def _default_event_space_bijector(self):
# TODO(b/145620027) Finalize choice of bijector.
return sigmoid_bijector.Sigmoid(low=tf.constant(-np.pi,
dtype=self.dtype),
high=tf.constant(np.pi,
dtype=self.dtype),
validate_args=self.validate_args)
def _negative_concentration_bijector(self):
# Constructed dynamically so that `loc + scale / concentration` is
# tape-safe.
high = self.loc + tf.math.abs(self.scale / self.concentration)
return sigmoid_bijector.Sigmoid(low=self.loc,
high=high,
validate_args=self.validate_args)
def __init__(self,
temperature,
logits=None,
probs=None,
validate_args=False,
allow_nan_stats=True,
name="RelaxedBernoulli"):
"""Construct RelaxedBernoulli distributions.
Args:
temperature: An 0-D `Tensor`, representing the temperature
of a set of RelaxedBernoulli distributions. The temperature should be
positive.
logits: An N-D `Tensor` representing the log-odds
of a positive event. Each entry in the `Tensor` parametrizes
an independent RelaxedBernoulli distribution where the probability of an
event is sigmoid(logits). Only one of `logits` or `probs` should be
passed in.
probs: An N-D `Tensor` representing the probability of a positive event.
Each entry in the `Tensor` parameterizes an independent Bernoulli
distribution. Only one of `logits` or `probs` should be passed in.
validate_args: Python `bool`, default `False`. When `True` distribution
parameters are checked for validity despite possibly degrading runtime
performance. When `False` invalid inputs may silently render incorrect
outputs.
allow_nan_stats: Python `bool`, default `True`. When `True`, statistics
(e.g., mean, mode, variance) use the value "`NaN`" to indicate the
result is undefined. When `False`, an exception is raised if one or
more of the statistic's batch members are undefined.
name: Python `str` name prefixed to Ops created by this class.
Raises:
ValueError: If both `probs` and `logits` are passed, or if neither.
"""
parameters = dict(locals())
with tf.compat.v1.name_scope(
name, values=[logits, probs, temperature]) as name:
dtype = dtype_util.common_dtype([logits, probs, temperature], tf.float32)
self._temperature = tf.convert_to_tensor(
value=temperature, name="temperature", dtype=dtype)
if validate_args:
with tf.control_dependencies(
[tf.compat.v1.assert_positive(temperature)]):
self._temperature = tf.identity(self._temperature)
self._logits, self._probs = distribution_util.get_logits_and_probs(
logits=logits, probs=probs, validate_args=validate_args, dtype=dtype)
super(RelaxedBernoulli, self).__init__(
distribution=logistic.Logistic(
self._logits / self._temperature,
1. / self._temperature,
validate_args=validate_args,
allow_nan_stats=allow_nan_stats,
name=name + "/Logistic"),
bijector=sigmoid_bijector.Sigmoid(validate_args=validate_args),
validate_args=validate_args,
name=name)
self._parameters = parameters
def _default_event_space_bijector(self):
# TODO(b/145620027) Finalize choice of bijector.
return chain_bijector.Chain([
shift_bijector.Shift(shift=-np.pi,
validate_args=self.validate_args),
scale_bijector.Scale(scale=2. * np.pi,
validate_args=self.validate_args),
sigmoid_bijector.Sigmoid(validate_args=self.validate_args)
],
validate_args=self.validate_args)
def _default_event_space_bijector(self):
if tensor_util.is_ref(self.low) or tensor_util.is_ref(self.high):
scale = DeferredTensor(self.high, lambda x: x - self.low)
else:
scale = self.high - self.low
return chain_bijector.Chain([
shift_bijector.Shift(shift=self.low, validate_args=self.validate_args),
scale_bijector.Scale(scale=scale, validate_args=self.validate_args),
sigmoid_bijector.Sigmoid(validate_args=self.validate_args)
], validate_args=self.validate_args)
def _transformed_logistic(self):
logistic_scale = tf.math.reciprocal(self._temperature)
logits_parameter = self._logits_parameter_no_checks()
logistic_loc = logits_parameter * logistic_scale
return transformed_distribution.TransformedDistribution(
distribution=logistic.Logistic(
logistic_loc,
logistic_scale,
allow_nan_stats=self.allow_nan_stats),
bijector=sigmoid_bijector.Sigmoid())
def _default_event_space_bijector(self):
low = tfp_util.DeferredTensor(self.low, lambda x: x)
scale = tfp_util.DeferredTensor(self.high, lambda x: x - self.low)
return chain_bijector.Chain([
shift_bijector.Shift(shift=low, validate_args=self.validate_args),
scale_bijector.Scale(scale=scale,
validate_args=self.validate_args),
sigmoid_bijector.Sigmoid(validate_args=self.validate_args)
],
validate_args=self.validate_args)
def _negative_concentration_bijector(self):
