Chatterjee's Xi, its Applications, and Offshoots
XicorPy is a Python package implementing Chatterjee's Xi, and its various offshoots.
The package currently implements:
- Chatterjee's Xi1
- Modified Xi2
- Conditional Dependence Coefficient3
- Feature Selection via Feature Ordering by Conditional Independence (FOCI) Algorithm 3
Installation
The package is available on PyPI. You can install using pip: pip install xicorpy.
Usage
Compute Chatterjee's Xi:
import xicorpy
x = [10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5]
y = [8.04, 6.95, 7.58, 8.81, 8.33, 9.96, 7.24, 4.26, 10.84, 4.82, 5.68]
xi = xicorpy.compute_xi_correlation(x, y)
xi, p_value = xicorpy.compute_xi_correlation(x, y, get_p_values=True)
Compute Conditional Dependence Coefficient:
import numpy as np
import xicorpy
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)
# 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 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=2e-1)
# 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)
Select Features using FOCI:
import numpy as np
import xicorpy
n = 2000
p = 100
x = np.random.normal(0, 1, (n, p))
y = x[:, 0] * x[:, 1] + np.sin(x[:, 2] * x[:, 0])
# Select Features
selected = xicorpy.select_features_using_foci(y, x, num_features=10)
# Select Features with Initial Feature Set
selected = xicorpy.select_features_using_foci(y, x, num_features=10, init_selection=[0])