def __init__(self, layers=None):
get_session()
if layers is None:
self.layers = []
self.shape = []
self.n_vars = 0
self.n_params = 0
self.is_differentiable = True
self.is_multivariate = []
self.is_reparameterized = True
self.is_normal = True
self.is_entropy = True
else:
self.layers = layers
self.shape = [layer.shape for layer in self.layers]
self.n_vars = sum([layer.n_vars for layer in self.layers])
self.n_params = sum([layer.n_params for layer in self.layers])
self.is_differentiable = all([layer.is_differentiable
for layer in self.layers])
self.is_multivariate = [layer.is_multivariate for layer in self.layers]
self.is_reparameterized = all([layer.is_reparameterized
for layer in self.layers])
self.is_normal = all([isinstance(layer, Normal)
for layer in self.layers])
self.is_entropy = all(['entropy' in layer.__class__.__dict__
for layer in self.layers])
def __init__(self, layers=[]):
get_session()
self.layers = layers
if layers == []:
self.num_factors = 0
self.num_vars = 0
self.num_params = 0
self.is_reparam = True
self.is_normal = True
self.is_entropy = True
self.sample_tensor = []
else:
self.num_factors = sum(
[layer.num_factors for layer in self.layers])
self.num_vars = sum([layer.num_vars for layer in self.layers])
self.num_params = sum([layer.num_params for layer in self.layers])
self.is_reparam = all([
'reparam' in layer.__class__.__dict__ for layer in self.layers
])
self.is_normal = all(
[isinstance(layer, Normal) for layer in self.layers])
self.is_entropy = all([
'entropy' in layer.__class__.__dict__ for layer in self.layers
])
self.sample_tensor = [layer.sample_tensor for layer in self.layers]
def __init__(self, layers=None):
get_session()
if layers is None:
self.layers = []
self.shape = []
self.num_vars = 0
self.num_params = 0
self.is_reparam = True
self.is_normal = True
self.is_entropy = True
self.sample_tensor = []
self.is_multivariate = []
else:
self.layers = layers
self.shape = [layer.shape for layer in self.layers]
self.num_vars = sum([layer.num_vars for layer in self.layers])
self.num_params = sum([layer.num_params for layer in self.layers])
self.is_reparam = all(['reparam' in layer.__class__.__dict__
for layer in self.layers])
self.is_normal = all([isinstance(layer, Normal)
for layer in self.layers])
self.is_entropy = all(['entropy' in layer.__class__.__dict__
for layer in self.layers])
self.sample_tensor = [layer.sample_tensor for layer in self.layers]
self.is_multivariate = [layer.is_multivariate for layer in self.layers]
def __init__(self, layers=None):
get_session()
if layers is None:
self.layers = []
self.shape = []
self.n_vars = 0
self.n_params = 0
self.is_differentiable = True
self.is_multivariate = []
self.is_reparameterized = True
self.is_normal = True
self.is_entropy = True
else:
self.layers = layers
self.shape = [layer.shape for layer in self.layers]
self.n_vars = sum([layer.n_vars for layer in self.layers])
self.n_params = sum([layer.n_params for layer in self.layers])
self.is_differentiable = all(
[layer.is_differentiable for layer in self.layers])
self.is_multivariate = [
layer.is_multivariate for layer in self.layers
]
self.is_reparameterized = all(
[layer.is_reparameterized for layer in self.layers])
self.is_normal = all(
[isinstance(layer, Normal) for layer in self.layers])
self.is_entropy = all([
'entropy' in layer.__class__.__dict__ for layer in self.layers
])
def finalize(self):
get_session()
x = self.data.sample(self.n_data) # uses mini-batch
z, _ = self.variational.sample()
var_list = tf.get_collection(tf.GraphKeys.TRAINABLE_VARIABLES,
scope='variational')
inv_cov = hessian(self.model.log_prob(x, z), var_list)
print("Precision matrix:")
print(inv_cov.eval())
def finalize(self):
"""Function to call after convergence.
Computes the Hessian at the mode.
"""
get_session()
x = self.data.sample(self.n_data) # uses mini-batch
z = self.variational.sample()
var_list = tf.get_collection(tf.GraphKeys.TRAINABLE_VARIABLES,
scope='variational')
inv_cov = hessian(self.model.log_prob(x, z), var_list)
print("Precision matrix:")
print(inv_cov.eval())
def __init__(self, model, data=Data()):
"""Initialization.
Calls ``util.get_session()``
Parameters
----------
model : ed.Model
probability model
data : ed.Data, optional
observed data
"""
self.model = model
self.data = data
get_session()
def update(self, feed_dict=None):
"""Run one iteration of inference.
Parameters
----------
feed_dict : dict, optional
Feed dictionary for a TensorFlow session run. It is used to feed
placeholders that are not fed during initialization.
Returns
-------
dict
Dictionary of algorithm-specific information.
"""
if feed_dict is None:
feed_dict = {}
for key, value in six.iteritems(self.data):
if isinstance(key, tf.Tensor):
feed_dict[key] = value
sess = get_session()
t = sess.run(self.increment_t)
if self.debug:
sess.run(self.op_check)
if self.logging and self.n_print != 0:
if t == 1 or t % self.n_print == 0:
summary = sess.run(self.summarize, feed_dict)
self.train_writer.add_summary(summary, t)
return {'t': t}
def print_params(self):
sess = get_session()
m, s = sess.run([self.m, self.s])
print("mean:")
print(m)
print("std dev:")
print(s)
def print_params(self):
sess = get_session()
a, b = sess.run([self.a, self.b])
print("shape:")
print(a)
print("scale:")
print(b)
def update(self, feed_dict=None):
"""Run one iteration of inference.
Parameters
----------
feed_dict : dict, optional
Feed dictionary for a TensorFlow session run. It is used to feed
placeholders that are not fed during initialization.
Returns
-------
dict
Dictionary of algorithm-specific information.
"""
if feed_dict is None:
feed_dict = {}
for key, value in six.iteritems(self.data):
if isinstance(key, tf.Tensor):
feed_dict[key] = value
sess = get_session()
t = sess.run(self.increment_t)
if self.debug:
sess.run(self.op_check)
if self.logging and self.n_print != 0:
if t == 1 or t % self.n_print == 0:
summary = sess.run(self.summarize, feed_dict)
self.train_writer.add_summary(summary, t)
return {'t': t}
def print_params(self):
sess = get_session()
m, s = sess.run([self.m, self.s])
print("mean:")
print(m)
print("std dev:")
print(s)
def update(self, feed_dict=None):
"""Run one iteration of optimization.
