def test_all_finite_raises(self):
with self.test_session():
x = np.inf * tf.constant([-1.0, -2.0, -3.0, -4.0])
with self.assertRaisesOpError('Inf'):
log_sum_exp(x).eval()
x = tf.constant([-1.0, np.nan, -3.0, -4.0])
with self.assertRaisesOpError('NaN'):
log_sum_exp(x).eval()
def test_log_sum_exp_2d(self):
with self.test_session():
x = tf.constant([[-1.0], [-2.0], [-3.0], [-4.0]])
self.assertAllClose(log_sum_exp(x).eval(), -0.5598103014388045)
x = tf.constant([[-1.0, -2.0], [-3.0, -4.0]])
self.assertAllClose(log_sum_exp(x).eval(), -0.5598103014388045)
self.assertAllClose(
log_sum_exp(x, 0).eval(),
np.array([-0.87307198895702742, -1.8730719889570275]))
self.assertAllClose(
log_sum_exp(x, 1).eval(),
np.array([-0.68673831248177708, -2.6867383124817774]))
def test_log_sum_exp_2d(self):
with self.test_session():
x = tf.constant([[-1.0], [-2.0], [-3.0], [-4.0]])
self.assertAllClose(log_sum_exp(x).eval(),
-0.5598103014388045)
x = tf.constant([[-1.0, -2.0], [-3.0, -4.0]])
self.assertAllClose(log_sum_exp(x).eval(),
-0.5598103014388045)
self.assertAllClose(log_sum_exp(x, 0).eval(),
np.array([-0.87307198895702742,
-1.8730719889570275]))
self.assertAllClose(log_sum_exp(x, 1).eval(),
np.array([-0.68673831248177708,
-2.6867383124817774]))
def build_loss(self):
"""
Loss function to minimize, whose gradient is a stochastic
gradient inspired by adaptive importance sampling.
"""
# loss = E_{q(z; lambda)} [ w_norm(z; lambda) *
# ( log p(x, z) - log q(z; lambda) ) ]
# where
# w_norm(z; lambda) = w(z; lambda) / sum_z( w(z; lambda) )
# w(z; lambda) = p(x, z) / q(z; lambda)
#
# gradient = - E_{q(z; lambda)} [ w_norm(z; lambda) *
# grad_{lambda} log q(z; lambda) ]
x = self.data.sample(self.n_data)
z, self.samples = self.variational.sample(x, self.n_minibatch)
q_log_prob = tf.zeros([self.n_minibatch], dtype=tf.float32)
for i in range(self.variational.num_factors):
q_log_prob += self.variational.log_prob_zi(i, z)
# 1/B sum_{b=1}^B grad_log_q * w_norm
# = 1/B sum_{b=1}^B grad_log_q * exp{ log(w_norm) }
log_w = self.model.log_prob(x, z) - q_log_prob
# normalized log importance weights
log_w_norm = log_w - log_sum_exp(log_w)
w_norm = tf.exp(log_w_norm)
self.loss = tf.reduce_mean(w_norm * log_w)
return -tf.reduce_mean(q_log_prob * tf.stop_gradient(w_norm))
def log_prob(self, xs, zs):
"""Returns a vector [log p(xs, zs[1,:]), ..., log p(xs, zs[S,:])]."""
x = xs['x']
pi, mus, sigmas = self.unpack_params(zs)
log_prior = dirichlet.logpdf(pi, self.alpha)
log_prior += tf.reduce_sum(norm.logpdf(mus, 0, np.sqrt(self.c)))
log_prior += tf.reduce_sum(invgamma.logpdf(sigmas, self.a, self.b))
# Loop over each sample zs[s, :].
log_lik = []
N = get_dims(x)[0]
n_samples = get_dims(pi)[0]
for s in range(n_samples):
# log-likelihood is
# sum_{n=1}^N log sum_{k=1}^K exp( log pi_k + log N(x_n; mu_k, sigma_k) )
# Create a K x N matrix, whose entry (k, n) is
# log pi_k + log N(x_n; mu_k, sigma_k).
matrix = []
for k in range(self.K):
matrix += [
tf.ones(N) * tf.log(pi[s, k]) + multivariate_normal.logpdf(
x, mus[s, (k * self.D):((k + 1) * self.D)],
sigmas[s, (k * self.D):((k + 1) * self.D)])
]
matrix = tf.pack(matrix)
# log_sum_exp() along the rows is a vector, whose nth
# element is the log-likelihood of data point x_n.
vector = log_sum_exp(matrix, 0)
# Sum over data points to get the full log-likelihood.
log_lik_z = tf.reduce_sum(vector)
log_lik += [log_lik_z]
return log_prior + tf.pack(log_lik)
def log_prob(self, xs, zs):
"""Return a vector [log p(xs, zs[1,:]), ..., log p(xs, zs[S,:])]."""
