Revision

**b08f3062c96677de266af26767634fd7c6e6611d**authored by Alexander G. de G. Matthews on**09 September 2016, 10:59:46 UTC**, committed by James Hensman on**09 September 2016, 10:59:46 UTC*** Renaming tf_hacks to tf_wraps * Changing tf_hacks to tf_wraps in code. * adding a tf_hacks file that raises deprecationwarnings * release notes * bumpng version on docs * importing tf_hacks, tf_wraps

**1 parent**61b0659

kullback_leiblers.py

```
# Copyright 2016 James Hensman, alexggmatthews
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
import tensorflow as tf
from .tf_wraps import eye
from .scoping import NameScoped
@NameScoped("KL")
def gauss_kl_white(q_mu, q_sqrt):
"""
Compute the KL divergence from
q(x) = N(q_mu, q_sqrt^2)
to
p(x) = N(0, I)
We assume multiple independent distributions, given by the columns of
q_mu and the last dimension of q_sqrt.
q_mu is a matrix, each column contains a mean
q_sqrt is a 3D tensor, each matrix within is a lower triangular square-root
matrix of the covariance.
"""
KL = 0.5 * tf.reduce_sum(tf.square(q_mu)) # Mahalanobis term
KL += -0.5 * tf.cast(tf.reduce_prod(tf.shape(q_sqrt)[1:]), tf.float64) # constant term
L = tf.batch_matrix_band_part(tf.transpose(q_sqrt, (2, 0, 1)), -1, 0) # force lower triangle
KL -= 0.5 * tf.reduce_sum(tf.log(tf.square(tf.batch_matrix_diag_part(L)))) # logdet
KL += 0.5 * tf.reduce_sum(tf.square(L)) # Trace term.
return KL
@NameScoped("KL")
def gauss_kl_white_diag(q_mu, q_sqrt):
"""
Compute the KL divergence from
q(x) = N(q_mu, q_sqrt^2)
to
p(x) = N(0, I)
We assume multiple independent distributions, given by the columns of
q_mu and q_sqrt
q_mu is a matrix, each column contains a mean
q_sqrt is a matrix, each column represents the diagonal of a square-root
matrix of the covariance.
"""
KL = 0.5 * tf.reduce_sum(tf.square(q_mu)) # Mahalanobis term
KL += -0.5 * tf.cast(tf.size(q_sqrt), tf.float64)
KL += -0.5 * tf.reduce_sum(tf.log(tf.square(q_sqrt))) # Log-det of q-cov
KL += 0.5 * tf.reduce_sum(tf.square(q_sqrt)) # Trace term
return KL
@NameScoped("KL")
def gauss_kl_diag(q_mu, q_sqrt, K):
"""
Compute the KL divergence from
q(x) = N(q_mu, q_sqrt^2)
to
p(x) = N(0, K)
We assume multiple independent distributions, given by the columns of
q_mu and q_sqrt.
q_mu is a matrix, each column contains a mean
q_sqrt is a matrix, each column represents the diagonal of a square-root
matrix of the covariance of q.
K is a positive definite matrix: the covariance of p.
"""
L = tf.cholesky(K)
alpha = tf.matrix_triangular_solve(L, q_mu, lower=True)
KL = 0.5 * tf.reduce_sum(tf.square(alpha)) # Mahalanobis term.
num_latent = tf.cast(tf.shape(q_sqrt)[1], tf.float64)
KL += num_latent * 0.5 * tf.reduce_sum(
tf.log(tf.square(tf.diag_part(L)))) # Prior log-det term.
KL += -0.5 * tf.cast(tf.size(q_sqrt), tf.float64) # constant term
KL += -0.5 * tf.reduce_sum(tf.log(tf.square(q_sqrt))) # Log-det of q-cov
L_inv = tf.matrix_triangular_solve(L, eye(tf.shape(L)[0]), lower=True)
K_inv = tf.matrix_triangular_solve(tf.transpose(L), L_inv, lower=False)
KL += 0.5 * tf.reduce_sum(tf.expand_dims(tf.diag_part(K_inv), 1)
* tf.square(q_sqrt)) # Trace term.
return KL
@NameScoped("KL")
def gauss_kl(q_mu, q_sqrt, K):
"""
Compute the KL divergence from
q(x) = N(q_mu, q_sqrt^2)
to
p(x) = N(0, K)
We assume multiple independent distributions, given by the columns of
q_mu and the last dimension of q_sqrt.
q_mu is a matrix, each column contains a mean.
q_sqrt is a 3D tensor, each matrix within is a lower triangular square-root
matrix of the covariance of q.
K is a positive definite matrix: the covariance of p.
"""
L = tf.cholesky(K)
alpha = tf.matrix_triangular_solve(L, q_mu, lower=True)
KL = 0.5 * tf.reduce_sum(tf.square(alpha)) # Mahalanobis term.
num_latent = tf.cast(tf.shape(q_sqrt)[2], tf.float64)
KL += num_latent * 0.5 * tf.reduce_sum(tf.log(tf.square(tf.diag_part(L)))) # Prior log-det term.
KL += -0.5 * tf.cast(tf.reduce_prod(tf.shape(q_sqrt)[1:]), tf.float64) # constant term
Lq = tf.batch_matrix_band_part(tf.transpose(q_sqrt, (2, 0, 1)), -1, 0) # force lower triangle
KL += -0.5*tf.reduce_sum(tf.log(tf.square(tf.batch_matrix_diag_part(Lq)))) # logdet
L_tiled = tf.tile(tf.expand_dims(L, 0), tf.pack([tf.shape(Lq)[0], 1, 1]))
LiLq = tf.batch_matrix_triangular_solve(L_tiled, Lq, lower=True)
KL += 0.5 * tf.reduce_sum(tf.square(LiLq)) # Trace term
return KL
```

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