def transform(x, *args, **kwargs):
"""Transform a continuous random variable to the unconstrained space.
Transform selects among a number of defaults transformations which depend
on the support of the provided random variable.
Args:
x : RandomVariable.
Continuous random variable to transform.
*args, **kwargs : optional.
Arguments to overwrite when forming the ``TransformedDistribution``.
For example, one can manually specify the transformation by
passing in the ``bijector`` argument.
Returns:
RandomVariable.
A ``TransformedDistribution`` random variable, or the provided random
variable if no transformation was applied.
#### Examples
```python
x = Gamma(1.0, 1.0)
y = ed.transform(x)
sess = tf.Session()
sess.run(y)
-2.2279539
```
"""
if len(args) != 0 or kwargs.get('bijector', None) is not None:
return TransformedDistribution(x, *args, **kwargs)
try:
support = x.support
except AttributeError as e:
msg = """'{}' object has no 'support'
so cannot be transformed.""".format(type(x).__name__)
raise ValueError(msg)
if support == '01':
bij = bijectors.Invert(bijectors.Sigmoid())
elif support == 'nonnegative':
bij = bijectors.Invert(bijectors.Softplus())
elif support == 'simplex':
bij = bijectors.Invert(bijectors.SoftmaxCentered(event_ndims=1))
elif support == 'real' or support == 'multivariate_real':
return x
else:
msg = "'transform' does not handle supports of type '{}'".format(
support)
raise NotImplementedError(msg)
return TransformedDistribution(x, bij, *args, **kwargs)
def test_auto_transform_true(self):
with self.test_session() as sess:
# Match normal || softplus-inverse-normal distribution with
# automated transformation on latter (assuming it is softplus).
x = TransformedDistribution(
distribution=Normal(0.0, 0.5),
bijector=tf.contrib.distributions.bijectors.Softplus())
x.support = 'nonnegative'
qx = Normal(loc=tf.Variable(tf.random_normal([])),
scale=tf.nn.softplus(tf.Variable(tf.random_normal(
[]))))
inference = ed.KLqp({x: qx})
inference.initialize(auto_transform=True, n_samples=5, n_iter=1000)
tf.global_variables_initializer().run()
for _ in range(inference.n_iter):
info_dict = inference.update()
# Check approximation on constrained space has same moments as
# target distribution.
n_samples = 10000
x_mean, x_var = tf.nn.moments(x.sample(n_samples), 0)
x_unconstrained = inference.transformations[x]
qx_constrained = transform(
qx, bijectors.Invert(x_unconstrained.bijector))
qx_mean, qx_var = tf.nn.moments(qx_constrained.sample(n_samples),
0)
stats = sess.run([x_mean, qx_mean, x_var, qx_var])
self.assertAllClose(info_dict['loss'], 0.0, rtol=0.2, atol=0.2)
self.assertAllClose(stats[0], stats[1], rtol=1e-1, atol=1e-1)
self.assertAllClose(stats[2], stats[3], rtol=1e-1, atol=1e-1)
def initialize(self,
n_iter=1000,
n_print=None,
scale=None,
auto_transform=True,
logdir=None,
log_timestamp=True,
log_vars=None,
debug=False):
"""Initialize inference algorithm. It initializes hyperparameters
and builds ops for the algorithm's computation graph.
Any derived class of `Inference` **must** implement this method.
No methods which build ops should be called outside `initialize()`.
Args:
n_iter: int, optional.
Number of iterations for algorithm when calling `run()`.
Alternatively if controlling inference manually, it is the
expected number of calls to `update()`; this number determines
tracking information during the print progress.
n_print: int, optional.
Number of iterations for each print progress. To suppress print
progress, then specify 0. Default is `int(n_iter / 100)`.
scale: dict of RandomVariable to tf.Tensor, optional.
A tensor to scale computation for any random variable that it is
binded to. Its shape must be broadcastable; it is multiplied
element-wise to the random variable. For example, this is useful
for mini-batch scaling when inferring global variables, or
applying masks on a random variable.
auto_transform: bool, optional.
Whether to automatically transform continuous latent variables
of unequal support to be on the unconstrained space. It is
only applied if the argument is `True`, the latent variable
pair are `ed.RandomVariable`s with the `support` attribute,
the supports are both continuous and unequal.
logdir: str, optional.
Directory where event file will be written. For details,
see `tf.summary.FileWriter`. Default is to log nothing.
log_timestamp: bool, optional.
If True (and `logdir` is specified), create a subdirectory of
`logdir` to save the specific run results. The subdirectory's
name is the current UTC timestamp with format 'YYYYMMDD_HHMMSS'.
log_vars: list, optional.
Specifies the list of variables to log after each `n_print`
steps. If None, will log all variables. If `[]`, no variables
will be logged. `logdir` must be specified for variables to be
logged.
debug: bool, optional.
If True, add checks for `NaN` and `Inf` to all computations
in the graph. May result in substantially slower execution
times.