# Constructed dynamically so that `scale * reciprocal(concentration)` is
# tape-safe.
return chain_bijector.Chain([
shift_bijector.Shift(shift=self.loc, validate_args=self.validate_args),
# TODO(b/146568897): Resolve numerical issues by implementing a new
# bijector instead of multiplying `scale` by `(1. - 1e-6)`.
scale_bijector.Scale(
scale=-(self.scale *
tf.math.reciprocal(self.concentration) * (1. - 1e-6)),
validate_args=self.validate_args),
sigmoid_bijector.Sigmoid(validate_args=self.validate_args)
], validate_args=self.validate_args)
def _default_event_space_bijector(self):
# TODO(b/146568897): Resolve numerical issues by implementing a new bijector
# instead of multiplying `scale` by `(1. - 1e-6)`.
if tensor_util.is_ref(self.low) or tensor_util.is_ref(self.high):
scale = DeferredTensor(
self.high,
lambda x: (x - self.low) * (1. - 1e-6),
shape=tf.broadcast_static_shape(self.high.shape, self.low.shape))
else:
scale = (self.high - self.low) * (1. - 1e-6)
return chain_bijector.Chain([
shift_bijector.Shift(shift=self.low, validate_args=self.validate_args),
scale_bijector.Scale(scale=scale, validate_args=self.validate_args),
sigmoid_bijector.Sigmoid(validate_args=self.validate_args)
], validate_args=self.validate_args)
def __init__(self,
loc,
scale,
validate_args=False,
allow_nan_stats=True,
name='LogitNormal'):
"""Construct a logit-normal distribution.
The LogititNormal distribution models positive-valued random variables whose
logit (i.e., sigmoid_inverse, i.e., `log(p) - log1p(-p)`) is normally
distributed with mean `loc` and standard deviation `scale`. It is
constructed as the sigmoid transformation, (i.e., `1 / (1 + exp(-x))`) of a
Normal distribution.
Args:
loc: Floating-point `Tensor`; the mean of the underlying
Normal distribution(s). Must broadcast with `scale`.
scale: Floating-point `Tensor`; the stddev of the underlying
Normal distribution(s). Must broadcast with `loc`.
validate_args: Python `bool`, default `False`. Whether to validate input
with asserts. If `validate_args` is `False`, and the inputs are
invalid, correct behavior is not guaranteed.
allow_nan_stats: Python `bool`, default `True`. If `False`, raise an
exception if a statistic (e.g. mean/mode/etc...) is undefined for any
batch member If `True`, batch members with valid parameters leading to
undefined statistics will return NaN for this statistic.
name: The name to give Ops created by the initializer.
"""
parameters = dict(locals())
with tf.name_scope(name) as name:
super(LogitNormal,
self).__init__(distribution=normal.Normal(loc=loc,
scale=scale),
bijector=sigmoid_bijector.Sigmoid(),
validate_args=validate_args,
parameters=parameters,
name=name)
def _default_event_space_bijector(self):
return sigmoid_bijector.Sigmoid(low=self.low,
high=self.high,
validate_args=self.validate_args)
def _default_event_space_bijector(self): return sigmoid_bijector.Sigmoid(validate_args=self.validate_args)
def _asvi_convex_update_for_base_distribution(dist,
mean_field=False,
initial_prior_weight=0.5,
sample_shape=None):
"""Creates a trainable surrogate for a (non-meta, non-joint) distribution."""
