomar & Verdu.

from dit.distconst import product_distribution
from dit.divergences import kullback_leibler_divergence
from dit.helpers import normalize_rvs

[docs]def lautum_information(dist, rvs=None, crvs=None, rv_mode=None): """ Computes the lautum information. Parameters ---------- dist : Distribution The distribution from which the lautum information is calculated. rvs : list, None A list of lists. Each inner list specifies the indexes of the random variables used to calculate the lautum information. If None, then the lautum information 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 ------- L : float The lautum information. Examples -------- >>> outcomes = ['000', '001', '010', '011', '100', '101', '110', '111'] >>> pmf = [3/16, 1/16, 1/16, 3/16, 1/16, 3/16, 3/16, 1/16] >>> d = dit.Distribution(outcomes, pmf) >>> dit.other.lautum_information(d) 0.20751874963942196 >>> dit.other.lautum_information(d, rvs=[[0], [1]]) 0.0 Raises ------ ditException Raised if `dist` is not a joint distribution or if `rvs` or `crvs` contain non-existent random variables. """ rvs, crvs, rv_mode = normalize_rvs(dist, rvs, crvs, rv_mode) pd = product_distribution(dist, rvs=rvs + [crvs], rv_mode=rv_mode) L = kullback_leibler_divergence(pd, dist, rvs=rvs, crvs=crvs, rv_mode=rv_mode) return L