"""
self.n_iter = n_iter
if n_print is None:
self.n_print = int(n_iter / 100)
else:
self.n_print = n_print
self.progbar = Progbar(self.n_iter)
self.t = tf.Variable(0, trainable=False, name="iteration")
self.increment_t = self.t.assign_add(1)
if scale is None:
scale = {}
elif not isinstance(scale, dict):
raise TypeError("scale must be a dict object.")
self.scale = scale
# map from original latent vars to unconstrained versions
self.transformations = {}
if auto_transform:
latent_vars = self.latent_vars.copy()
# latent_vars maps original latent vars to constrained Q's.
# latent_vars_unconstrained maps unconstrained vars to unconstrained Q's.
self.latent_vars = {}
self.latent_vars_unconstrained = {}
for z, qz in six.iteritems(latent_vars):
if hasattr(z, 'support') and hasattr(qz, 'support') and \
z.support != qz.support and qz.support != 'point':
# transform z to an unconstrained space
z_unconstrained = transform(z)
self.transformations[z] = z_unconstrained
# make sure we also have a qz that covers the unconstrained space
if qz.support == "points":
qz_unconstrained = qz
else:
qz_unconstrained = transform(qz)
self.latent_vars_unconstrained[
z_unconstrained] = qz_unconstrained
# additionally construct the transformation of qz
# back into the original constrained space
if z_unconstrained != z:
qz_constrained = transform(
qz_unconstrained,
bijectors.Invert(z_unconstrained.bijector))
try: # attempt to pushforward the params of Empirical distributions
qz_constrained.params = z_unconstrained.bijector.inverse(
qz_unconstrained.params)
except: # qz_unconstrained is not an Empirical distribution
pass
else:
qz_constrained = qz_unconstrained
self.latent_vars[z] = qz_constrained
else:
self.latent_vars[z] = qz
self.latent_vars_unconstrained[z] = qz
del latent_vars
if logdir is not None:
self.logging = True
if log_timestamp:
logdir = os.path.expanduser(logdir)
logdir = os.path.join(
logdir,
datetime.strftime(datetime.utcnow(), "%Y%m%d_%H%M%S"))
self._summary_key = tf.get_default_graph().unique_name("summaries")
self._set_log_variables(log_vars)
self.train_writer = tf.summary.FileWriter(logdir,
tf.get_default_graph())
else:
self.logging = False
self.debug = debug
if self.debug:
self.op_check = tf.add_check_numerics_ops()
# Store reset ops which user can call. Subclasses should append
# any ops needed to reset internal variables in inference.
self.reset = [tf.variables_initializer([self.t])]
def initialize(self,
n_iter=1000,
n_print=None,
scale=None,
auto_transform=True,
logdir=None,
log_timestamp=True,
log_vars=None,
debug=False,
optimizer=None,
var_list=None,
use_prettytensor=False,
global_step=None,
n_samples=1,
kl_scaling=None,
maxnorm=5.):
if kl_scaling is None:
kl_scaling = {}
if n_samples <= 0:
raise ValueError(
"n_samples should be greater than zero: {}".format(n_samples))
self.n_samples = n_samples
self.kl_scaling = kl_scaling
# from inference.py
self.n_iter = n_iter
if n_print is None:
self.n_print = int(n_iter / 100)
else:
self.n_print = n_print
self.progbar = Progbar(self.n_iter)
self.t = tf.Variable(0, trainable=False, name="iteration")
self.increment_t = self.t.assign_add(1)
if scale is None:
scale = {}
elif not isinstance(scale, dict):
raise TypeError("scale must be a dict object.")