x = xs['x']
pi, mus, sigmas = zs
log_prior = dirichlet.logpdf(pi, self.alpha)
log_prior += tf.reduce_sum(norm.logpdf(mus, 0, np.sqrt(self.c)), 1)
log_prior += tf.reduce_sum(invgamma.logpdf(sigmas, self.a, self.b), 1)
# Loop over each sample zs[s, :].
log_lik = []
N = get_dims(x)[0]
n_samples = get_dims(pi)[0]
for s in range(n_samples):
# log-likelihood is
# sum_{n=1}^N log sum_{k=1}^K exp( log pi_k + log N(x_n; mu_k, sigma_k) )
# Create a K x N matrix, whose entry (k, n) is
# log pi_k + log N(x_n; mu_k, sigma_k).
matrix = []
for k in range(self.K):
matrix += [tf.ones(N)*tf.log(pi[s, k]) +
multivariate_normal.logpdf(x,
mus[s, (k*self.D):((k+1)*self.D)],
sigmas[s, (k*self.D):((k+1)*self.D)])]
matrix = tf.pack(matrix)
# log_sum_exp() along the rows is a vector, whose nth
# element is the log-likelihood of data point x_n.
vector = log_sum_exp(matrix, 0)
# Sum over data points to get the full log-likelihood.
log_lik_z = tf.reduce_sum(vector)
log_lik += [log_lik_z]
return log_prior + tf.pack(log_lik)
def log_prob(self, xs, zs):
"""Return scalar, the log joint density log p(xs, zs)."""
x = xs["x"]
pi, mus, sigmas = zs["pi"], zs["mu"], zs["sigma"]
log_prior = dirichlet.logpdf(pi, self.alpha)
log_prior += tf.reduce_sum(norm.logpdf(mus, 0.0, self.c))
log_prior += tf.reduce_sum(invgamma.logpdf(sigmas, self.a, self.b))
# log-likelihood is
# sum_{n=1}^N log sum_{k=1}^K exp( log pi_k + log N(x_n; mu_k, sigma_k) )
# Create a K x N matrix, whose entry (k, n) is
# log pi_k + log N(x_n; mu_k, sigma_k).
N = get_dims(x)[0]
matrix = []
for k in range(self.K):
matrix += [
tf.ones(N) * tf.log(pi[k])
+ multivariate_normal_diag.logpdf(
x, mus[(k * self.D) : ((k + 1) * self.D)], sigmas[(k * self.D) : ((k + 1) * self.D)]
)
]
matrix = tf.pack(matrix)
# log_sum_exp() along the rows is a vector, whose nth
# element is the log-likelihood of data point x_n.
vector = log_sum_exp(matrix, 0)
# Sum over data points to get the full log-likelihood.
log_lik = tf.reduce_sum(vector)
return log_prior + log_lik
def build_loss(self):
"""
Loss function to minimize, whose gradient is a stochastic
gradient inspired by adaptive importance sampling.
"""
# loss = E_{q(z; lambda)} [ w_norm(z; lambda) *
# ( log p(x, z) - log q(z; lambda) ) ]
# where
# w_norm(z; lambda) = w(z; lambda) / sum_z( w(z; lambda) )
# w(z; lambda) = p(x, z) / q(z; lambda)
#
# gradient = - E_{q(z; lambda)} [ w_norm(z; lambda) *
# grad_{lambda} log q(z; lambda) ]
x = self.data.sample(self.n_data)
self.variational.set_params(self.variational.mapping(x))
q_log_prob = tf.zeros([self.n_minibatch], dtype=tf.float32)
for i in range(self.variational.num_factors):
q_log_prob += self.variational.log_prob_zi(i, self.samples)
# 1/B sum_{b=1}^B grad_log_q * w_norm
# = 1/B sum_{b=1}^B grad_log_q * exp{ log(w_norm) }
log_w = self.model.log_prob(x, self.samples) - q_log_prob
# normalized log importance weights
log_w_norm = log_w - log_sum_exp(log_w)
w_norm = tf.exp(log_w_norm)
self.losses = w_norm * log_w
return -tf.reduce_mean(q_log_prob * tf.stop_gradient(w_norm))
def log_prob(self, xs, zs):
"""Return scalar, the log joint density log p(xs, zs)."""
