def _sample_n(self, n, seed=None):
power = tf.convert_to_tensor(self.power)
shape = ps.concat([[n], ps.shape(power)], axis=0)
numpy_dtype = dtype_util.as_numpy_dtype(power.dtype)
seed = samplers.sanitize_seed(seed, salt='zipf')
# Because `_hat_integral` is montonically decreasing, the bounds for u will
# switch.
# Compute the hat_integral explicitly here since we can calculate the log of
# the inputs statically in float64 with numpy.
maxval_u = tf.math.exp(-(power - 1.) * numpy_dtype(np.log1p(0.5)) -
tf.math.log(power - 1.)) + 1.
minval_u = tf.math.exp(
-(power - 1.) *
numpy_dtype(np.log1p(dtype_util.max(self.dtype) - 0.5)) -
tf.math.log(power - 1.))
def loop_body(should_continue, k, seed):
"""Resample the non-accepted points."""
u_seed, next_seed = samplers.split_seed(seed)
# Uniform variates must be sampled from the open-interval `(0, 1)` rather
# than `[0, 1)`. To do so, we use
# `np.finfo(dtype_util.as_numpy_dtype(self.dtype)).tiny`
# because it is the smallest, positive, 'normal' number. A 'normal' number
# is such that the mantissa has an implicit leading 1. Normal, positive
# numbers x, y have the reasonable property that, `x + y >= max(x, y)`. In
# this case, a subnormal number (i.e., np.nextafter) can cause us to
# sample 0.
u = samplers.uniform(
shape,
minval=np.finfo(dtype_util.as_numpy_dtype(power.dtype)).tiny,
maxval=numpy_dtype(1.),
dtype=power.dtype,
seed=u_seed)
# We use (1 - u) * maxval_u + u * minval_u rather than the other way
# around, since we want to draw samples in (minval_u, maxval_u].
u = maxval_u + (minval_u - maxval_u) * u
# set_shape needed here because of b/139013403
tensorshape_util.set_shape(u, should_continue.shape)
# Sample the point X from the continuous density h(x) \propto x^(-power).
x = self._hat_integral_inverse(u, power=power)
# Rejection-inversion requires a `hat` function, h(x) such that
# \int_{k - .5}^{k + .5} h(x) dx >= pmf(k + 1) for points k in the
# support. A natural hat function for us is h(x) = x^(-power).
#
# After sampling X from h(x), suppose it lies in the interval
# (K - .5, K + .5) for integer K. Then the corresponding K is accepted if
# if lies to the left of x_K, where x_K is defined by:
# \int_{x_k}^{K + .5} h(x) dx = H(x_K) - H(K + .5) = pmf(K + 1),
# where H(x) = \int_x^inf h(x) dx.
# Solving for x_K, we find that x_K = H_inverse(H(K + .5) + pmf(K + 1)).
# Or, the acceptance condition is X <= H_inverse(H(K + .5) + pmf(K + 1)).
# Since X = H_inverse(U), this simplifies to U <= H(K + .5) + pmf(K + 1).
# Update the non-accepted points.
# Since X \in (K - .5, K + .5), the sample K is chosen as floor(X + 0.5).
k = tf.where(should_continue, tf.floor(x + 0.5), k)
accept = (u <= self._hat_integral(k + .5, power=power) +
tf.exp(self._log_prob(k + 1, power=power)))
return [should_continue & (~accept), k, next_seed]
should_continue, samples, _ = tf.while_loop(
cond=lambda should_continue, *ignore: tf.reduce_any(should_continue
),
body=loop_body,
loop_vars=[
tf.ones(shape, dtype=tf.bool), # should_continue
tf.zeros(shape, dtype=power.dtype), # k
seed, # seed
],
maximum_iterations=self.sample_maximum_iterations,
)
samples = samples + 1.
if self.validate_args and dtype_util.is_integer(self.dtype):
samples = distribution_util.embed_check_integer_casting_closed(
samples, target_dtype=self.dtype, assert_positive=True)
samples = tf.cast(samples, self.dtype)
if self.validate_args:
npdt = dtype_util.as_numpy_dtype(self.dtype)
v = npdt(
dtype_util.min(npdt) if dtype_util.is_integer(npdt) else np.nan
)
samples = tf.where(should_continue, v, samples)
return samples
def _cast_dtype(dtype):
if dtype_util.as_numpy_dtype(dtype) is np.int64:
return tf.float64
elif dtype_util.is_integer(dtype):
return tf.float32
return dtype
def testIsInteger(self): self.assertFalse(dtype_util.is_integer(np.float64))
def __init__(self, permutation, axis=-1, validate_args=False, name=None):
"""Creates the `Permute` bijector.