self.scale = scale
self.transformations = {}
if auto_transform:
latent_vars = self.latent_vars.copy()
self.latent_vars = {}
self.latent_vars_unconstrained = {}
for z, qz in six.iteritems(latent_vars):
if hasattr(z, 'support') and hasattr(qz, 'support') and \
z.support != qz.support and qz.support != 'point':
z_unconstrained = transform(z)
self.transformations[z] = z_unconstrained
if qz.support == "points":
qz_unconstrained = qz
else:
qz_unconstrained = transform(qz)
self.latent_vars_unconstrained[
z_unconstrained] = qz_unconstrained
if z_unconstrained != z:
qz_constrained = transform(
qz_unconstrained,
bijectors.Invert(z_unconstrained.bijector))
try:
qz_constrained.params = \
z_unconstrained.bijector.inverse(
qz_unconstrained.params)
except:
pass
else:
qz_constrained = qz_unconstrained
self.latent_vars[z] = qz_constrained
else:
self.latent_vars[z] = qz
self.latent_vars_unconstrained[z] = qz
del latent_vars
if logdir is not None:
self.logging = True
if log_timestamp:
logdir = os.path.expanduser(logdir)
logdir = os.path.join(
logdir,
datetime.strftime(datetime.utcnow(), "%Y%m%d_%H%M%S"))
self._summary_key = tf.get_default_graph().unique_name("summaries")
self._set_log_variables(log_vars)
self.train_writer = tf.summary.FileWriter(logdir,
tf.get_default_graph())
else:
self.logging = False
self.debug = debug
if self.debug:
self.op_check = tf.add_check_numerics_ops()
self.reset = [tf.variables_initializer([self.t])]
# from variational_inference.py
if var_list is None:
var_list = set()
trainables = tf.trainable_variables()
for z, qz in six.iteritems(self.latent_vars):
var_list.update(get_variables(z, collection=trainables))
var_list.update(get_variables(qz, collection=trainables))
for x, qx in six.iteritems(self.data):
if isinstance(x, RandomVariable) and \
not isinstance(qx, RandomVariable):
var_list.update(get_variables(x, collection=trainables))
var_list = list(var_list)
self.loss, grads_and_vars = self.build_loss_and_gradients(var_list)
clipped_grads_and_vars = []
for grad, var in grads_and_vars:
if "kernel" in var.name or "bias" in var.name:
clipped_grads_and_vars.append((tf.clip_by_norm(grad,
maxnorm,
axes=[0]), var))
else:
clipped_grads_and_vars.append((grad, var))
# for grad, var in grads_and_vars:
# clipped_grads_and_vars.append(
# (tf.clip_by_value(grad, -1000., 1000.), var))
del grads_and_vars
if self.logging:
tf.summary.scalar("loss",
self.loss,
collections=[self._summary_key])
for grad, var in clipped_grads_and_vars:
tf.summary.histogram("gradient/" + var.name.replace(':', '/'),
grad,
collections=[self._summary_key])
tf.summary.scalar("gradient_norm/" + var.name.replace(':', '/'),
tf.norm(grad),
collections=[self._summary_key])
self.summarize = tf.summary.merge_all(key=self._summary_key)
if optimizer is None and global_step is None:
global_step = tf.Variable(0, trainable=False, name="global_step")
if isinstance(global_step, tf.Variable):
starter_learning_rate = 0.1
learning_rate = tf.train.exponential_decay(starter_learning_rate,
global_step,
100,
0.9,
staircase=True)
else:
learning_rate = 0.01
# Build optimizer.
if optimizer is None:
optimizer = tf.train.AdamOptimizer(learning_rate)
elif isinstance(optimizer, str):
if optimizer == 'gradientdescent':
optimizer = tf.train.GradientDescentOptimizer(learning_rate)
elif optimizer == 'adadelta':
optimizer = tf.train.AdadeltaOptimizer(learning_rate)
elif optimizer == 'adagrad':
optimizer = tf.train.AdagradOptimizer(learning_rate)
elif optimizer == 'momentum':
optimizer = tf.train.MomentumOptimizer(learning_rate, 0.9)
elif optimizer == 'adam':
optimizer = tf.train.AdamOptimizer(learning_rate)
elif optimizer == 'ftrl':
optimizer = tf.train.FtrlOptimizer(learning_rate)
elif optimizer == 'rmsprop':
optimizer = tf.train.RMSPropOptimizer(learning_rate)
else:
raise ValueError('Optimizer class not found:', optimizer)
elif not isinstance(optimizer, tf.train.Optimizer):
raise TypeError(
"Optimizer must be str, tf.train.Optimizer, or None.")
with tf.variable_scope(None, default_name="optimizer") as scope:
if not use_prettytensor:
self.train = optimizer.apply_gradients(clipped_grads_and_vars,
global_step=global_step)
else:
import prettytensor as pt
self.train = pt.apply_optimizer(optimizer,
losses=[self.loss],
global_step=global_step,
var_list=var_list)
self.reset.append(
tf.variables_initializer(
tf.get_collection(tf.GraphKeys.GLOBAL_VARIABLES,
scope=scope.name)))
probs=p,
concentrations=conc_param *
tf.ones(n_samples, dtype=np.float32),
sample_shape=n_samples,
value=tf.zeros(n_samples, dtype="float32"))
# INFERENCE
#qp = edward.models.BetaWithSoftplusConcentration(tf.Variable(1.), tf.Variable(1.))
qp = ed.models.Normal(loc=tf.get_variable("qp/loc", []),
scale=tf.nn.softplus(tf.get_variable("qp/scale", [])))
qconc = ed.models.Normal(loc=tf.get_variable("qconc/loc", []),
scale=tf.nn.softplus(
tf.get_variable("qconc/scale", [])))
inference = ed.KLqp({p: qp, conc_param: qconc}, data={x: x_data})
inference.run()
# PRINT RESULTS
qp_samples = ed.transform(
qp, bijectors.Invert(
inference.transformations[p].bijector)).sample(100).eval()
print("True prob success: {:.2f}, inferred {:.3f} +- {:.2f}".format(
p_true, qp_samples.mean(), np.sqrt(qp_samples.var())))
qconc_samples = ed.transform(
qconc, bijectors.Invert(
inference.transformations[conc_param].bijector)).sample(100).eval()
print("True concentration: {:.2f}, Inferred: {:.3f} +- {:.2f}".format(
true_conc, qconc_samples.mean(), np.sqrt(qconc_samples.var())))