x = xs['x']
pi, mus, sigmas = zs['pi'], zs['mu'], zs['sigma']
log_prior = dirichlet.logpdf(pi, self.alpha)
log_prior += tf.reduce_sum(norm.logpdf(mus, 0.0, self.c))
log_prior += tf.reduce_sum(invgamma.logpdf(sigmas, self.a, self.b))
# log-likelihood is
# sum_{n=1}^N log sum_{k=1}^K exp( log pi_k + log N(x_n; mu_k, sigma_k) )
# Create a K x N matrix, whose entry (k, n) is
# log pi_k + log N(x_n; mu_k, sigma_k).
N = get_dims(x)[0]
matrix = []
for k in range(self.K):
matrix += [tf.ones(N) * tf.log(pi[k]) +
multivariate_normal_diag.logpdf(x,
mus[(k * self.D):((k + 1) * self.D)],
sigmas[(k * self.D):((k + 1) * self.D)])]
matrix = tf.pack(matrix)
# log_sum_exp() along the rows is a vector, whose nth
# element is the log-likelihood of data point x_n.
vector = log_sum_exp(matrix, 0)
# Sum over data points to get the full log-likelihood.
log_lik = tf.reduce_sum(vector)
return log_prior + log_lik
def build_loss(self):
"""
Loss function to minimize, whose gradient is a stochastic
gradient inspired by adaptive importance sampling.
loss = E_{p(z | x)} [ log p(z | x) - log q(z; lambda) ]
is equivalent to minimizing
E_{p(z | x)} [ log p(x, z) - log q(z; lambda) ]
\approx 1/B sum_{b=1}^B
w_norm(z^b; lambda) (log p(x, z^b) - log q(z^b; lambda))
with gradient
\approx - 1/B sum_{b=1}^B
w_norm(z^b; lambda) grad_{lambda} log q(z^b; lambda)
where + z^b ~ q(z^b; lambda)
+ w_norm(z^b; lambda) = w(z^b; lambda) / sum_{b=1}^B w(z^b; lambda)
+ w(z^b; lambda) = p(x, z^b) / q(z^b; lambda)
"""
x = self.data.sample(self.n_data)
z, self.samples = self.variational.sample(self.n_minibatch)
q_log_prob = tf.zeros([self.n_minibatch], dtype=tf.float32)
for i in range(self.variational.num_factors):
q_log_prob += self.variational.log_prob_i(i, tf.stop_gradient(z))
# normalized importance weights
log_w = self.model.log_prob(x, z) - q_log_prob
log_w_norm = log_w - log_sum_exp(log_w)
w_norm = tf.exp(log_w_norm)
self.loss = tf.reduce_mean(w_norm * log_w)
return -tf.reduce_mean(q_log_prob * tf.stop_gradient(w_norm))
def test_accuracy(self):
sess = tf.InteractiveSession()
x = tf.constant([[-1.0], [-2.0], [-3.0], [-4.0]])
result = log_sum_exp(x)
hand_derived_result = -0.5598103014388045
self.assertAlmostEqual(result.eval(), hand_derived_result)
def test_accuracy(self):
sess = tf.InteractiveSession()
x = tf.constant([[-1.0], [-2.0], [-3.0], [-4.0]])
result = log_sum_exp(x)
hand_derived_result = -0.5598103014388045
self.assertAlmostEqual(result.eval(), hand_derived_result)
def log_prob(self, xs, zs):
"""
Return scalar, the log joint density log p(xs, zs).
Given n_minibatch data points, n_samples of variables
Summing over the datapoints makes sense since the joint is the only place in the
estiamtion of the gradient that has the data points, and its the log, so we can sum
over them
BUT summing over the variables doenst make sense,its supposed to be one at a time
"""
x = xs['x']
pi, mus, sigmas = zs['pi'], zs['mu'], zs['sigma']
# print(get_dims(x)) #[n_minibatch, D]
# print(get_dims(pi)) #[K]
# print(get_dims(mus)) #[K*D]
# print(get_dims(sigmas)) #[K*D]
log_prior = dirichlet.logpdf(pi, self.alpha)
log_prior += tf.reduce_sum(norm.logpdf(mus, 0.0, self.c))
log_prior += tf.reduce_sum(invgamma.logpdf(sigmas, self.a, self.b))