Args:
permutation: An `int`-like vector-shaped `Tensor` representing the
permutation to apply to the `axis` dimension of the transformed
`Tensor`.
axis: Scalar `int` `Tensor` representing the dimension over which to
`tf.gather`. `axis` must be relative to the end (reading left to right)
thus must be negative.
Default value: `-1` (i.e., right-most).
validate_args: Python `bool` indicating whether arguments should be
checked for correctness.
name: Python `str`, name given to ops managed by this object.
Raises:
TypeError: if `not dtype_util.is_integer(permutation.dtype)`.
ValueError: if `permutation` does not contain exactly one of each of
`{0, 1, ..., d}`.
NotImplementedError: if `axis` is not known prior to graph execution.
NotImplementedError: if `axis` is not negative.
"""
with tf.name_scope(name or "permute") as name:
axis = tf.convert_to_tensor(axis, name="axis")
if not dtype_util.is_integer(axis.dtype):
raise TypeError("axis.dtype ({}) should be `int`-like.".format(
dtype_util.name(axis.dtype)))
permutation = tf.convert_to_tensor(permutation, name="permutation")
if not dtype_util.is_integer(permutation.dtype):
raise TypeError(
"permutation.dtype ({}) should be `int`-like.".format(
dtype_util.name(permutation.dtype)))
p = tf.get_static_value(permutation)
if p is not None:
if set(p) != set(np.arange(p.size)):
raise ValueError(
"Permutation over `d` must contain exactly one of "
"each of `{0, 1, ..., d}`.")
elif validate_args:
p, _ = tf.math.top_k(-permutation,
k=tf.shape(permutation)[-1],
sorted=True)
permutation = distribution_util.with_dependencies([
assert_util.assert_equal(
-p,
tf.range(tf.size(p)),
message=(
"Permutation over `d` must contain exactly one of "
"each of `{0, 1, ..., d}`.")),
], permutation)
axis_ = tf.get_static_value(axis)
if axis_ is None:
raise NotImplementedError(
"`axis` must be known prior to graph "
"execution.")
elif axis_ >= 0:
raise NotImplementedError(
"`axis` must be relative the rightmost "
"dimension, i.e., negative.")
else:
forward_min_event_ndims = int(np.abs(axis_))
self._permutation = permutation
self._axis = axis
super(Permute, self).__init__(
forward_min_event_ndims=forward_min_event_ndims,
is_constant_jacobian=True,
validate_args=validate_args,
name=name)
def percentile(x,
q,
axis=None,
interpolation=None,
keepdims=False,
validate_args=False,
preserve_gradients=True,
keep_dims=None,
name=None):
"""Compute the `q`-th percentile(s) of `x`.
Given a vector `x`, the `q`-th percentile of `x` is the value `q / 100` of the
way from the minimum to the maximum in a sorted copy of `x`.
The values and distances of the two nearest neighbors as well as the
`interpolation` parameter will determine the percentile if the normalized
ranking does not match the location of `q` exactly.
This function is the same as the median if `q = 50`, the same as the minimum
if `q = 0` and the same as the maximum if `q = 100`.
Multiple percentiles can be computed at once by using `1-D` vector `q`.
Dimension zero of the returned `Tensor` will index the different percentiles.
Compare to `numpy.percentile`.
Args:
x: Numeric `N-D` `Tensor` with `N > 0`. If `axis` is not `None`,
`x` must have statically known number of dimensions.
q: Scalar or vector `Tensor` with values in `[0, 100]`. The percentile(s).
axis: Optional `0-D` or `1-D` integer `Tensor` with constant values. The
axis that index independent samples over which to return the desired
percentile. If `None` (the default), treat every dimension as a sample
dimension, returning a scalar.
interpolation : {'nearest', 'linear', 'lower', 'higher', 'midpoint'}.
Default value: 'nearest'. This specifies the interpolation method to
use when the desired quantile lies between two data points `i < j`:
* linear: i + (j - i) * fraction, where fraction is the fractional part
of the index surrounded by i and j.
* lower: `i`.
* higher: `j`.
* nearest: `i` or `j`, whichever is nearest.
* midpoint: (i + j) / 2.
`linear` and `midpoint` interpolation do not work with integer dtypes.
keepdims: Python `bool`. If `True`, the last dimension is kept with size 1
If `False`, the last dimension is removed from the output shape.
validate_args: Whether to add runtime checks of argument validity. If
False, and arguments are incorrect, correct behavior is not guaranteed.
preserve_gradients: Python `bool`. If `True`, ensure that gradient w.r.t
the percentile `q` is preserved in the case of linear interpolation.
