Source code for dit.multivariate.tse_complexity

The TSE Complexity.
from __future__ import division

from itertools import combinations

from ..shannon import conditional_entropy as H
from ..helpers import normalize_rvs
from ..math.misc import combinations as nCk
from ..utils import unitful

__all__ = [

[docs]@unitful def tse_complexity(dist, rvs=None, crvs=None, rv_mode=None): """ Calculates the TSE complexity. Parameters ---------- dist : Distribution The distribution from which the TSE complexity is calculated. rvs : list, None The indexes of the random variable used to calculate the TSE complexity between. If None, then the TSE complexity is calculated over all random variables. crvs : list, None The indexes of the random variables to condition on. If None, then no variables are condition 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 ------- TSE : float The TSE complexity. 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) joint = H(dist, set().union(*rvs), crvs, rv_mode=rv_mode) N = len(rvs) def sub_entropies(k): """ Compute the average entropy of all subsets of `rvs` of size `k`. """ sub_rvs = (set().union(*rv) for rv in combinations(rvs, k)) subH = sum(H(dist, rv, crvs, rv_mode=rv_mode) for rv in sub_rvs) subH /= nCk(N, k) return subH TSE = sum(sub_entropies(k) - k/N * joint for k in range(1, N)) return TSE