Args:
feed_dict: dict, optional.
Feed dictionary for a TensorFlow session run. It is used to feed
placeholders that are not fed during initialization.
Returns:
dict.
Dictionary of algorithm-specific information. In this case, the
loss function value after one iteration.
"""
if feed_dict is None:
feed_dict = {}
for key, value in six.iteritems(self.data):
if isinstance(key, tf.Tensor) and "Placeholder" in key.op.type:
feed_dict[key] = value
sess = get_session()
_, t, loss = sess.run([self.train, self.increment_t, self.loss],
feed_dict)
if self.debug:
sess.run(self.op_check, feed_dict)
if self.logging and self.n_print != 0:
if t == 1 or t % self.n_print == 0:
summary = sess.run(self.summarize, feed_dict)
self.train_writer.add_summary(summary, t)
return {'t': t, 'loss': loss}
def update(self, feed_dict=None):
"""Run one iteration of inference.
Any derived class of `Inference` **must** implement this method.
Args:
feed_dict: dict, optional.
Feed dictionary for a TensorFlow session run. It is used to feed
placeholders that are not fed during initialization.
Returns:
dict.
Dictionary of algorithm-specific information.
"""
if feed_dict is None:
feed_dict = {}
for key, value in six.iteritems(self.data):
if isinstance(key, tf.Tensor) and "Placeholder" in key.op.type:
feed_dict[key] = value
sess = get_session()
t = sess.run(self.increment_t)
if self.debug:
sess.run(self.op_check, feed_dict)
if self.logging and self.n_print != 0:
if t == 1 or t % self.n_print == 0:
summary = sess.run(self.summarize, feed_dict)
self.train_writer.add_summary(summary, t)
return {'t': t}
def update(self, feed_dict=None):
"""Run one iteration of sampling for Monte Carlo.
Parameters
----------
feed_dict : dict, optional
Feed dictionary for a TensorFlow session run. It is used to feed
placeholders that are not fed during initialization.
Returns
-------
dict
Dictionary of algorithm-specific information. In this case, the
acceptance rate of samples since (and including) this iteration.
Notes
-----
We run the increment of t separately from other ops. Whether the
others op run with the t before incrementing or after incrementing
depends on which is run faster in the TensorFlow graph. Running it
separately forces a consistent behavior.
"""
if feed_dict is None:
feed_dict = {}
for key, value in six.iteritems(self.data):
if isinstance(key, tf.Tensor):
feed_dict[key] = value
sess = get_session()
_, accept_rate = sess.run([self.train, self.n_accept_over_t],
feed_dict)
t = sess.run(self.increment_t)
return {'t': t, 'accept_rate': accept_rate}
def update(self, feed_dict=None):
"""Run one iteration of optimizer for variational inference.
Parameters
----------
feed_dict : dict, optional
Feed dictionary for a TensorFlow session run. It is used to feed
placeholders that are not fed during initialization.
Returns
-------
dict
Dictionary of algorithm-specific information. In this case, the
loss function value after one iteration.
"""
if feed_dict is None:
feed_dict = {}
for key, value in six.iteritems(self.data):
if isinstance(key, tf.Tensor):
feed_dict[key] = value
sess = get_session()
_, t, loss = sess.run([self.train, self.increment_t, self.loss], feed_dict)
return {'t': t, 'loss': loss}
def update(self, feed_dict=None):
"""Run one iteration of optimization.
Args:
feed_dict: dict, optional.
Feed dictionary for a TensorFlow session run. It is used to feed
placeholders that are not fed during initialization.
Returns:
dict.
Dictionary of algorithm-specific information. In this case, the
loss function value after one iteration.
"""
if feed_dict is None:
feed_dict = {}
for key, value in six.iteritems(self.data):
if isinstance(key, tf.Tensor) and "Placeholder" in key.op.type:
feed_dict[key] = value
sess = get_session()
_, t, loss = sess.run([self.train, self.increment_t, self.loss], feed_dict)
if self.debug:
sess.run(self.op_check, feed_dict)
if self.logging and self.n_print != 0:
if t == 1 or t % self.n_print == 0:
if self.summarize is not None:
summary = sess.run(self.summarize, feed_dict)
self.train_writer.add_summary(summary, t)
return {'t': t, 'loss': loss}
def update(self, feed_dict=None):
"""Run one iteration of inference.
Any derived class of `Inference` **must** implement this method.
Args:
feed_dict: dict, optional.
Feed dictionary for a TensorFlow session run. It is used to feed
placeholders that are not fed during initialization.
Returns:
dict.
Dictionary of algorithm-specific information.
"""
if feed_dict is None:
feed_dict = {}
for key, value in six.iteritems(self.data):
if isinstance(key, tf.Tensor) and "Placeholder" in key.op.type:
feed_dict[key] = value
sess = get_session()
t = sess.run(self.increment_t)
if self.debug:
sess.run(self.op_check, feed_dict)
if self.logging and self.n_print != 0:
if t == 1 or t % self.n_print == 0:
summary = sess.run(self.summarize, feed_dict)
self.train_writer.add_summary(summary, t)
return {'t': t}
def print_params(self):
sess = get_session()
a, b = sess.run([self.a, self.b])
print("shape:")
print(a)
print("scale:")
print(b)
def __init__(self, model, data=None):
"""Initialization.
Parameters
----------
model : ed.Model
probability model
data : dict, optional
Data dictionary. For TensorFlow, Python, and Stan models,
the key type is a string; for PyMC3, the key type is a
Theano shared variable. For TensorFlow, Python, and PyMC3
models, the value type is a NumPy array or TensorFlow
tensor; for Stan, the value type is the type
according to the Stan program's data block.
Notes
-----
If ``data`` is not passed in, the dictionary is empty.
Three options are available for batch training:
1. internally if user passes in data as a dictionary of NumPy
arrays;
2. externally if user passes in data as a dictionary of
TensorFlow placeholders (and manually feeds them);
3. externally if user passes in data as TensorFlow tensors
which are the outputs of data readers.
