def GaussianKLD(mu1, lv1, mu2, lv2):
''' Kullback-Leibler divergence of two Gaussians
*Assuming that each dimension is independent
mu: mean
lv: log variance
Equation: http://stats.stackexchange.com/questions/7440/kl-divergence-between-two-univariate-gaussians
'''
with tf.name_scope('GaussianKLD'):
v1 = tf.exp(lv1)
v2 = tf.exp(lv2)
mu_diff_sq = tf.square(mu1 - mu2)
dimwise_kld = .5 * (
(lv2 - lv1) + tf.div(v1 + mu_diff_sq, v2 + EPSILON) - 1.)
return tf.reduce_sum(dimwise_kld, -1)
# Verification by CMU's implementation
# http://www.cs.cmu.edu/~chanwook/MySoftware/rm1_Spk-by-Spk_MLLR/rm1_PNCC_MLLR_1/rm1/python/sphinx/divergence.py
# def gau_kl(pm, pv, qm, qv):
# """
# Kullback-Liebler divergence from Gaussian pm,pv to Gaussian qm,qv.
# Also computes KL divergence from a single Gaussian pm,pv to a set
# of Gaussians qm,qv.
# Diagonal covariances are assumed. Divergence is expressed in nats.
# """
# if (len(qm.shape) == 2):
# axis = 1
# else:
# axis = 0
# # Determinants of diagonal covariances pv, qv
# dpv = pv.prod()
# dqv = qv.prod(axis)
# # Inverse of diagonal covariance qv
# iqv = 1./qv
# # Difference between means pm, qm
# diff = qm - pm
# return (0.5 *
# (np.log(dqv / dpv) # log |\Sigma_q| / |\Sigma_p|
# + (iqv * pv).sum(axis) # + tr(\Sigma_q^{-1} * \Sigma_p)
# + (diff * iqv * diff).sum(axis) # + (\mu_q-\mu_p)^T\Sigma_q^{-1}(\mu_q-\mu_p)
# - len(pm))) # - N
评论列表
文章目录