If `False`, the gradient will be (incorrectly) zero when `q` corresponds
to a point in `x`.
keep_dims: deprecated, use keepdims instead.
name: A Python string name to give this `Op`. Default is 'percentile'
Returns:
A `(rank(q) + N - len(axis))` dimensional `Tensor` of same dtype as `x`, or,
if `axis` is `None`, a `rank(q)` `Tensor`. The first `rank(q)` dimensions
index quantiles for different values of `q`.
Raises:
ValueError: If argument 'interpolation' is not an allowed type.
ValueError: If interpolation type not compatible with `dtype`.
#### Examples
```python
# Get 30th percentile with default ('nearest') interpolation.
x = [1., 2., 3., 4.]
tfp.stats.percentile(x, q=30.)
==> 2.0
# Get 30th percentile with 'linear' interpolation.
x = [1., 2., 3., 4.]
tfp.stats.percentile(x, q=30., interpolation='linear')
==> 1.9
# Get 30th and 70th percentiles with 'lower' interpolation
x = [1., 2., 3., 4.]
tfp.stats.percentile(x, q=[30., 70.], interpolation='lower')
==> [1., 3.]
# Get 100th percentile (maximum). By default, this is computed over every dim
x = [[1., 2.]
[3., 4.]]
tfp.stats.percentile(x, q=100.)
==> 4.
# Treat the leading dim as indexing samples, and find the 100th quantile (max)
# over all such samples.
x = [[1., 2.]
[3., 4.]]
tfp.stats.percentile(x, q=100., axis=[0])
==> [3., 4.]
```
"""
keepdims = keepdims if keep_dims is None else keep_dims
del keep_dims
name = name or 'percentile'
allowed_interpolations = {'linear', 'lower', 'higher', 'nearest', 'midpoint'}
if interpolation is None:
interpolation = 'nearest'
else:
if interpolation not in allowed_interpolations:
raise ValueError(
'Argument `interpolation` must be in {}. Found {}.'.format(
allowed_interpolations, interpolation))
with tf.name_scope(name):
x = tf.convert_to_tensor(x, name='x')
if (interpolation in {'linear', 'midpoint'} and
dtype_util.is_integer(x.dtype)):
raise TypeError('{} interpolation not allowed with dtype {}'.format(
interpolation, x.dtype))
# Double is needed here and below, else we get the wrong index if the array
# is huge along axis.
q = tf.cast(q, tf.float64)
_get_static_ndims(q, expect_ndims_no_more_than=1)
if validate_args:
q = distribution_util.with_dependencies([
assert_util.assert_rank_in(q, [0, 1]),
assert_util.assert_greater_equal(q, tf.cast(0., tf.float64)),
assert_util.assert_less_equal(q, tf.cast(100., tf.float64))
], q)
# Move `axis` dims of `x` to the rightmost, call it `y`.
if axis is None:
y = tf.reshape(x, [-1])
else:
x_ndims = _get_static_ndims(
x, expect_static=True, expect_ndims_at_least=1)
axis = _make_static_axis_non_negative_list(axis, x_ndims)
y = _move_dims_to_flat_end(x, axis, x_ndims, right_end=True)
frac_at_q_or_above = 1. - q / 100.
# Sort everything, not just the top 'k' entries, which allows multiple calls
# to sort only once (under the hood) and use CSE.
sorted_y = _sort_tensor(y)
d = tf.cast(tf.shape(y)[-1], tf.float64)
def _get_indices(interp_type):
"""Get values of y at the indices implied by interp_type."""
# Note `lower` <--> ceiling. Confusing, huh? Due to the fact that
# _sort_tensor sorts highest to lowest, tf.ceil corresponds to the higher
# index, but the lower value of y!
if interp_type == 'lower':
indices = tf.math.ceil((d - 1) * frac_at_q_or_above)
elif interp_type == 'higher':
indices = tf.floor((d - 1) * frac_at_q_or_above)
elif interp_type == 'nearest':
indices = tf.round((d - 1) * frac_at_q_or_above)
# d - 1 will be distinct from d in int32, but not necessarily double.
# So clip to avoid out of bounds errors.
return tf.clip_by_value(
tf.cast(indices, tf.int32), 0,
tf.shape(y)[-1] - 1)
if interpolation in ['nearest', 'lower', 'higher']:
gathered_y = tf.gather(sorted_y, _get_indices(interpolation), axis=-1)
elif interpolation == 'midpoint':
gathered_y = 0.5 * (
tf.gather(sorted_y, _get_indices('lower'), axis=-1) +
tf.gather(sorted_y, _get_indices('higher'), axis=-1))
elif interpolation == 'linear':
# Copy-paste of docstring on interpolation:
# linear: i + (j - i) * fraction, where fraction is the fractional part
# of the index surrounded by i and j.
larger_y_idx = _get_indices('lower')
exact_idx = (d - 1) * frac_at_q_or_above
if preserve_gradients:
# If q corresponds to a point in x, we will initially have
# larger_y_idx == smaller_y_idx.
# This results in the gradient w.r.t. fraction being zero (recall `q`
# enters only through `fraction`...and see that things cancel).
# The fix is to ensure that smaller_y_idx and larger_y_idx are always
# separated by exactly 1.
smaller_y_idx = tf.maximum(larger_y_idx - 1, 0)
larger_y_idx = tf.minimum(smaller_y_idx + 1, tf.shape(y)[-1] - 1)
fraction = tf.cast(larger_y_idx, tf.float64) - exact_idx
else:
smaller_y_idx = _get_indices('higher')
fraction = tf.math.ceil((d - 1) * frac_at_q_or_above) - exact_idx
fraction = tf.cast(fraction, y.dtype)
gathered_y = (
tf.gather(sorted_y, larger_y_idx, axis=-1) * (1 - fraction) +
tf.gather(sorted_y, smaller_y_idx, axis=-1) * fraction)
# Propagate NaNs
if x.dtype in (tf.bfloat16, tf.float16, tf.float32, tf.float64):
# Apparently tf.is_nan doesn't like other dtypes
nan_batch_members = tf.reduce_any(tf.math.is_nan(x), axis=axis)
right_rank_matched_shape = tf.pad(
tf.shape(nan_batch_members),
paddings=[[0, tf.rank(q)]],
constant_values=1)
nan_batch_members = tf.reshape(
nan_batch_members, shape=right_rank_matched_shape)
nan = np.array(np.nan, dtype_util.as_numpy_dtype(gathered_y.dtype))
gathered_y = tf.where(nan_batch_members, nan, gathered_y)
# Expand dimensions if requested
if keepdims:
if axis is None:
ones_vec = tf.ones(
shape=[_get_best_effort_ndims(x) + _get_best_effort_ndims(q)],
dtype=tf.int32)
gathered_y *= tf.ones(ones_vec, dtype=x.dtype)
else:
gathered_y = _insert_back_keepdims(gathered_y, axis)
# If q is a scalar, then result has the right shape.
# If q is a vector, then result has trailing dim of shape q.shape, which
# needs to be rotated to dim 0.
return distribution_util.rotate_transpose(gathered_y, tf.rank(q))
def _parameter_control_dependencies(self, is_init):
assertions = []
# Check num_steps is a scalar that's at least 1.
if is_init != tensor_util.is_ref(self.num_steps):
num_steps = tf.convert_to_tensor(self.num_steps)
num_steps_ = tf.get_static_value(num_steps)
if num_steps_ is not None:
if np.ndim(num_steps_) != 0:
raise ValueError(
'`num_steps` must be a scalar but it has rank {}'.
format(np.ndim(num_steps_)))
if num_steps_ < 1:
raise ValueError('`num_steps` must be at least 1.')
elif self.validate_args:
message = '`num_steps` must be a scalar'
assertions.append(
assert_util.assert_rank_at_most(self.num_steps,
0,
message=message))
assertions.append(
assert_util.assert_greater_equal(
num_steps,
1,
message='`num_steps` must be at least 1.'))
# Check that the initial distribution has scalar events over the
# integers.
if is_init and not dtype_util.is_integer(
self.initial_distribution.dtype):
raise ValueError(
'`initial_distribution.dtype` ({}) is not over integers'.
format(dtype_util.name(self.initial_distribution.dtype)))
if tensorshape_util.rank(
self.initial_distribution.event_shape) is not None:
if tensorshape_util.rank(
self.initial_distribution.event_shape) != 0:
raise ValueError(
'`initial_distribution` must have scalar `event_dim`s')
elif self.validate_args:
assertions += [
assert_util.assert_equal(
tf.size(self.initial_distribution.event_shape_tensor()),
0,
message=
'`initial_distribution` must have scalar `event_dim`s'),
]
# Check that the transition distribution is over the integers.
if (is_init and
not dtype_util.is_integer(self.transition_distribution.dtype)):
raise ValueError(
'`transition_distribution.dtype` ({}) is not over integers'.