"""
sess = get_session()
self.model = model
if data is None:
data = {}
if isinstance(model, StanModel):
# Stan models do no support data subsampling because they
# take arbitrary data structure types in the data block
# and not just NumPy arrays (this makes it unamenable to
# TensorFlow placeholders). Therefore fix the data
# dictionary ``self.data`` at compile time to ``data``.
self.data = data
else:
self.data = {}
for key, value in six.iteritems(data):
if isinstance(value, tf.Tensor):
# If ``data`` has TensorFlow placeholders, the user
# must manually feed them at each step of
# inference.
# If ``data`` has tensors that are the output of
# data readers, then batch training operates
# according to the reader.
self.data[key] = value
elif isinstance(value, np.ndarray):
# If ``data`` has NumPy arrays, store the data
# in the computational graph.
placeholder = tf.placeholder(tf.float32, value.shape)
var = tf.Variable(placeholder, trainable=False, collections=[])
self.data[key] = var
sess.run(var.initializer, {placeholder: value})
else:
raise NotImplementedError()
def update(self, feed_dict=None, variables=None):
"""Run one iteration of optimization.
Parameters
----------
feed_dict : dict, optional
Feed dictionary for a TensorFlow session run. It is used to feed
placeholders that are not fed during initialization.
variables : str, optional
Which set of variables to update. Either "Disc" or "Gen".
Default is both.
Returns
-------
dict
Dictionary of algorithm-specific information. In this case, the
iteration number and generative and discriminative losses.
Notes
-----
The outputted iteration number is the total number of calls to
``update``. Each update may include updating only a subset of
parameters.
"""
if feed_dict is None:
feed_dict = {}
for key, value in six.iteritems(self.data):
if isinstance(key, tf.Tensor):
if "Placeholder" in key.op.type:
feed_dict[key] = value
sess = get_session()
if variables is None:
_, _, t, loss, loss_d = sess.run([
self.train, self.train_d, self.increment_t, self.loss,
self.loss_d
], feed_dict)
elif variables == "Gen":
_, t, loss = sess.run([self.train, self.increment_t, self.loss],
feed_dict)
loss_d = 0.0
elif variables == "Disc":
_, t, loss_d = sess.run(
[self.train_d, self.increment_t, self.loss_d], feed_dict)
loss = 0.0
else:
raise NotImplementedError()
if self.debug:
sess.run(self.op_check)
if self.logging and self.n_print != 0:
if t == 1 or t % self.n_print == 0:
if self.summarize is not None:
summary = sess.run(self.summarize, feed_dict)
self.train_writer.add_summary(summary, t)
return {'t': t, 'loss': loss, 'loss_d': loss_d}
def __str__(self):
try:
sess = get_session()
mu, chol = sess.run([self.distribution.mu, self.distribution.chol])
return "mu: \n" + mu.__str__() + "\n" + \
"chol: \n" + chol.__str__()
except:
return super(MultivariateNormalCholesky, self).__str__()
def update(self, feed_dict=None, variables=None):
info_dict = super(WGANInference, self).update(feed_dict, variables)
sess = get_session()
if self.clip_op is not None and variables in (None, "Disc"):
sess.run(self.clip_op)
return info_dict
def update(self, feed_dict=None, variables=None):
info_dict = super(WGANInference, self).update(feed_dict, variables)
sess = get_session()
if variables is None or variables == "Disc":
sess.run(self.clip_d)
return info_dict
def __str__(self):
try:
sess = get_session()
n, alpha = sess.run([self.distribution.n, self.distribution.alpha])
return "n: \n" + n.__str__() + "\n" + \
"alpha: \n" + alpha.__str__()
except:
return super(DirichletMultinomial, self).__str__()
def __str__(self):
try:
sess = get_session()
a, b = sess.run([self.distribution.a, self.distribution.b])
return "a: \n" + a.__str__() + "\n" + \
"b: \n" + b.__str__()
except:
return super(Beta, self).__str__()
def update(self, feed_dict=None, variables=None):
info_dict = super(WGANInference, self).update(feed_dict, variables)
sess = get_session()
if self.clip_op is not None and variables in (None, "Disc"):
sess.run(self.clip_op)
return info_dict
def sample(self, size=1):
"""x ~ p(x | params)"""
sess = get_session()
a, b = sess.run([self.alpha, self.beta])
x = np.zeros((size, self.num_vars))
for d in range(self.num_vars):
x[:, d] = invgamma.rvs(a[d], b[d], size=size)
return x
def sample(self, size=1):
"""z ~ q(z | lambda)"""
sess = get_session()
a, b = sess.run([self.a, self.b])
z = np.zeros((size, self.num_vars))
for d in range(self.num_vars):
z[:, d] = invgamma.rvs(a[d], b[d], size=size)
return z
def sample(self, size=1):
"""z ~ q(z | lambda)"""
sess = get_session()
a, b = sess.run([self.a, self.b])
z = np.zeros((size, self.num_vars))
for d in range(self.num_vars):
z[:, d] = invgamma.rvs(a[d], b[d], size=size)
return z
def __str__(self):
try:
sess = get_session()
loc, scale = sess.run(
[self.distribution.loc, self.distribution.scale])
return "loc: \n" + loc.__str__() + "\n" + \
"scale: \n" + scale.__str__()
except:
return super(Laplace, self).__str__()
def __str__(self):
try:
sess = get_session()
mu, diag_stdev = sess.run(
[self.distribution.mu, self.distribution.diag_stdev])
return "mu: \n" + mu.__str__() + "\n" + \
"diag_stdev: \n" + diag_stdev.__str__()
except:
return super(MultivariateNormalDiag, self).__str__()
def __str__(self):
try:
sess = get_session()
alpha, beta = sess.run(
[self.distribution.alpha, self.distribution.beta])
return "alpha: \n" + alpha.__str__() + "\n" + \
"beta: \n" + beta.__str__()
except:
return super(InverseGamma, self).__str__()
def __str__(self):
try:
sess = get_session()
mu, sigma = sess.run(
[self.distribution.mu, self.distribution.sigma])
return "mu: \n" + mu.__str__() + "\n" + \
"sigma: \n" + sigma.__str__()
except:
return super(Normal, self).__str__()
def update(self, feed_dict=None, variables=None):
"""Run one iteration of optimization.
Args:
feed_dict: dict, optional.
Feed dictionary for a TensorFlow session run. It is used to feed
placeholders that are not fed during initialization.
variables: str, optional.
Which set of variables to update. Either "Disc" or "Gen".
Default is both.
