Compute measure of dependence

dependence_factor.py

import numpy as np


def dependence_factor(a, b, norm=True):
    """Compute measure of dependence between a and b.

    Independent means that Pab(i,j) - Pa(i) * Pa(j) == 0 for all i and j, where
    i and j are the individual values that the variables a and b can take.

    If norm=True, this function returns a value between 0 and 1, where 1 means
    that the variables are perfectly dependent, and 0 means the variables are
    perfectly independent.

    If norm=False, this function returns the mean absolute deviation from 0.
    The larger this result, the more dependent are a and b.
    """
    Pa = [np.mean(a == 0), np.mean(a == 1)]
    Pb = [np.mean(b == 0), np.mean(b == 1)]

    Pab = np.array([[np.mean(np.logical_and(a == 0, b == 0)),
                     np.mean(np.logical_and(a == 0, b == 1))],
                    [np.mean(np.logical_and(a == 1, b == 0)),
                     np.mean(np.logical_and(a == 1, b == 1))]])

    agreement = Pab - np.outer(Pa, Pb)
    mad = np.mean(np.abs(agreement))

    if norm:
        return mad / dependence_factor(a, a, norm=False)
    else:
        return mad


A = '0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0'

a = np.array([float(a) for a in A.split()])
a, a_lagged = a[2:], a[:-2]

# we can also use a larger sample:
# a = np.random.binomial(1, 0.02, 1002)
# a, a_lagged = a[2:], a[:-2]

print('a[n], a[n]: {:.2f}'.format(dependence_factor(a, a)))
print('a[n], a[n-2]: {:.2f}'.format(dependence_factor(a, a_lagged)))
print('a[n], a[n] + a[n-2]: {:.2f}'.format(dependence_factor(a, a + a_lagged)))