def norm_posterior(dim, std0):
"""Initialise a posterior (diagonal) Normal distribution.
Parameters
----------
dim : tuple or list
the dimension of this distribution.
std0 : float
the initial (unoptimized) standard deviation of this distribution.
Returns
-------
Q : tf.distributions.Normal
the initialised posterior Normal object.
Note
----
This will make tf.Variables on the randomly initialised mean and standard
deviation of the posterior. The initialisation of the mean is from a Normal
with zero mean, and ``std0`` standard deviation, and the initialisation of
the standard deviation is from a gamma distribution with an alpha of
``std0`` and a beta of 1.
"""
mu_0 = tf.random_normal(dim, stddev=std0, seed=next(seedgen))
mu = tf.Variable(mu_0, name="W_mu_q")
std_0 = tf.random_gamma(alpha=std0, shape=dim, seed=next(seedgen))
std = pos(tf.Variable(std_0, name="W_std_q"))
Q = tf.distributions.Normal(loc=mu, scale=std)
return Q
def norm_prior(dim, std):
"""Initialise a prior (zero mean, isotropic) Normal distribution.
Parameters
----------
dim : tuple or list
the dimension of this distribution.
std : float
the prior standard deviation of this distribution.
Returns
-------
P : tf.distributions.Normal
the initialised prior Normal object.
Note
----
This will make a tf.Variable on the variance of the prior that is
initialised with ``std``.
"""
mu = tf.zeros(dim)
std = pos(tf.Variable(std, name="W_mu_p"))
P = tf.distributions.Normal(loc=mu, scale=std)
return P
def _initialise_variables(self, X):
"""Initialise the impute variables."""
datadim = int(X.shape[2])
impute_means = tf.Variable(tf.random_normal(shape=(1, datadim),
seed=next(seedgen)),
name="impute_scalars")
impute_stddev = tf.Variable(tf.random_gamma(alpha=1.,
shape=(1, datadim),
seed=next(seedgen)),
name="impute_scalars")
self.normal = tf.distributions.Normal(impute_means,
tf.sqrt(pos(impute_stddev)))
def _chollogdet(L):
"""Log det of a cholesky, where L is (..., D, D)."""
l = pos(tf.matrix_diag_part(L)) # keep > 0, and no vanashing gradient
logdet = 2. * tf.reduce_sum(tf.log(l))
return logdet