Returns:
dict.
Dictionary of algorithm-specific information. In this case, the
iteration number and generative and discriminative losses.
#### Notes
The outputted iteration number is the total number of calls to
`update`. Each update may include updating only a subset of
parameters.
"""
if feed_dict is None:
feed_dict = {}
for key, value in six.iteritems(self.data):
if isinstance(key, tf.Tensor) and "Placeholder" in key.op.type:
feed_dict[key] = value
sess = get_session()
if variables is None:
_, _, t, loss, loss_d = sess.run(
[self.train, self.train_d, self.increment_t, self.loss, self.loss_d],
feed_dict)
elif variables == "Gen":
_, t, loss = sess.run(
[self.train, self.increment_t, self.loss], feed_dict)
loss_d = 0.0
elif variables == "Disc":
_, t, loss_d = sess.run(
[self.train_d, self.increment_t, self.loss_d], feed_dict)
loss = 0.0
else:
raise NotImplementedError("variables must be None, 'Gen', or 'Disc'.")
if self.debug:
sess.run(self.op_check, feed_dict)
if self.logging and self.n_print != 0:
if t == 1 or t % self.n_print == 0:
if self.summarize is not None:
summary = sess.run(self.summarize, feed_dict)
self.train_writer.add_summary(summary, t)
return {'t': t, 'loss': loss, 'loss_d': loss_d}
def __init__(self, latent_vars=None, data=None):
"""Initialization.
Parameters
----------
latent_vars : dict, optional
Collection of latent variables (of type ``RandomVariable`` or
``tf.Tensor``) to perform inference on. Each random variable is
binded to another random variable; the latter will infer the
former conditional on data.
data : dict, optional
Data dictionary which binds observed variables (of type
``RandomVariable`` or ``tf.Tensor``) to their realizations (of
type ``tf.Tensor``). It can also bind placeholders (of type
``tf.Tensor``) used in the model to their realizations; and
prior latent variables (of type ``RandomVariable``) to posterior
latent variables (of type ``RandomVariable``).
Examples
--------
>>> mu = Normal(loc=tf.constant(0.0), scale=tf.constant(1.0))
>>> x = Normal(loc=tf.ones(50) * mu, scale=tf.constant(1.0))
>>>
>>> qmu_loc = tf.Variable(tf.random_normal([]))
>>> qmu_scale = tf.nn.softplus(tf.Variable(tf.random_normal([])))
>>> qmu = Normal(loc=qmu_loc, scale=qmu_scale)
>>>
>>> inference = ed.Inference({mu: qmu}, data={x: tf.zeros(50)})
"""
sess = get_session()
if latent_vars is None:
latent_vars = {}
if data is None:
data = {}
check_latent_vars(latent_vars)
self.latent_vars = latent_vars
check_data(data)
self.data = {}
for key, value in six.iteritems(data):
if isinstance(key, tf.Tensor) and "Placeholder" in key.op.type:
self.data[key] = value
elif isinstance(key, (RandomVariable, tf.Tensor)):
if isinstance(value, (RandomVariable, tf.Tensor)):
self.data[key] = value
elif isinstance(
value, (float, list, int, np.ndarray, np.number, str)):
# If value is a Python type, store it in the graph.
# Assign its placeholder with the key's data type.
with tf.variable_scope("data"):
ph = tf.placeholder(key.dtype, np.shape(value))
var = tf.Variable(ph, trainable=False, collections=[])
sess.run(var.initializer, {ph: value})
self.data[key] = var
def update(self):
"""Run one iteration of optimizer for variational inference.
Returns
-------
loss : double
Loss function values after one iteration.
"""
sess = get_session()
_, loss = sess.run([self.train, self.loss])
return loss
def update(self):
"""Runs one iteration of KLpq minimization.
Returns
-------
loss : double
KLpq loss function value after one iteration.
"""
sess = get_session()
feed_dict = self.variational.np_dict(self.zs)
_, loss = sess.run([self.train, self.loss], feed_dict)
return loss
def __str__(self):
try:
sess = get_session()
df, mu, sigma = sess.run([
self.distribution.df, self.distribution.mu,
self.distribution.sigma
])
return "df: \n" + df.__str__() + "\n" + \
"mu: \n" + mu.__str__() + "\n" + \
"sigma: \n" + sigma.__str__()
except:
return super(StudentT, self).__str__()
def __init__(self, layers=[]):
get_session()
self.layers = layers
if layers == []:
self.num_factors = 0
self.num_vars = 0
self.num_params = 0
self.is_reparam = True
self.is_normal = True
self.is_entropy = True
self.sample_tensor = []
else:
self.num_factors = sum([layer.num_factors for layer in self.layers])
self.num_vars = sum([layer.num_vars for layer in self.layers])
self.num_params = sum([layer.num_params for layer in self.layers])
self.is_reparam = all(['reparam' in layer.__class__.__dict__
for layer in self.layers])
self.is_normal = all([isinstance(layer, Normal)
for layer in self.layers])
self.is_entropy = all(['entropy' in layer.__class__.__dict__
for layer in self.layers])
self.sample_tensor = [layer.sample_tensor for layer in self.layers]
def __init__(self, shape=1):
"""Initialize.
Parameters
----------
shape : int, list, or tuple, optional
Shape of random variable(s). If ``is_multivariate=True``, then the
inner-most (right-most) dimension indicates the dimension of
the multivariate random variable. Otherwise, all dimensions
are conceptually the same.
"""
get_session()
if isinstance(shape, int):
shape = (shape, )
elif isinstance(shape, list):
shape = tuple(shape)
self.shape = shape
self.num_vars = np.prod(self.shape)
self.num_params = None
self.sample_tensor = False
self.is_multivariate = False
def __init__(self, shape=1):
"""Initialize.
Parameters
----------
shape : int, list, or tuple, optional
Shape of random variable(s). If ``is_multivariate=True``,
then the inner-most (right-most) dimension indicates the
multivariate dimension. Otherwise, all dimensions are
conceptually the same.
"""
get_session()
if isinstance(shape, int):
shape = (shape, )
elif isinstance(shape, list):
shape = tuple(shape)
self.shape = shape
self.n_vars = np.prod(self.shape)
self.n_params = None
self.is_differentiable = False
self.is_multivariate = False
self.is_reparameterized = False
def __init__(self, latent_vars=None, data=None):
"""Create an inference algorithm.