# log-likelihood is
# sum_{n=1}^N log sum_{k=1}^K exp( log pi_k + log N(x_n; mu_k, sigma_k) )
# Create a K x N matrix, whose entry (k, n) is
# log pi_k + log N(x_n; mu_k, sigma_k).
n_minibatch = get_dims(x)[
0] #this is [n_minibatch, D], with [0] its just n_minibatch
#OH I think they compute the matrix so that they can do log sum exp, since they need to find the max value
matrix = []
for k in range(self.K):
# bbbb = tf.log(pi[k])
# print(get_dims(bbbb))
# aaaa= multivariate_normal_diag.logpdf(x, mus[(k * self.D):((k + 1) * self.D)], sigmas[(k * self.D):((k + 1) * self.D)])
# print(get_dims(aaaa))
# fadad
matrix += [
tf.ones(n_minibatch) * tf.log(pi[k]) +
multivariate_normal_diag.logpdf(
x, mus[(k * self.D):((k + 1) * self.D)],
sigmas[(k * self.D):((k + 1) * self.D)])
]
matrix = tf.pack(matrix)
# log_sum_exp() along the rows is a vector, whose nth
# element is the log-likelihood of data point x_n.
vector = log_sum_exp(matrix, 0)
# Sum over data points to get the full log-likelihood.
log_lik = tf.reduce_sum(vector)
return log_prior + log_lik
def build_loss(self):
"""Loss function to minimize.
Defines a stochastic gradient of
.. math::
KL( p(z |x) || q(z) )
=
E_{p(z | x)} [ \log p(z | x) - \log q(z; \lambda) ]
based on importance sampling.
Computed as
.. math::
1/B \sum_{b=1}^B [ w_{norm}(z^b; \lambda) *
(\log p(x, z^b) - \log q(z^b; \lambda) ]
where
.. math::
z^b \sim q(z^b; \lambda)
w_{norm}(z^b; \lambda) = w(z^b; \lambda) / \sum_{b=1}^B ( w(z^b; \lambda) )
w(z^b; \lambda) = p(x, z^b) / q(z^b; \lambda)
which gives a gradient
.. math::
- 1/B \sum_{b=1}^B
w_{norm}(z^b; \lambda) \partial_{\lambda} \log q(z^b; \lambda)
"""
x = self.data.sample(self.n_data)
self.zs = self.variational.sample(self.n_minibatch)
z = self.zs
# normalized importance weights
q_log_prob = self.variational.log_prob(stop_gradient(z))
log_w = self.model.log_prob(x, z) - q_log_prob
log_w_norm = log_w - log_sum_exp(log_w)
w_norm = tf.exp(log_w_norm)
self.loss = tf.reduce_mean(w_norm * log_w)
return -tf.reduce_mean(q_log_prob * tf.stop_gradient(w_norm))
def build_loss(self):
"""Build loss function. Its automatic differentiation
is a stochastic gradient of
.. math::
KL( p(z |x) || q(z) )
=
E_{p(z | x)} [ \log p(z | x) - \log q(z; \lambda) ]
based on importance sampling.
Computed as
.. math::
1/B \sum_{b=1}^B [ w_{norm}(z^b; \lambda) *
(\log p(x, z^b) - \log q(z^b; \lambda) ]
where
.. math::
z^b \sim q(z^b; \lambda)
w_{norm}(z^b; \lambda) = w(z^b; \lambda) / \sum_{b=1}^B ( w(z^b; \lambda) )
w(z^b; \lambda) = p(x, z^b) / q(z^b; \lambda)
which gives a gradient
.. math::
- 1/B \sum_{b=1}^B
w_{norm}(z^b; \lambda) \partial_{\lambda} \log q(z^b; \lambda)
"""
x = self.data
z = self.variational.sample(self.n_samples)
# normalized importance weights
q_log_prob = self.variational.log_prob(stop_gradient(z))
log_w = self.model.log_prob(x, z) - q_log_prob
log_w_norm = log_w - log_sum_exp(log_w)
w_norm = tf.exp(log_w_norm)
self.loss = tf.reduce_mean(w_norm * log_w)
return -tf.reduce_mean(q_log_prob * stop_gradient(w_norm))
def build_loss_and_gradients(self, var_list):
"""Build loss function
.. math::
KL( p(z |x) || q(z) )
=
E_{p(z | x)} [ \log p(z | x) - \log q(z; \lambda) ]
and stochastic gradients based on importance sampling.
