Conditional Dependence Coefficient
Conditional Dependence Coefficient1 measures if Y is a function of Z|X (represented at T(Y, Z|X)), where Z and X can both be multi-variate.
When X is not present, it reduces to T(Y, Z).
The coefficient is computed by comparing the nearest neighbour of consecutive rows of Z when Y is sorted.
It is 0 if Y is completely independent of Z|X, and 1 if Y is a measurable function of Z|X.
Usage
Make a random 10000 x 3 array:
Y is independent of each column. But it is a function of all three put together.
import numpy as np
n = 10000
p = 3
x = np.random.uniform(0, 1, (n, p))
# y is independent of each x, but is a function of all three put together
y = np.mod(x.sum(axis=1), 1)
Compute T(Y, Z):
import xicorpy
# y is independent of x, so coeff is 0.
c = xicorpy.compute_conditional_dependence(y, x[:, 0])
assert np.allclose(c, 0, atol=1e-2)
# y is independent of any two x columns too, so coeff is again 0.
c = xicorpy.compute_conditional_dependence(y, x[:, :1])
assert np.allclose(c, 0, atol=1e-2)
c = xicorpy.compute_conditional_dependence(y, x[:, 1:])
assert np.allclose(c, 0, atol=1e-2)
# y is a function of all three put together. Now coeff is close to 1.
c = xicorpy.compute_conditional_dependence(y, x)
assert np.allclose(c, 1, atol=1e-1)
Compute T(Y, Z | X):
# Given col1, and col2, y is a function of col3.
c = xicorpy.compute_conditional_dependence(y, x[:, 0], x[:, 1:])
assert np.allclose(c, 1, atol=1e-2)
Compute coefficient for each column of X:
c = xicorpy.compute_conditional_dependence_1d(y, x)
assert isinstance(c, dict)
assert sorted(c.keys()) == [0, 1, 2]
c = xicorpy.compute_conditional_dependence_1d(y, x[:, :2], x[:, 2])
assert isinstance(c, dict)
assert sorted(c.keys()) == [0, 1]