Args:
latent_vars: dict, optional.
Collection of latent variables (of type `RandomVariable` or
`tf.Tensor`) to perform inference on. Each random variable is
binded to another random variable; the latter will infer the
former conditional on data.
data: dict, optional.
Data dictionary which binds observed variables (of type
`RandomVariable` or `tf.Tensor`) to their realizations (of
type `tf.Tensor`). It can also bind placeholders (of type
`tf.Tensor`) used in the model to their realizations; and
prior latent variables (of type `RandomVariable`) to posterior
latent variables (of type `RandomVariable`).
"""
sess = get_session()
if latent_vars is None:
latent_vars = {}
if data is None:
data = {}
check_latent_vars(latent_vars)
self.latent_vars = latent_vars
check_data(data)
self.data = {}
for key, value in six.iteritems(data):
if isinstance(key, tf.Tensor) and "Placeholder" in key.op.type:
self.data[key] = value
elif isinstance(key, (RandomVariable, tf.Tensor)):
if isinstance(value, (RandomVariable, tf.Tensor)):
self.data[key] = value
elif isinstance(
value, (float, list, int, np.ndarray, np.number, str)):
# If value is a Python type, store it in the graph.
# Assign its placeholder with the key's data type.
with tf.variable_scope(None, default_name="data"):
ph = tf.placeholder(key.dtype, np.shape(value))
var = tf.Variable(ph, trainable=False, collections=[])
sess.run(var.initializer, {ph: value})
self.data[key] = var
def update(self, feed_dict=None):
"""Run one iteration of sampling for Monte Carlo.
Parameters
----------
feed_dict : dict, optional
Feed dictionary for a TensorFlow session run. It is used to feed
placeholders that are not fed during initialization.
Returns
-------
dict
Dictionary of algorithm-specific information. In this case, the
acceptance rate of samples since (and including) this iteration.
Notes
-----
We run the increment of ``t`` separately from other ops. Whether the
others op run with the ``t`` before incrementing or after incrementing
depends on which is run faster in the TensorFlow graph. Running it
separately forces a consistent behavior.
"""
if feed_dict is None:
feed_dict = {}
for key, value in six.iteritems(self.data):
if isinstance(key, tf.Tensor):
feed_dict[key] = value
sess = get_session()
_, accept_rate = sess.run([self.train, self.n_accept_over_t], feed_dict)
t = sess.run(self.increment_t)
if self.debug:
sess.run(self.op_check)
if self.logging and self.n_print != 0:
if t == 1 or t % self.n_print == 0:
summary = sess.run(self.summarize, feed_dict)
self.train_writer.add_summary(summary, t)
return {'t': t, 'accept_rate': accept_rate}
def __init__(self, latent_vars=None, data=None):
"""Create an inference algorithm.
Args:
latent_vars: dict, optional.
Collection of latent variables (of type `RandomVariable` or
`tf.Tensor`) to perform inference on. Each random variable is
binded to another random variable; the latter will infer the
former conditional on data.
data: dict, optional.
Data dictionary which binds observed variables (of type
`RandomVariable` or `tf.Tensor`) to their realizations (of
type `tf.Tensor`). It can also bind placeholders (of type
`tf.Tensor`) used in the model to their realizations; and
prior latent variables (of type `RandomVariable`) to posterior
latent variables (of type `RandomVariable`).
"""
sess = get_session()
if latent_vars is None:
latent_vars = {}
if data is None:
data = {}
check_latent_vars(latent_vars)
self.latent_vars = latent_vars
check_data(data)
self.data = {}
for key, value in six.iteritems(data):
if isinstance(key, tf.Tensor) and "Placeholder" in key.op.type:
self.data[key] = value
elif isinstance(key, (RandomVariable, tf.Tensor)):
if isinstance(value, (RandomVariable, tf.Tensor)):
self.data[key] = value
elif isinstance(value, (float, list, int, np.ndarray, np.number, str)):
# If value is a Python type, store it in the graph.
# Assign its placeholder with the key's data type.
with tf.variable_scope("data"):
ph = tf.placeholder(key.dtype, np.shape(value))
var = tf.Variable(ph, trainable=False, collections=[])
sess.run(var.initializer, {ph: value})
self.data[key] = var
def update(self, feed_dict=None):
"""Run one iteration of sampling.
Args:
feed_dict: dict.
Feed dictionary for a TensorFlow session run. It is used to feed
placeholders that are not fed during initialization.
Returns:
dict.
Dictionary of algorithm-specific information. In this case, the
acceptance rate of samples since (and including) this iteration.
#### Notes
We run the increment of `t` separately from other ops. Whether the
others op run with the `t` before incrementing or after incrementing
depends on which is run faster in the TensorFlow graph. Running it
separately forces a consistent behavior.
"""
if feed_dict is None:
feed_dict = {}
for key, value in six.iteritems(self.data):
if isinstance(key, tf.Tensor) and "Placeholder" in key.op.type:
feed_dict[key] = value
sess = get_session()
_, accept_rate = sess.run([self.train, self.n_accept_over_t],
feed_dict)
t = sess.run(self.increment_t)
if self.debug:
sess.run(self.op_check, feed_dict)
if self.logging and self.n_print != 0:
if t == 1 or t % self.n_print == 0:
summary = sess.run(self.summarize, feed_dict)
self.train_writer.add_summary(summary, t)
return {'t': t, 'accept_rate': accept_rate}
def finalize(self, feed_dict=None):
"""Function to call after convergence.
Computes the Hessian at the mode.
Args:
feed_dict: dict, optional.
Feed dictionary for a TensorFlow session run during evaluation
of Hessian. It is used to feed placeholders that are not fed
during initialization.
"""
if feed_dict is None:
feed_dict = {}
for key, value in six.iteritems(self.data):
if isinstance(key, tf.Tensor) and "Placeholder" in key.op.type:
feed_dict[key] = value
sess = get_session()
sess.run(self.finalize_ops, feed_dict)
super(Laplace, self).finalize()
def finalize(self, feed_dict=None):
"""Function to call after convergence.
Computes the Hessian at the mode.
Args:
feed_dict: dict, optional.
Feed dictionary for a TensorFlow session run during evaluation
of Hessian. It is used to feed placeholders that are not fed
during initialization.