format(dtype_util.name(self.transition_distribution.dtype)))
# Check observations have non-scalar batches.
# The graph version of this assertion is incorporated as
# a control dependency of the transition/observation
# compatibility test.
if tensorshape_util.rank(
self.observation_distribution.batch_shape) == 0:
raise ValueError(
"`observation_distribution` can't have scalar batches")
# Check transitions have non-scalar batches.
# The graph version of this assertion is incorporated as
# a control dependency of the transition/observation
# compatibility test.
if tensorshape_util.rank(
self.transition_distribution.batch_shape) == 0:
raise ValueError(
"`transition_distribution` can't have scalar batches")
# Check compatibility of transition distribution and observation
# distribution.
tdbs = self.transition_distribution.batch_shape
odbs = self.observation_distribution.batch_shape
if (tensorshape_util.dims(tdbs) is not None
and tf.compat.dimension_value(odbs[-1]) is not None):
if (tf.compat.dimension_value(tdbs[-1]) !=
tf.compat.dimension_value(odbs[-1])):
raise ValueError(
'`transition_distribution` and `observation_distribution` '
'must agree on last dimension of batch size')
elif self.validate_args:
tdbs = self.transition_distribution.batch_shape_tensor()
odbs = self.observation_distribution.batch_shape_tensor()
transition_precondition = assert_util.assert_greater(
tf.size(tdbs),
0,
message=('`transition_distribution` can\'t have scalar '
'batches'))
observation_precondition = assert_util.assert_greater(
tf.size(odbs),
0,
message=('`observation_distribution` can\'t have scalar '
'batches'))
with tf.control_dependencies(
[transition_precondition, observation_precondition]):
assertions += [
assert_util.assert_equal(
tdbs[-1],
odbs[-1],
message=('`transition_distribution` and '
'`observation_distribution` '
'must agree on last dimension of batch size'))
]
return assertions
def _sample_n(self, n, seed=None):
shape = tf.concat([[n], self.batch_shape_tensor()], axis=0)
has_seed = seed is not None
seed = SeedStream(seed, salt="zipf")
minval_u = self._hat_integral(0.5) + 1.
maxval_u = self._hat_integral(tf.int64.max - 0.5)
def loop_body(should_continue, k):
"""Resample the non-accepted points."""
# The range of U is chosen so that the resulting sample K lies in
# [0, tf.int64.max). The final sample, if accepted, is K + 1.
u = tf.random.uniform(shape,
minval=minval_u,
maxval=maxval_u,
dtype=self.power.dtype,
seed=seed())
# Sample the point X from the continuous density h(x) \propto x^(-power).
x = self._hat_integral_inverse(u)
# Rejection-inversion requires a `hat` function, h(x) such that
# \int_{k - .5}^{k + .5} h(x) dx >= pmf(k + 1) for points k in the
# support. A natural hat function for us is h(x) = x^(-power).
#
# After sampling X from h(x), suppose it lies in the interval
# (K - .5, K + .5) for integer K. Then the corresponding K is accepted if
# if lies to the left of x_K, where x_K is defined by:
# \int_{x_k}^{K + .5} h(x) dx = H(x_K) - H(K + .5) = pmf(K + 1),
# where H(x) = \int_x^inf h(x) dx.
# Solving for x_K, we find that x_K = H_inverse(H(K + .5) + pmf(K + 1)).
# Or, the acceptance condition is X <= H_inverse(H(K + .5) + pmf(K + 1)).
# Since X = H_inverse(U), this simplifies to U <= H(K + .5) + pmf(K + 1).
# Update the non-accepted points.
# Since X \in (K - .5, K + .5), the sample K is chosen as floor(X + 0.5).
k = tf.where(should_continue, tf.floor(x + 0.5), k)
accept = (u <= self._hat_integral(k + .5) +
tf.exp(self._log_prob(k + 1)))
return [should_continue & (~accept), k]
should_continue, samples = tf.while_loop(
cond=lambda should_continue, *ignore: tf.reduce_any(should_continue
),
body=loop_body,
loop_vars=[
tf.ones(shape, dtype=tf.bool), # should_continue
tf.zeros(shape, dtype=self.power.dtype), # k
],
parallel_iterations=1 if has_seed else 10,
maximum_iterations=self.sample_maximum_iterations,
)
samples = samples + 1.