The loss function can be estimated as
.. math::
1/B \sum_{b=1}^B [ w_{norm}(z^b; \lambda) *
(\log p(x, z^b) - \log q(z^b; \lambda) ],
where
.. math::
z^b \sim q(z^b; \lambda),
w_{norm}(z^b; \lambda) = w(z^b; \lambda) / \sum_{b=1}^B (w(z^b; \lambda)),
w(z^b; \lambda) = p(x, z^b) / q(z^b; \lambda).
This provides a gradient,
.. math::
- 1/B \sum_{b=1}^B [ w_{norm}(z^b; \lambda) *
\partial_{\lambda} \log q(z^b; \lambda) ].
"""
p_log_prob = [0.0] * self.n_samples
q_log_prob = [0.0] * self.n_samples
for s in range(self.n_samples):
z_sample = {}
for z, qz in six.iteritems(self.latent_vars):
# Copy q(z) to obtain new set of posterior samples.
qz_copy = copy(qz, scope='inference_' + str(s))
z_sample[z] = qz_copy.value()
q_log_prob[s] += tf.reduce_sum(
qz.log_prob(tf.stop_gradient(z_sample[z])))
if self.model_wrapper is None:
# Form dictionary in order to replace conditioning on prior or
# observed variable with conditioning on a specific value.
dict_swap = z_sample
for x, qx in six.iteritems(self.data):
if isinstance(x, RandomVariable):
if isinstance(qx, RandomVariable):
qx_copy = copy(qx, scope='inference_' + str(s))
dict_swap[x] = qx_copy.value()
else:
dict_swap[x] = qx
for z in six.iterkeys(self.latent_vars):
z_copy = copy(z, dict_swap, scope='inference_' + str(s))
p_log_prob[s] += tf.reduce_sum(
z_copy.log_prob(dict_swap[z]))
for x in six.iterkeys(self.data):
if isinstance(x, RandomVariable):
x_copy = copy(x,
dict_swap,
scope='inference_' + str(s))
p_log_prob[s] += tf.reduce_sum(
x_copy.log_prob(dict_swap[x]))
else:
x = self.data
p_log_prob[s] = self.model_wrapper.log_prob(x, z_sample)
p_log_prob = tf.pack(p_log_prob)
q_log_prob = tf.pack(q_log_prob)
log_w = p_log_prob - q_log_prob
log_w_norm = log_w - log_sum_exp(log_w)
w_norm = tf.exp(log_w_norm)
loss = tf.reduce_mean(w_norm * log_w)
grads = tf.gradients(
-tf.reduce_mean(q_log_prob * tf.stop_gradient(w_norm)),
[v.ref() for v in var_list])
grads_and_vars = list(zip(grads, var_list))
return loss, grads_and_vars
def build_loss_and_gradients(self, var_list):
"""Build loss function
.. math::
\\text{KL}( p(z \mid x) || q(z) )
= \mathbb{E}_{p(z \mid x)} [ \log p(z \mid x) - \log q(z; \lambda) ]
and stochastic gradients based on importance sampling.
The loss function can be estimated as
.. math::
\\frac{1}{B} \sum_{b=1}^B [
w_{norm}(z^b; \lambda) (\log p(x, z^b) - \log q(z^b; \lambda) ],
where for :math:`z^b \sim q(z^b; \lambda)`,
.. math::
w_{norm}(z^b; \lambda) = w(z^b; \lambda) / \sum_{b=1}^B w(z^b; \lambda)
normalizes the importance weights, :math:`w(z^b; \lambda) = p(x,
z^b) / q(z^b; \lambda)`.
This provides a gradient,
.. math::
- \\frac{1}{B} \sum_{b=1}^B [
w_{norm}(z^b; \lambda) \\nabla_{\lambda} \log q(z^b; \lambda) ].
"""
p_log_prob = [0.0] * self.n_samples
q_log_prob = [0.0] * self.n_samples
for s in range(self.n_samples):
scope = 'inference_' + str(id(self)) + '/' + str(s)
z_sample = {}
for z, qz in six.iteritems(self.latent_vars):
# Copy q(z) to obtain new set of posterior samples.
qz_copy = copy(qz, scope=scope)
z_sample[z] = qz_copy.value()
q_log_prob[s] += tf.reduce_sum(
qz.log_prob(tf.stop_gradient(z_sample[z])))
if self.model_wrapper is None:
# Form dictionary in order to replace conditioning on prior or
# observed variable with conditioning on a specific value.
dict_swap = z_sample
for x, qx in six.iteritems(self.data):
if isinstance(x, RandomVariable):
if isinstance(qx, RandomVariable):
qx_copy = copy(qx, scope=scope)
dict_swap[x] = qx_copy.value()
else:
dict_swap[x] = qx
for z in six.iterkeys(self.latent_vars):
z_copy = copy(z, dict_swap, scope=scope)
p_log_prob[s] += tf.reduce_sum(z_copy.log_prob(dict_swap[z]))
for x in six.iterkeys(self.data):
if isinstance(x, RandomVariable):
x_copy = copy(x, dict_swap, scope=scope)
p_log_prob[s] += tf.reduce_sum(x_copy.log_prob(dict_swap[x]))
else:
x = self.data
p_log_prob[s] = self.model_wrapper.log_prob(x, z_sample)
p_log_prob = tf.pack(p_log_prob)
q_log_prob = tf.pack(q_log_prob)
log_w = p_log_prob - q_log_prob
log_w_norm = log_w - log_sum_exp(log_w)
w_norm = tf.exp(log_w_norm)
if var_list is None:
var_list = tf.trainable_variables()
loss = tf.reduce_mean(w_norm * log_w)
grads = tf.gradients(
-tf.reduce_mean(q_log_prob * tf.stop_gradient(w_norm)),
[v.ref() for v in var_list])
grads_and_vars = list(zip(grads, var_list))
return loss, grads_and_vars
def test_log_sum_exp_2d(self):
with self.test_session():
x = tf.constant([[-1.0], [-2.0], [-3.0], [-4.0]])
self.assertAllClose(log_sum_exp(x).eval(),
-0.5598103014388045)
def build_loss(self):
"""Build loss function. Its automatic differentiation
is a stochastic gradient of
.. math::
KL( p(z |x) || q(z) )
=
E_{p(z | x)} [ \log p(z | x) - \log q(z; \lambda) ]
based on importance sampling.
Computed as
.. math::
1/B \sum_{b=1}^B [ w_{norm}(z^b; \lambda) *
(\log p(x, z^b) - \log q(z^b; \lambda) ]
where
.. math::
z^b \sim q(z^b; \lambda)
w_{norm}(z^b; \lambda) = w(z^b; \lambda) / \sum_{b=1}^B (w(z^b; \lambda))
w(z^b; \lambda) = p(x, z^b) / q(z^b; \lambda)
which gives a gradient
.. math::
- 1/B \sum_{b=1}^B
w_{norm}(z^b; \lambda) \partial_{\lambda} \log q(z^b; \lambda)
"""
p_log_prob = [0.0] * self.n_samples
q_log_prob = [0.0] * self.n_samples
for s in range(self.n_samples):
z_sample = {}
for z, qz in six.iteritems(self.latent_vars):
# Copy q(z) to obtain new set of posterior samples.
qz_copy = copy(qz, scope='inference_' + str(s))
z_sample[z] = qz_copy.value()
q_log_prob[s] += tf.reduce_sum(
qz.log_prob(tf.stop_gradient(z_sample[z])))
if self.model_wrapper is None:
for z in six.iterkeys(self.latent_vars):
# Copy p(z), replacing any conditioning on prior with
# conditioning on posterior sample.
z_copy = copy(z,
dict_swap=z_sample,
scope='inference_' + str(s))
p_log_prob[s] += tf.reduce_sum(z_copy.log_prob(
z_sample[z]))
for x, obs in six.iteritems(self.data):
if isinstance(x, RandomVariable):
# Copy p(x | z), replacing any conditioning on prior with
# conditioning on posterior sample.
x_copy = copy(x,
dict_swap=z_sample,
scope='inference_' + str(s))
p_log_prob[s] += tf.reduce_sum(x_copy.log_prob(obs))
else:
x = self.data
p_log_prob[s] = self.model_wrapper.log_prob(x, z_sample)
p_log_prob = tf.pack(p_log_prob)
q_log_prob = tf.pack(q_log_prob)
log_w = p_log_prob - q_log_prob
log_w_norm = log_w - log_sum_exp(log_w)
w_norm = tf.exp(log_w_norm)
self.loss = tf.reduce_mean(w_norm * log_w)
return -tf.reduce_mean(q_log_prob * tf.stop_gradient(w_norm))
def test_2d():
x = tf.constant([[-1.0], [-2.0], [-3.0], [-4.0]])
val_ed = log_sum_exp(x)
val_true = -0.5598103014388045
assert np.allclose(val_ed.eval(), val_true)