"""
if feed_dict is None:
feed_dict = {}
for key, value in six.iteritems(self.data):
if isinstance(key, tf.Tensor) and "Placeholder" in key.op.type:
feed_dict[key] = value
sess = get_session()
sess.run(self.finalize_ops, feed_dict)
super(Laplace, self).finalize()
def finalize(self, feed_dict=None):
"""Function to call after convergence.
Computes the Hessian at the mode.
Parameters
----------
feed_dict : dict, optional
Feed dictionary for a TensorFlow session run during evaluation
of Hessian. It is used to feed placeholders that are not fed
during initialization.
"""
if feed_dict is None:
feed_dict = {}
for key, value in six.iteritems(self.data):
if isinstance(key, tf.Tensor) and "Placeholder" in key.op.type:
feed_dict[key] = value
var_list = list(six.itervalues(self.latent_vars))
hessians = tf.hessians(self.loss, var_list)
assign_ops = []
for z, hessian in zip(six.iterkeys(self.latent_vars), hessians):
qz = self.latent_vars_normal[z]
sigma_var = get_variables(qz.sigma)[0]
if isinstance(qz, MultivariateNormalCholesky):
sigma = tf.matrix_inverse(tf.cholesky(hessian))
elif isinstance(qz, MultivariateNormalDiag):
sigma = 1.0 / tf.diag_part(hessian)
else: # qz is MultivariateNormalFull
sigma = tf.matrix_inverse(hessian)
assign_ops.append(sigma_var.assign(sigma))
sess = get_session()
sess.run(assign_ops, feed_dict)
self.latent_vars = self.latent_vars_normal.copy()
del self.latent_vars_normal
super(Laplace, self).finalize()
def eval_model(Xx, Yy, nom, probabilities=None,
dataset=None, qw=None, qb=None):
if probabilities is None:
ans = get_y_preds(Xx, Yy, qvars=[qw, qb], n_samples=10000)
zw, zb = [np.mean(an, axis=0) for an in ans]
probabilities = sigmoid(Xx.dot(zw) + zb)
ins = pd.DataFrame(probabilities, columns=['prob'])
ins['target'] = Yy
ins['guess'] = ins['prob'].round().clip(0, 1)
print(nom, '\n------')
print('acc:', (ins['target'] == ins['guess']).mean())
print('sk.logloss:', log_loss(ins['target'], ins['prob']))
sess = get_session()
print('ed.logloss (corrected):', sess.run(
binary_crossentropy(ins['target'], -np.log(1 / ins['prob'] - 1))))
print('ed.logloss (current):',
sess.run(binary_crossentropy(ins['target'], ins['prob'])))
if dataset is not None:
if nom == 'ins':
eras = dataset.training_data['era']
else:
eras = dataset.prediction_data['era']
big_ins = pd.concat([pd.DataFrame(Xx), eras, ins], axis=1).dropna()
consist = 0
for x in big_ins.era.unique():
lil_ins = big_ins[big_ins.era == x]
lloss = log_loss(lil_ins['target'], lil_ins['prob'])
print(x.replace("era", "regime"),
'(%s) :' % str(float(len(lil_ins)) / len(big_ins))[:5],
(lil_ins['target'] == lil_ins['guess']).mean(),
lloss)
if lloss < -np.log(.5):
consist += 1
print('consistency:', float(consist) / len(big_ins.era.unique()))
print('')
return ins
def ppc(T, data, latent_vars=None, n_samples=100):
"""Posterior predictive check
(Rubin, 1984; Meng, 1994; Gelman, Meng, and Stern, 1996).
PPC's form an empirical distribution for the predictive discrepancy,
$p(T\mid x) = \int p(T(x^{\\text{rep}})\mid z) p(z\mid x) dz$
by drawing replicated data sets $x^{\\text{rep}}$ and
calculating $T(x^{\\text{rep}})$ for each data set. Then it
compares it to $T(x)$.
If `data` is inputted with the prior predictive distribution, then
it is a prior predictive check (Box, 1980).
Args:
T: function.
Discrepancy function, which takes a dictionary of data and
dictionary of latent variables as input and outputs a `tf.Tensor`.
data: dict.
Data to compare to. It binds observed variables (of type
`RandomVariable` or `tf.Tensor`) to their realizations (of
type `tf.Tensor`). It can also bind placeholders (of type
`tf.Tensor`) used in the model to their realizations.
latent_vars: dict, optional.
Collection of random variables (of type `RandomVariable` or
`tf.Tensor`) binded to their inferred posterior. This argument
is used when the discrepancy is a function of latent variables.
n_samples: int, optional.
Number of replicated data sets.
Returns:
list of np.ndarray.
List containing the reference distribution, which is a NumPy array
with `n_samples` elements,
$(T(x^{{\\text{rep}},1}, z^{1}), ...,
T(x^{\\text{rep,nsamples}}, z^{\\text{nsamples}}))$
and the realized discrepancy, which is a NumPy array with
`n_samples` elements,
$(T(x, z^{1}), ..., T(x, z^{\\text{nsamples}})).$
#### Examples
```python
# build posterior predictive after inference:
# it is parameterized by a posterior sample
x_post = ed.copy(x, {z: qz, beta: qbeta})
# posterior predictive check
# T is a user-defined function of data, T(data)
T = lambda xs, zs: tf.reduce_mean(xs[x_post])
ed.ppc(T, data={x_post: x_train})
# in general T is a discrepancy function of the data (both response and
# covariates) and latent variables, T(data, latent_vars)
T = lambda xs, zs: tf.reduce_mean(zs[z])
ed.ppc(T, data={y_post: y_train, x_ph: x_train},
latent_vars={z: qz, beta: qbeta})
# prior predictive check
# run ppc on original x
ed.ppc(T, data={x: x_train})
```
"""
sess = get_session()
if not callable(T):
raise TypeError("T must be a callable function.")
check_data(data)
if latent_vars is None:
latent_vars = {}
check_latent_vars(latent_vars)
if not isinstance(n_samples, int):
raise TypeError("n_samples must have type int.")