if self.validate_args and dtype_util.is_integer(self.dtype):
samples = distribution_util.embed_check_integer_casting_closed(
samples, target_dtype=self.dtype, assert_positive=True)
samples = tf.cast(samples, self.dtype)
if self.validate_args:
npdt = dtype_util.as_numpy_dtype(self.dtype)
v = npdt(
dtype_util.min(npdt) if dtype_util.is_integer(npdt) else np.nan
)
samples = tf.where(should_continue, v, samples)
return samples
def _parameter_control_dependencies(self, is_init):
assertions = []
if is_init and not dtype_util.is_integer(self.mixture_distribution.dtype):
raise ValueError(
'`mixture_distribution.dtype` ({}) is not over integers'.format(
dtype_util.name(self.mixture_distribution.dtype)))
if tensorshape_util.rank(self.mixture_distribution.event_shape) is not None:
if tensorshape_util.rank(self.mixture_distribution.event_shape) != 0:
raise ValueError('`mixture_distribution` must have scalar `event_dim`s')
elif self.validate_args:
assertions += [
assert_util.assert_equal(
tf.size(self.mixture_distribution.event_shape_tensor()),
0,
message='`mixture_distribution` must have scalar `event_dim`s'),
]
# pylint: disable=protected-access
mixture_dist_param = (self.mixture_distribution._probs
if self.mixture_distribution._logits is None
else self.mixture_distribution._logits)
km = tf.compat.dimension_value(
tensorshape_util.with_rank_at_least(mixture_dist_param.shape, 1)[-1])
kc = tf.compat.dimension_value(
tensorshape_util.with_rank_at_least(
self.components_distribution.batch_shape, 1)[-1])
component_bst = None
if km is not None and kc is not None:
if km != kc:
raise ValueError('`mixture_distribution` components ({}) does not '
'equal `components_distribution.batch_shape[-1]` '
'({})'.format(km, kc))
elif self.validate_args:
if km is None:
mixture_dist_param = tf.convert_to_tensor(mixture_dist_param)
km = tf.shape(mixture_dist_param)[-1]
if kc is None:
component_bst = self.components_distribution.batch_shape_tensor()
kc = component_bst[-1]
assertions += [
assert_util.assert_equal(
km,
kc,
message=('`mixture_distribution` components does not equal '
'`components_distribution.batch_shape[-1]`')),
]
mdbs = self.mixture_distribution.batch_shape
cdbs = tensorshape_util.with_rank_at_least(
self.components_distribution.batch_shape, 1)[:-1]
if (tensorshape_util.is_fully_defined(mdbs)
and tensorshape_util.is_fully_defined(cdbs)):
if tensorshape_util.rank(mdbs) != 0 and mdbs != cdbs:
raise ValueError(
'`mixture_distribution.batch_shape` (`{}`) is not '
'compatible with `components_distribution.batch_shape` '
'(`{}`)'.format(tensorshape_util.as_list(mdbs),
tensorshape_util.as_list(cdbs)))
elif self.validate_args:
if not tensorshape_util.is_fully_defined(mdbs):
mixture_dist_param = tf.convert_to_tensor(mixture_dist_param)
mdbs = tf.shape(mixture_dist_param)[:-1]
if not tensorshape_util.is_fully_defined(cdbs):
if component_bst is None:
component_bst = self.components_distribution.batch_shape_tensor()
cdbs = component_bst[:-1]
assertions += [
assert_util.assert_equal(
distribution_utils.pick_vector(
tf.equal(tf.shape(mdbs)[0], 0), cdbs, mdbs),
cdbs,
message=(
'`mixture_distribution.batch_shape` is not '
'compatible with `components_distribution.batch_shape`'))
]
return assertions
def __init__(self,
mixture_distribution,
components_distribution,
reparameterize=False,
validate_args=False,
allow_nan_stats=True,
name="MixtureSameFamily"):
"""Construct a `MixtureSameFamily` distribution.
Args:
mixture_distribution: `tfp.distributions.Categorical`-like instance.
Manages the probability of selecting components. The number of
categories must match the rightmost batch dimension of the
`components_distribution`. Must have either scalar `batch_shape` or
`batch_shape` matching `components_distribution.batch_shape[:-1]`.
components_distribution: `tfp.distributions.Distribution`-like instance.
Right-most batch dimension indexes components.
reparameterize: Python `bool`, default `False`. Whether to reparameterize
samples of the distribution using implicit reparameterization gradients
[(Figurnov et al., 2018)][1]. The gradients for the mixture logits are
equivalent to the ones described by [(Graves, 2016)][2]. The gradients
for the components parameters are also computed using implicit
reparameterization (as opposed to ancestral sampling), meaning that
all components are updated every step.
Only works when:
(1) components_distribution is fully reparameterized;
(2) components_distribution is either a scalar distribution or
fully factorized (tfd.Independent applied to a scalar distribution);
(3) batch shape has a known rank.
Experimental, may be slow and produce infs/NaNs.
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 not dtype_util.is_integer(mixture_distribution.dtype)`.
ValueError: if mixture_distribution does not have scalar `event_shape`.
ValueError: if `mixture_distribution.batch_shape` and
`components_distribution.batch_shape[:-1]` are both fully defined and
the former is neither scalar nor equal to the latter.
ValueError: if `mixture_distribution` categories does not equal
`components_distribution` rightmost batch shape.
