It doesnt appear to be a regular log norm pdf as seen in https://en.wikipedia.org/wiki/Log-normal_distribution
https://www.tensorflow.org/tutorials/generative/cvae
def log_normal_pdf(sample, mean, logvar, raxis=1):
log2pi = tf.math.log(2. * np.pi)
return tf.reduce_sum(
-.5 * ((sample - mean) ** 2. * tf.exp(-logvar) + logvar + log2pi),
axis=raxis)
This is the logarithm of the probability according to a normal distribution. I.e. log(p(x)) where p is a normal/Gaussian distribution. The naming is a little confusing though.
In case anyone else wanders down this rabbit hole, the previous answer checks out: "the logarithm of the pdf according to a normal distribution". Here's a simple check that you can run based on the gaussian function definition from wiki:
import numpy as np
def log_normal_pdf(sample, mean, std):
"""Function from tensorflow VAE example"""
logvar = np.log(std**2)
log2pi = np.log(2*np.pi)
return -.5 * ((sample - mean) ** 2. * np.exp(-logvar) + logvar + log2pi)
def test(sample, mean, std):
"""Alternate calc taking the log of the wiki gaussian function"""
out = (1 / (std * np.sqrt(2*np.pi))) * np.exp(-0.5 * (sample-mean)**2 / std**2)
return np.log(out)
print(log_normal_pdf(9, 10, 1))
print(test(9, 10, 1))