# Build replicated latent variables.
zrep = {key: tf.convert_to_tensor(value)
for key, value in six.iteritems(latent_vars)}
# Build replicated data.
xrep = {x: (x.value() if isinstance(x, RandomVariable) else obs)
for x, obs in six.iteritems(data)}
# Create feed_dict for data placeholders that the model conditions
# on; it is necessary for all session runs.
feed_dict = {key: value for key, value in six.iteritems(data)
if isinstance(key, tf.Tensor) and "Placeholder" in key.op.type}
# Calculate discrepancy over many replicated data sets and latent
# variables.
Trep = T(xrep, zrep)
Tobs = T(data, zrep)
Treps = []
Ts = []
for _ in range(n_samples):
# Take a forward pass (session run) to get new samples for
# each calculation of the discrepancy.
# Alternatively, we could unroll the graph by registering this
# operation `n_samples` times, each for different parent nodes
# representing `xrep` and `zrep`. But it's expensive.
Treps += [sess.run(Trep, feed_dict)]
Ts += [sess.run(Tobs, feed_dict)]
return [np.stack(Treps), np.stack(Ts)]
def __init__(self, num_factors=1):
get_session()
self.num_factors = num_factors
self.num_vars = None
self.num_params = None
self.sample_tensor = False
def ppc(T, data, latent_vars=None, model_wrapper=None, n_samples=100):
"""Posterior predictive check
(Rubin, 1984; Meng, 1994; Gelman, Meng, and Stern, 1996).
If ``latent_vars`` is inputted as ``None``, then it is a prior
predictive check (Box, 1980).
PPC's form an empirical distribution for the predictive discrepancy,
.. math::
p(T) = \int p(T(x^{rep}) | z) p(z | x) dz
by drawing replicated data sets xrep and calculating
:math:`T(x^{rep})` for each data set. Then it compares it to
:math:`T(x)`.
Parameters
----------
T : function
Discrepancy function, which takes a dictionary of data and
dictionary of latent variables as input and outputs a ``tf.Tensor``.
data : dict
Data to compare to. It binds observed variables (of type
``RandomVariable``) to their realizations (of type ``tf.Tensor``). It
can also bind placeholders (of type ``tf.Tensor``) used in the model
to their realizations.
latent_vars : dict of str to RandomVariable, optional
Collection of random variables binded to their inferred posterior.
It is an optional argument, necessary for when the discrepancy is
a function of latent variables.
model_wrapper : ed.Model, optional
An optional wrapper for the probability model. It must have a
``sample_likelihood`` method. If ``latent_vars`` is not specified,
it must also have a ``sample_prior`` method, as ``ppc`` will
default to a prior predictive check. ``data`` is also changed. For
TensorFlow, Python, and Stan models, the key type is a string; for
PyMC3, the key type is a Theano shared variable. For TensorFlow,
Python, and PyMC3 models, the value type is a NumPy array or
TensorFlow placeholder; for Stan, the value type is the type
according to the Stan program's data block.
n_samples : int, optional
Number of replicated data sets.
Returns
-------
list of np.ndarray
List containing the reference distribution, which is a NumPy
array of size elements,
.. math::
(T(x^{rep,1}, z^{1}), ..., T(x^{rep,size}, z^{size}))
and the realized discrepancy, which is a NumPy array of size
elements,
.. math::
(T(x, z^{1}), ..., T(x, z^{size})).
Examples
--------
>>> # build posterior predictive after inference: it is
>>> # parameterized by posterior means
>>> x_post = copy(x, {z: qz.mean(), beta: qbeta.mean()})
>>>
>>> # posterior predictive check
>>> # T is a user-defined function of data, T(data)
>>> T = lambda xs, zs: tf.reduce_mean(xs[x_post])
>>> ppc(T, data={x_post: x_train})
>>>
>>> # in general T is a discrepancy function of the data (both response and
>>> # covariates) and latent variables, T(data, latent_vars)
>>> T = lambda xs, zs: tf.reduce_mean(zs['z'])
>>> ppc(T, data={y_post: y_train, x_ph: x_train},
... latent_vars={'z': qz, 'beta': qbeta})
>>>
>>> # prior predictive check
>>> # running ppc on original x
>>> ppc(T, data={x: x_train})
"""
sess = get_session()
# Sample to get replicated data sets and latent variables.
if model_wrapper is None:
if latent_vars is None:
zrep = None
else:
zrep = {key: value.value()
for key, value in six.iteritems(latent_vars)}
xrep = {}
for x, obs in six.iteritems(data):
if isinstance(x, RandomVariable):
# Replace observed data with replicated data.
xrep[x] = x.value()
else:
xrep[x] = obs
else:
if latent_vars is None:
zrep = model_wrapper.sample_prior()
else:
zrep = {key: value.value()
for key, value in six.iteritems(latent_vars)}
xrep = model_wrapper.sample_likelihood(zrep)
# Create feed_dict for data placeholders that the model conditions
# on; it is necessary for all session runs.
feed_dict = {x: obs for x, obs in six.iteritems(data)
if not isinstance(x, RandomVariable) and
not isinstance(x, str)}
# Calculate discrepancy over many replicated data sets and latent
# variables.
Trep = T(xrep, zrep)
Tobs = T(data, zrep)
Treps = []
Ts = []
for s in range(n_samples):
# Take a forward pass (session run) to get new samples for
# each calculation of the discrepancy.
# Note that alternatively we can unroll the graph by registering
# this operation ``n_samples`` times, each for different parent
# nodes representing ``xrep`` and ``zrep``.
Treps += [sess.run(Trep, feed_dict)]
Ts += [sess.run(Tobs, feed_dict)]
return [np.stack(Treps), np.stack(Ts)]
def ppc(model, variational=None, data=None, T=None, size=100):
"""Posterior predictive check.
(Rubin, 1984; Meng, 1994; Gelman, Meng, and Stern, 1996)
If no posterior approximation is provided through ``variational``,
then we default to a prior predictive check (Box, 1980).
PPC's form an empirical distribution for the predictive discrepancy,
.. math::
p(T) = \int p(T(yrep) | z) p(z | y) dz
by drawing replicated data sets yrep and calculating
:math:`T(yrep)` for each data set. Then it compares it to
:math:`T(y)`.
Parameters
----------
model : ed.Model
class object that implements the ``sample_likelihood`` method
variational : ed.Variational, optional
latent variable distribution q(z) to sample from. It is an
approximation to the posterior, e.g., a variational
approximation or an empirical distribution from MCMC samples.
If not specified, samples will be obtained from the model
through the ``sample_prior`` method.
data : dict, optional
Observed data to compare to. If not specified, will return
only the reference distribution with an assumed replicated
data set size of 1. For TensorFlow, Python, and Stan models,
the key type is a string; for PyMC3, the key type is a Theano
shared variable. For TensorFlow, Python, and PyMC3 models, the
value type is a NumPy array or TensorFlow placeholder; for
Stan, the value type is the type according to the Stan
program's data block.