#### References
[1]: Michael Figurnov, Shakir Mohamed and Andriy Mnih. Implicit
reparameterization gradients. In _Neural Information Processing
Systems_, 2018. https://arxiv.org/abs/1805.08498
[2]: Alex Graves. Stochastic Backpropagation through Mixture Density
Distributions. _arXiv_, 2016. https://arxiv.org/abs/1607.05690
"""
parameters = dict(locals())
with tf.name_scope(name) as name:
self._mixture_distribution = mixture_distribution
self._components_distribution = components_distribution
self._runtime_assertions = []
s = components_distribution.event_shape_tensor()
self._event_ndims = tf.compat.dimension_value(s.shape[0])
if self._event_ndims is None:
self._event_ndims = tf.size(input=s)
self._event_size = tf.reduce_prod(input_tensor=s)
if not dtype_util.is_integer(mixture_distribution.dtype):
raise ValueError(
"`mixture_distribution.dtype` ({}) is not over integers".
format(dtype_util.name(mixture_distribution.dtype)))
if (tensorshape_util.rank(mixture_distribution.event_shape)
is not None and tensorshape_util.rank(
mixture_distribution.event_shape) != 0):
raise ValueError(
"`mixture_distribution` must have scalar `event_dim`s")
elif validate_args:
self._runtime_assertions += [
assert_util.assert_equal(
tf.size(
input=mixture_distribution.event_shape_tensor()),
0,
message=
"`mixture_distribution` must have scalar `event_dim`s"
),
]
mdbs = mixture_distribution.batch_shape
cdbs = tensorshape_util.with_rank_at_least(
components_distribution.batch_shape, 1)[:-1]
if tensorshape_util.is_fully_defined(
mdbs) and tensorshape_util.is_fully_defined(cdbs):
if tensorshape_util.rank(mdbs) != 0 and mdbs != cdbs:
raise ValueError(
"`mixture_distribution.batch_shape` (`{}`) is not "
"compatible with `components_distribution.batch_shape` "
"(`{}`)".format(tensorshape_util.as_list(mdbs),
tensorshape_util.as_list(cdbs)))
elif validate_args:
mdbs = mixture_distribution.batch_shape_tensor()
cdbs = components_distribution.batch_shape_tensor()[:-1]
self._runtime_assertions += [
assert_util.assert_equal(
distribution_utils.pick_vector(
mixture_distribution.is_scalar_batch(), cdbs,
mdbs),
cdbs,
message=
("`mixture_distribution.batch_shape` is not "
"compatible with `components_distribution.batch_shape`"
))
]
km = tf.compat.dimension_value(
tensorshape_util.with_rank_at_least(
mixture_distribution.logits.shape, 1)[-1])
kc = tf.compat.dimension_value(
tensorshape_util.with_rank_at_least(
components_distribution.batch_shape, 1)[-1])
if km is not None and kc is not None and km != kc:
raise ValueError(
"`mixture_distribution components` ({}) does not "
"equal `components_distribution.batch_shape[-1]` "
"({})".format(km, kc))
elif validate_args:
km = tf.shape(input=mixture_distribution.logits)[-1]
kc = components_distribution.batch_shape_tensor()[-1]
self._runtime_assertions += [
assert_util.assert_equal(
km,
kc,
message=(
"`mixture_distribution components` does not equal "
"`components_distribution.batch_shape[-1:]`")),
]
elif km is None:
km = tf.shape(input=mixture_distribution.logits)[-1]
self._num_components = km
self._reparameterize = reparameterize
if reparameterize:
# Note: tfd.Independent passes through the reparameterization type hence
# we do not need separate logic for Independent.
if (self._components_distribution.reparameterization_type !=
reparameterization.FULLY_REPARAMETERIZED):
raise ValueError("Cannot reparameterize a mixture of "
"non-reparameterized components.")
reparameterization_type = reparameterization.FULLY_REPARAMETERIZED
else:
reparameterization_type = reparameterization.NOT_REPARAMETERIZED
super(MixtureSameFamily, self).__init__(
dtype=self._components_distribution.dtype,
reparameterization_type=reparameterization_type,
validate_args=validate_args,
allow_nan_stats=allow_nan_stats,
parameters=parameters,
graph_parents=(
self._mixture_distribution._graph_parents # pylint: disable=protected-access
+ self._components_distribution._graph_parents), # pylint: disable=protected-access
name=name)
def _is_equal_or_close(self, a, b):
if dtype_util.is_integer(self.outcomes.dtype):
return tf.equal(a, b)
return tf.abs(a - b) < self._atol + self._rtol * tf.abs(b)
def _float_dtype_like(dtype):
if dtype_util.as_numpy_dtype(dtype) == np.int64:
return tf.float64
if dtype_util.is_integer(dtype):
return tf.float32
return dtype
def __init__(self,
perm=None,
rightmost_transposed_ndims=None,
validate_args=False,
name='transpose'):
"""Instantiates the `Transpose` bijector.
