Add joint probability distribution calculations

joint_probability_distribution.py

@@ -0,0 +1,107 @@
+import numpy as np
+from scipy.stats.contingency import margins
+
+
+def entropy(array):
+    """
+    Calculates the entropy of a discrete random variable
+    :param array: probabilities of the discrete random variable
+    :return: Entropy of the discrete random variable described by array
+    """
+    return -1 * np.sum(array * np.log2(array))
+
+
+def relative_entropy(p, q):
+    """
+    Calculates the Kullback-Leibler distance between two discrete random variables p, q D(p||q)
+    :param p: discrete random variable
+    :param q: discrete random variable
+    :return: Kullback-Leibler distance D(p||q)
+    """
+    logarithms = np.log2(p / q, out=np.zeros_like(p), where=(p != 0))
+    return np.sum(np.multiply(p, logarithms))
+
+
+class JointProbabilityDistribution:
+    def __init__(self, matrix):
+        self.matrix = matrix
+
+    @property
+    def all(self):
+        marginal_distributions = self.marginal_distributions
+        conditional_entropy = self.conditional_entropy
+        return {
+            'marginal distribution x': marginal_distributions[0],
+            'marginal distribution y': marginal_distributions[1],
+            'joined entropy': self.joined_entropy,
+            'marginal entropy x': entropy(marginal_distributions[0]),
+            'marginal entropy y': entropy(marginal_distributions[1]),
+            'conditional entropy x|y': conditional_entropy[0],
+            'conditional entropy y|x': conditional_entropy[1],
+            'relative entropy x||y': self.relative_entropy('x'),
+            'relative entropy y||x': self.relative_entropy('y'),
+            'joined distribution': self.matrix
+        }
+
+    @property
+    def marginal_distributions(self):
+        x, y = margins(self.matrix)
+        return x.T.flatten(), y.flatten()
+
+    @property
+    def joined_entropy(self):
+        logarithms = np.log2(self.matrix, out=np.zeros_like(self.matrix), where=(self.matrix != 0))
+        products = np.multiply(self.matrix, logarithms)
+        return -1 * np.sum(products)
+
+    @property
+    def conditional_entropy(self):
+        return self.__conditional_entropy(axis=0), self.__conditional_entropy(axis=1)
+
+    def relative_entropy(self, first='x'):
+        marginal_distributions = self.marginal_distributions
+
+        if first == 'x':
+            p, q = marginal_distributions
+        elif first == 'y':
+            q, p = marginal_distributions
+        else:
+            raise ValueError('Permitted values: {x,y}')
+        return relative_entropy(p, q)
+
+    @property
+    def mutual_information(self):
+        x, y = self.marginal_distributions
+        p = self.matrix
+        q = np.multiply(x, y)
+        return relative_entropy(p, q)
+
+    def __conditional_entropy(self, axis=0):
+        axis_a, axis_b = (0, 1) if axis == 0 else (1, 0)
+
+        p_b = self.marginal_distributions[axis_a]
+
+        result = 0
+
+        for i in range(self.matrix.shape[axis_a]):
+            for j in range(self.matrix.shape[axis_b]):
+                if self.matrix[i, j] == 0:
+                    continue
+                p_xy = self.matrix[i, j]
+                p_a_given_b = p_xy / p_b[j]
+                result += p_xy * np.log2(p_a_given_b)
+
+        return -1 * result
+
+
+if __name__ == '__main__':
+    matrix = np.matrix([
+        [1 / 8, 1 / 16, 1 / 32, 1 / 32],
+        [1 / 16, 1 / 8, 1 / 32, 1 / 32],
+        [1 / 16, 1 / 16, 1 / 16, 1 / 16],
+        [1 / 4, 0, 0, 0],
+    ])
+    jointProbabilityDistribution = JointProbabilityDistribution(matrix)
+
+    for key, value in jointProbabilityDistribution.all.items():
+        print(f'{key}: {value}')