T : function, optional
Discrepancy function, which takes a data dictionary and list
of latent variables as input and outputs a tf.Tensor. Default
is the identity function.
size : int, optional
number of replicated data sets
Returns
-------
list
List containing the reference distribution, which is a Numpy
vector of size elements,
.. math::
(T(yrep^{1}, z^{1}), ..., T(yrep^{size}, z^{size}))
and the realized discrepancy, which is a NumPy vector of size
elements,
.. math::
(T(y, z^{1}), ..., T(y, z^{size})).
If the discrepancy function is not specified, then the list
contains the full data distribution where each element is a
data set (dictionary).
"""
sess = get_session()
if data is None:
N = 1
y = {}
else:
# Assume all values have the same data set size.
N = get_dims(list(six.itervalues(data))[0])[0]
y = data
# 1. Sample from posterior (or prior).
# We must fetch zs out of the session because sample_likelihood()
# may require a SciPy-based sampler.
if variational is not None:
zs = variational.sample(size=size)
# This is to avoid fetching, e.g., a placeholder x with the
# dictionary {x: np.array()}. TensorFlow will raise an error.
if isinstance(zs, list):
zs = [tf.identity(zs_elem) for zs_elem in zs]
else:
zs = tf.identity(zs)
zs = sess.run(zs)
else:
zs = model.sample_prior(size=size)
zs = zs.eval()
# 2. Sample from likelihood.
yreps = model.sample_likelihood(zs, size=N)
# 3. Calculate discrepancy.
if T is None:
if y is None:
return yreps
else:
return [yreps, y]
Tyreps = []
Tys = []
for yrep, z in zip(yreps, tf.unpack(zs)):
Tyreps += [T(yrep, z)]
if y is not None:
Tys += [T(y, z)]
if y is None:
return sess.run(tf.pack(Tyreps))
else:
return sess.run([tf.pack(Tyreps), tf.pack(Tys)])
def evaluate(metrics, model, variational, data, y_true=None):
"""Evaluate fitted model using a set of metrics.
Parameters
----------
metrics : list or str
List of metrics or a single metric.
model : ed.Model
Probability model p(x, z)
variational : ed.Variational
Variational approximation to the posterior p(z | x)
data : dict
Data dictionary to evaluate model with. For TensorFlow,
Python, and Stan models, the key type is a string; for PyMC3,
the key type is a Theano shared variable. For TensorFlow,
Python, and PyMC3 models, the value type is a NumPy array or
TensorFlow placeholder; for Stan, the value type is the type
according to the Stan program's data block.
y_true : np.ndarray or tf.Tensor
True values to compare to in supervised learning tasks.
Returns
-------
list or float
A list of evaluations or a single evaluation.
Raises
------
NotImplementedError
If an input metric does not match an implemented metric in Edward.
"""
sess = get_session()
# Monte Carlo estimate the mean of the posterior predictive:
# 1. Sample a batch of latent variables from posterior
n_minibatch = 100
zs = variational.sample(size=n_minibatch)
# 2. Make predictions, averaging over each sample of latent variables
y_pred = model.predict(data, zs)
# Evaluate y_pred according to y_true for all metrics.
evaluations = []
if isinstance(metrics, str):
metrics = [metrics]
for metric in metrics:
if metric == 'accuracy' or metric == 'crossentropy':
# automate binary or sparse cat depending on max(y_true)
support = tf.reduce_max(y_true).eval()
if support <= 1:
metric = 'binary_' + metric
else:
metric = 'sparse_categorical_' + metric
if metric == 'binary_accuracy':
evaluations += [sess.run(binary_accuracy(y_true, y_pred))]
elif metric == 'categorical_accuracy':
evaluations += [sess.run(categorical_accuracy(y_true, y_pred))]
elif metric == 'sparse_categorical_accuracy':
evaluations += [sess.run(sparse_categorical_accuracy(y_true, y_pred))]
elif metric == 'log_loss' or metric == 'binary_crossentropy':
evaluations += [sess.run(binary_crossentropy(y_true, y_pred))]
elif metric == 'categorical_crossentropy':
evaluations += [sess.run(categorical_crossentropy(y_true, y_pred))]
elif metric == 'sparse_categorical_crossentropy':
evaluations += [sess.run(sparse_categorical_crossentropy(y_true, y_pred))]
elif metric == 'hinge':
evaluations += [sess.run(hinge(y_true, y_pred))]
elif metric == 'squared_hinge':
evaluations += [sess.run(squared_hinge(y_true, y_pred))]
elif metric == 'mse' or metric == 'MSE' or \
metric == 'mean_squared_error':
evaluations += [sess.run(mean_squared_error(y_true, y_pred))]
elif metric == 'mae' or metric == 'MAE' or \
metric == 'mean_absolute_error':
evaluations += [sess.run(mean_absolute_error(y_true, y_pred))]
elif metric == 'mape' or metric == 'MAPE' or \
metric == 'mean_absolute_percentage_error':
evaluations += [sess.run(mean_absolute_percentage_error(y_true, y_pred))]
elif metric == 'msle' or metric == 'MSLE' or \
metric == 'mean_squared_logarithmic_error':
evaluations += [sess.run(mean_squared_logarithmic_error(y_true, y_pred))]
elif metric == 'poisson':
evaluations += [sess.run(poisson(y_true, y_pred))]
elif metric == 'cosine' or metric == 'cosine_proximity':
evaluations += [sess.run(cosine_proximity(y_true, y_pred))]
elif metric == 'log_lik' or metric == 'log_likelihood':
evaluations += [sess.run(y_pred)]
else:
raise NotImplementedError()
if len(evaluations) == 1:
return evaluations[0]
else:
return evaluations
def __str__(self):
sess = get_session()
a, b = sess.run([self.alpha, self.beta])
return "shape: \n" + a.__str__() + "\n" + \
"scale: \n" + b.__str__()
def sample(self, size=1):
sess = get_session()
a, b = sess.run([self.alpha, self.beta])
return invgamma.rvs(a, b, size=size)
def __str__(self):
sess = get_session()
m, s = sess.run([self.loc, self.scale])
return "mean: \n" + m.__str__() + "\n" + \
"std dev: \n" + s.__str__()
