用python 实现条件互信息计算

上面的回答中已经给出了Python实现条件互信息的代码，但是这里再给一个更详细的代码：

import numpy as np
from scipy import special, stats

def conditional_mutual_information(x, y, z):
    # Compute mutual information between x and y
    mi_xy = mutual_information(x, y)

    # Compute mutual information between x and y conditioned on z
    mi_xyz = mutual_information(np.column_stack((x, z)), np.column_stack((y, z)))
    mi_xz = mutual_information(z, x)
    mi_yz = mutual_information(z, y)

    # Compute conditional mutual information
    cmi = mi_xy - mi_xz - mi_yz + mi_xyz

    return cmi

def mutual_information(x, y):
    # Compute joint probability distribution
    p_xy, _, _ = np.histogram2d(x, y)

    # Compute marginal probability distributions
    p_x = p_xy.sum(axis=1)
    p_y = p_xy.sum(axis=0)

    # Compute entropy of marginal probability distributions
    h_x = entropy(p_x)
    h_y = entropy(p_y)

    # Compute entropy of joint probability distribution
    h_xy = entropy(p_xy.reshape(-1))

    # Compute mutual information
    mi = h_x + h_y - h_xy

    return mi

def entropy(p):
    # Compute entropy of probability distribution
    p = p[np.nonzero(p)]
    return -np.sum(p * np.log2(p))

# Example usage
x = np.random.normal(0, 1, size=1000)
y = x ** 2 + np.random.normal(0, 0.5, size=1000)
z = np.random.binomial(1, 0.5, size=1000)

cmi = conditional_mutual_information(x, y, z)
print("CMI between x and y conditioned on z:", cmi)

此代码实现了条件互信息和互信息的计算。其中，`conditional_mutual_information`函数计算条件互信息，`mutual_information`函数计算互信息，`entropy`函数计算熵。使用示例数据进行测试，输出CMI的值。