posterior_batch_shape = dist.batch_shape_tensor()
if sample_shape is not None:
posterior_batch_shape = ps.concat([
posterior_batch_shape,
distribution_util.expand_to_vector(sample_shape)
],
axis=0)
temp_params_dict = {'name': _get_name(dist)}
all_parameter_properties = dist.parameter_properties(dtype=dist.dtype)
for param, prior_value in dist.parameters.items():
if (param in (_NON_STATISTICAL_PARAMS + _NON_TRAINABLE_PARAMS)
or prior_value is None):
temp_params_dict[param] = prior_value
continue
param_properties = all_parameter_properties[param]
try:
bijector = param_properties.default_constraining_bijector_fn()
except NotImplementedError:
bijector = identity.Identity()
param_shape = ps.concat([
posterior_batch_shape,
ps.shape(prior_value)[ps.rank(prior_value) -
param_properties.event_ndims:]
],
axis=0)
# Initialize the mean-field parameter as a (constrained) standard
# normal sample.
# pylint: disable=cell-var-from-loop
# Safe because the state utils guarantee to either call `init_fn`
# immediately upon yielding, or not at all.
mean_field_parameter = yield trainable_state_util.Parameter(
init_fn=lambda seed: ( # pylint: disable=g-long-lambda
bijector.forward(
samplers.normal(shape=bijector.inverse_event_shape(
param_shape),
seed=seed))),
name='mean_field_parameter_{}_{}'.format(_get_name(dist), param),
constraining_bijector=bijector)
if mean_field:
temp_params_dict[param] = mean_field_parameter
else:
prior_weight = yield trainable_state_util.Parameter(
init_fn=lambda: tf.fill( # pylint: disable=g-long-lambda
dims=param_shape,
value=tf.cast(initial_prior_weight,
tf.convert_to_tensor(prior_value).dtype)),
name='prior_weight_{}_{}'.format(_get_name(dist), param),
constraining_bijector=sigmoid.Sigmoid())
temp_params_dict[param] = prior_weight * prior_value + (
(1. - prior_weight) * mean_field_parameter)
# pylint: enable=cell-var-from-loop
return type(dist)(**temp_params_dict)
def __init__(self,
temperature,
logits=None,
probs=None,
validate_args=False,
allow_nan_stats=True,
name='RelaxedBernoulli'):
"""Construct RelaxedBernoulli distributions.
Args:
temperature: A `Tensor`, representing the temperature of a set of
RelaxedBernoulli distributions. The temperature values should be
positive.
logits: An N-D `Tensor` representing the log-odds
of a positive event. Each entry in the `Tensor` parametrizes
an independent RelaxedBernoulli distribution where the probability of an
event is sigmoid(logits). Only one of `logits` or `probs` should be
passed in.
probs: An N-D `Tensor` representing the probability of a positive event.
Each entry in the `Tensor` parameterizes an independent Bernoulli
distribution. Only one of `logits` or `probs` should be passed in.
validate_args: Python `bool`, default `False`. When `True` distribution
parameters are checked for validity despite possibly degrading runtime
performance. When `False` invalid inputs may silently render incorrect
outputs.
allow_nan_stats: Python `bool`, default `True`. When `True`, statistics
(e.g., mean, mode, variance) use the value "`NaN`" to indicate the
result is undefined. When `False`, an exception is raised if one or
more of the statistic's batch members are undefined.
name: Python `str` name prefixed to Ops created by this class.
Raises:
ValueError: If both `probs` and `logits` are passed, or if neither.
"""
parameters = dict(locals())
with tf.name_scope(name) as name:
dtype = dtype_util.common_dtype([logits, probs, temperature],
tf.float32)
self._temperature = tensor_util.convert_nonref_to_tensor(
temperature, name='temperature', dtype=dtype)
self._probs = tensor_util.convert_nonref_to_tensor(probs,
name='probs',
dtype=dtype)
self._logits = tensor_util.convert_nonref_to_tensor(logits,
name='logits',
dtype=dtype)
if logits is None:
logits_parameter = tfp_util.DeferredTensor(
lambda x: tf.math.log(x) - tf.math.log1p(-x), self._probs)
else:
logits_parameter = self._logits
shape = tf.broadcast_static_shape(logits_parameter.shape,
self._temperature.shape)
logistic_scale = tfp_util.DeferredTensor(tf.math.reciprocal,
self._temperature)
logistic_loc = tfp_util.DeferredTensor(
lambda x: x * logistic_scale, logits_parameter, shape=shape)
self._transformed_logistic = (
transformed_distribution.TransformedDistribution(
distribution=logistic.Logistic(
logistic_loc,
logistic_scale,
allow_nan_stats=allow_nan_stats,
name=name + '/Logistic'),
bijector=sigmoid_bijector.Sigmoid()))
super(RelaxedBernoulli,
self).__init__(dtype=dtype,
reparameterization_type=reparameterization.
