Cauchy-Schwarz divergence

cs_divergence.py

from math import sqrt
from math import log

from scipy.stats import gaussian_kde

def cs_divergence(p1, p2):
    """
    Calculates the Cauchy-Schwarz divergence between two probabilities distribution. CS divergence is symmetrical,
    hence the order of the arguments does not matter. The result is from interval [0, infinity], 
    where 0 is obtained when the two probabilities distributions are same.

    Args:
        p1 (numpy array): first pdfs
        p2 (numpy array): second pdfs
    Returns:
        float: CS divergence
    """
    r = range(0, p1.shape[0])
    p1_kernel = gaussian_kde(p1)
    p2_kernel = gaussian_kde(p2)
    p1_computed = p1_kernel(r)
    p2_computed = p2_kernel(r)
    numerator = sum(p1_computed * p2_computed)
    denominator = sqrt(sum(p1_computed ** 2) * sum(p2_computed**2))
    return -log(numerator/denominator)