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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""This module implements the work on `Causal Inference on Discrete Data via
Estimating Distance Correlations`. For more detail, please refer to the
manuscript at http://www.mitpressjournals.org/doi/pdf/10.1162/NECO_a_00820
"""
import numpy as np
from dcor import dcor
def dc(X, Y):
"""Computes dCorr(P(X), P(Y|X)), and dCorr(P(Y), P(X|Y)).
Args:
X (nested sequence): nested sequence of discrete outcomes
Y (nested sequence): nested sequence of discrete outcomes
Returns:
(float, float): (dCorr(P(X), P(Y|X)), dCorr(P(Y), P(X|Y)))
"""
assert len(X) == len(Y)
marg_X, cond_X, marg_Y, cond_Y = distributions(X, Y)
dXtoY = dcor(marg_X, cond_Y)[0]
dYtoX = dcor(marg_Y, cond_X)[0]
return (dXtoY, dYtoX)
def distributions(X, Y):
"""Computes empirical marginal and conditional distributions of X and Y.
Args:
X (nested sequence): nested sequence of discrete outcomes
Y (nested sequence): nested sequence of discrete outcomes
Returns:
(sequence, sequence, sequence, sequence): (P(X), P(X|Y), P(Y), P(Y|X)).
If X has L unique values, and Y has M unique values. The dimension are
as follows: P(X)=Lx1, P(Y|X)=LxM, P(Y)=Mx1, and P(X|Y)=MxL.
"""
N = len(X)
unq_X = set(map(tuple, X))
unq_Y = set(map(tuple, Y))
idx = range(N)
idx_X = dict(zip(unq_X, idx))
idx_Y = dict(zip(unq_Y, idx))
freq_XY = np.zeros((len(unq_X), len(unq_Y)))
for i in range(N):
ix = idx_X[tuple(X[i])]
iy = idx_Y[tuple(Y[i])]
freq_XY[ix, iy] += 1
freq_X = np.sum(freq_XY, axis=1)[np.newaxis]
freq_Y = np.sum(freq_XY, axis=0)[np.newaxis]
marg_X = (freq_X / np.sum(freq_X)).transpose()
marg_Y = (freq_Y / np.sum(freq_Y)).transpose()
freqs_X = np.tile(freq_X.transpose(), (1, len(unq_Y)))
freqs_Y = np.tile(freq_Y, (len(unq_X), 1))
cond_X = (freq_XY / freqs_X).transpose()
cond_Y = (freq_XY / freqs_Y)
return marg_X, cond_X, marg_Y, cond_Y
if __name__ == "__main__":
X = [[2, 3], [2, 3], [2, 4], [2], [2], [3], [3], [3, 4], [2, 3], [2]]
Y = [[1], [1], [1], [1], [1], [0], [0], [0], [0], [0]]
print(dc(X, Y))
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