FULLY_REPARAMETERIZED,
validate_args=validate_args,
allow_nan_stats=allow_nan_stats,
parameters=parameters,
name=name)
def __init__(self,
loc,
scale,
num_probit_terms_approx=2,
validate_args=False,
allow_nan_stats=True,
name='LogitNormal'):
"""Construct a logit-normal distribution.
The LogitNormal distribution models random variables between 0 and 1 whose
logit (i.e., sigmoid_inverse, i.e., `log(p) - log1p(-p)`) is normally
distributed with mean `loc` and standard deviation `scale`. It is
constructed as the sigmoid transformation, (i.e., `1 / (1 + exp(-x))`) of a
Normal distribution.
Args:
loc: Floating-point `Tensor`; the mean of the underlying
Normal distribution(s). Must broadcast with `scale`.
scale: Floating-point `Tensor`; the stddev of the underlying
Normal distribution(s). Must broadcast with `loc`.
num_probit_terms_approx: The `k` used in the approximation,
`sigmoid(x) approx= sum_i^k p[k,i] Normal(0, c[k, i]).cdf(x)`
where `sum_i^k p[k,i]=1` and `p[k,i],c[k,i] > 0`
[(Monahan and Stefanski, 1989)][1] and used in `mean_*_approx` functions
[(Owen, 1980)][2]. Must be a python scalar integer between `1` and `8`
(inclusive). Using `num_probit_terms_approx=2` should result in
`mean_approx` error not exceeding `10**-4`.
Default value: `2`.
validate_args: Python `bool`, default `False`. Whether to validate input
with asserts. If `validate_args` is `False`, and the inputs are
invalid, correct behavior is not guaranteed.
allow_nan_stats: Python `bool`, default `True`. If `False`, raise an
exception if a statistic (e.g. mean/mode/etc...) is undefined for any
batch member If `True`, batch members with valid parameters leading to
undefined statistics will return NaN for this statistic.
name: The name to give Ops created by the initializer.
#### References
[1]: Monahan, John H., and Leonard A. Stefanski. Normal scale mixture
approximations to the logistic distribution with applications. North
Carolina State University. Dept. of Statistics, 1989.
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.154.5032
[2]: Owen, Donald Bruce. "A table of normal integrals: A table."
Communications in Statistics-Simulation and Computation 9.4 (1980):
389-419.
https://www.tandfonline.com/doi/abs/10.1080/03610918008812164
"""
parameters = dict(locals())
num_probit_terms_approx = int(num_probit_terms_approx)
if num_probit_terms_approx < 1 or num_probit_terms_approx > 8:
raise ValueError(
'Argument `num_probit_terms_approx` must be an integer between '
'`1` and `8` (inclusive).')
self._num_probit_terms_approx = num_probit_terms_approx
with tf.name_scope(name) as name:
super(LogitNormal,
self).__init__(distribution=normal_lib.Normal(loc=loc,
scale=scale),
bijector=sigmoid_bijector.Sigmoid(),
validate_args=validate_args,
parameters=parameters,
name=name)
def _default_event_space_bijector(self):
# TODO(b/145620027) Finalize choice of bijector.
return sigmoid_bijector.Sigmoid(validate_args=self.validate_args)
def _asvi_convex_update_for_base_distribution(dist,
mean_field,
initial_prior_weight,
sample_shape=None,
variables=None,
seed=None):
"""Creates a trainable surrogate for a (non-meta, non-joint) distribution."""
if variables is None:
variables = {}
posterior_batch_shape = dist.batch_shape_tensor()
if sample_shape is not None:
posterior_batch_shape = ps.concat([
posterior_batch_shape,
distribution_util.expand_to_vector(sample_shape)
],
axis=0)
# Create variables backing each parameter, if needed.
all_parameter_properties = dist.parameter_properties(dtype=dist.dtype)
for param, prior_value in dist.parameters.items():
if (param in variables
or param in (_NON_STATISTICAL_PARAMS + _NON_TRAINABLE_PARAMS)
or prior_value is None):
continue
param_properties = all_parameter_properties[param]
try:
bijector = param_properties.default_constraining_bijector_fn()
except NotImplementedError:
bijector = identity.Identity()
param_shape = ps.concat([
posterior_batch_shape,
ps.shape(prior_value)[ps.rank(prior_value) -
param_properties.event_ndims:]
],
axis=0)
prior_weight = (
None if mean_field # pylint: disable=g-long-ternary
else tfp_util.TransformedVariable(initial_value=tf.fill(
dims=param_shape,
value=tf.cast(initial_prior_weight,
tf.convert_to_tensor(prior_value).dtype)),
bijector=sigmoid.Sigmoid(),
name='prior_weight/{}/{}'.format(
_get_name(dist), param)))
# Initialize the mean-field parameter as a (constrained) standard
# normal sample.
seed, param_seed = samplers.split_seed(seed)
variables[param] = ASVIParameters(
prior_weight=prior_weight,
mean_field_parameter=tfp_util.TransformedVariable(
initial_value=bijector.forward(
samplers.normal(
shape=bijector.inverse_event_shape(param_shape),
seed=param_seed)),
bijector=bijector,
name='mean_field_parameter/{}/{}'.format(
_get_name(dist), param)))
temp_params_dict = {'name': _get_name(dist)}
for param, prior_value in dist.parameters.items():
if param in (_NON_STATISTICAL_PARAMS +
_NON_TRAINABLE_PARAMS) or prior_value is None:
temp_params_dict[param] = prior_value
else:
if mean_field:
temp_params_dict[param] = variables[param].mean_field_parameter
else:
temp_params_dict[param] = (
variables[param].prior_weight * prior_value +
((1. - variables[param].prior_weight) *
variables[param].mean_field_parameter))
return type(dist)(**temp_params_dict), variables
def _make_asvi_trainable_variables(prior,
mean_field=False,
initial_prior_weight=0.5):
"""Generates parameter dictionaries given a prior distribution and list."""
with tf.name_scope('make_asvi_trainable_variables'):
param_dicts = []
prior_dists = prior._get_single_sample_distributions() # pylint: disable=protected-access
for dist in prior_dists:
original_dist = dist.distribution if isinstance(dist, Root) else dist
substituted_dist = _as_trainable_family(original_dist)
# Grab the base distribution if it exists
try:
actual_dist = substituted_dist.distribution
except AttributeError:
actual_dist = substituted_dist
new_params_dict = {}
# Build trainable ASVI representation for each distribution's parameters.
parameter_properties = actual_dist.parameter_properties(
dtype=actual_dist.dtype)
if isinstance(original_dist, sample.Sample):
posterior_batch_shape = ps.concat([
actual_dist.batch_shape_tensor(),
distribution_util.expand_to_vector(original_dist.sample_shape)
], axis=0)
else:
posterior_batch_shape = actual_dist.batch_shape_tensor()
for param, value in actual_dist.parameters.items():
if param in (_NON_STATISTICAL_PARAMS +
_NON_TRAINABLE_PARAMS) or value is None:
continue
actual_event_shape = parameter_properties[param].shape_fn(
actual_dist.event_shape_tensor())
try:
bijector = parameter_properties[
param].default_constraining_bijector_fn()
except NotImplementedError:
bijector = identity.Identity()
if mean_field:
prior_weight = None
else:
unconstrained_ones = tf.ones(
shape=ps.concat([
posterior_batch_shape,
bijector.inverse_event_shape_tensor(
actual_event_shape)
], axis=0),
dtype=tf.convert_to_tensor(value).dtype)
prior_weight = tfp_util.TransformedVariable(
initial_prior_weight * unconstrained_ones,
bijector=sigmoid.Sigmoid(),
name='prior_weight/{}/{}'.format(dist.name, param))
# If the prior distribution was a tfd.Sample wrapping a base
# distribution, we want to give every single sample in the prior its
# own lambda and alpha value (rather than having a single lambda and
# alpha).
if isinstance(original_dist, sample.Sample):
value = tf.reshape(
value,
ps.concat([
actual_dist.batch_shape_tensor(),
ps.ones(ps.rank_from_shape(original_dist.sample_shape)),
actual_event_shape
],
axis=0))
value = tf.broadcast_to(
value,
ps.concat([posterior_batch_shape, actual_event_shape], axis=0))
new_params_dict[param] = ASVIParameters(
prior_weight=prior_weight,
mean_field_parameter=tfp_util.TransformedVariable(
value,
bijector=bijector,
name='mean_field_parameter/{}/{}'.format(dist.name, param)))
param_dicts.append(new_params_dict)
return param_dicts