Args:
perm: Positive `int32` vector-shaped `Tensor` representing permutation of
rightmost dims (for forward transformation). Note that the `0`th index
represents the first of the rightmost dims and the largest value must be
`rightmost_transposed_ndims - 1` and corresponds to `tf.rank(x) - 1`.
Only one of `perm` and `rightmost_transposed_ndims` can (and must) be
specified. The number of elements in a permutation must have a value
that can be determined statically.
Default value:
`tf.range(start=rightmost_transposed_ndims, limit=-1, delta=-1)`.
rightmost_transposed_ndims: Positive `int32` scalar-shaped `Tensor`
representing the number of rightmost dimensions to permute.
Only one of `perm` and `rightmost_transposed_ndims` can (and must) be
specified. If `rightmost_transposed_ndims` is specified, the rightmost
dims are reversed. This argument must have a value that can be
determined statically.
Default value: `tf.size(perm)`.
validate_args: Python `bool` indicating whether arguments should be
checked for correctness.
name: Python `str` name given to ops managed by this object.
Raises:
ValueError: if both or neither `perm` and `rightmost_transposed_ndims` are
specified.
NotImplementedError: if `rightmost_transposed_ndims` is not known prior to
graph execution.
"""
parameters = dict(locals())
with tf.name_scope(name) as name:
# We need to determine `forward_min_event_ndims` statically, which
# requires that we know `rightmost_transposed_ndims` statically.
# So the corresponding assertions go here rather than in
# `_parameter_control_dependencies`
if (rightmost_transposed_ndims is None) == (perm is None):
raise ValueError('Must specify exactly one of '
'`rightmost_transposed_ndims` and `perm`.')
if rightmost_transposed_ndims is not None:
rightmost_transposed_ndims = tensor_util.convert_nonref_to_tensor(
rightmost_transposed_ndims, dtype_hint=np.int32)
if not dtype_util.is_integer(rightmost_transposed_ndims.dtype):
raise TypeError(
'`rightmost_transposed_ndims` must be integer type.')
rightmost_transposed_ndims_ = tf.get_static_value(
rightmost_transposed_ndims)
if rightmost_transposed_ndims_ is None:
raise NotImplementedError(
'`rightmost_transposed_ndims` must be '
'known prior to graph execution.')
msg = '`rightmost_transposed_ndims` must be non-negative.'
if rightmost_transposed_ndims_ < 0:
raise ValueError(
msg[:-1] +
', saw: {}.'.format(rightmost_transposed_ndims_))
perm_start = (distribution_util.prefer_static_value(
rightmost_transposed_ndims) - 1)
perm = tf.range(start=perm_start,
limit=-1,
delta=-1,
name='perm')
else: # perm is not None:
perm = tensor_util.convert_nonref_to_tensor(
perm, dtype_hint=np.int32, name='perm')
rightmost_transposed_ndims = tf.size(
perm, name='rightmost_transposed_ndims')
rightmost_transposed_ndims_ = tf.get_static_value(
rightmost_transposed_ndims)
# TODO(b/110828604): If bijector base class ever supports dynamic
# `min_event_ndims`, then this class already works dynamically and the
# following five lines can be removed.
if rightmost_transposed_ndims_ is None:
raise NotImplementedError(
'`rightmost_transposed_ndims` must be '
'known prior to graph execution.')
else:
rightmost_transposed_ndims_ = int(rightmost_transposed_ndims_)
self._perm = perm
self._rightmost_transposed_ndims = rightmost_transposed_ndims
self._initial_rightmost_transposed_ndims = rightmost_transposed_ndims_
super(Transpose, self).__init__(
forward_min_event_ndims=rightmost_transposed_ndims_,
is_constant_jacobian=True,
validate_args=validate_args,
parameters=parameters,
name=name)
def _float_dtype_like(dtype):
if dtype is tf.int64:
return tf.float64
if dtype_util.is_integer(dtype):
return tf.float32
return dtype
def _potential_scale_reduction_single_state(state, independent_chain_ndims,
split_chains, validate_args):
"""potential_scale_reduction for one single state `Tensor`."""
# casting integers to floats for floating-point division
# check to see if the `state` is a numpy object for the numpy test suite
if dtype_util.as_numpy_dtype(state.dtype) is np.int64:
state = tf.cast(state, tf.float64)
elif dtype_util.is_integer(state.dtype):
state = tf.cast(state, tf.float32)
with tf.name_scope('potential_scale_reduction_single_state'):
# We assume exactly one leading dimension indexes e.g. correlated samples
# from each Markov chain.
state = tf.convert_to_tensor(state, name='state')
n_samples_ = tf.compat.dimension_value(state.shape[0])
if n_samples_ is not None: # If available statically.
if split_chains and n_samples_ < 4:
raise ValueError(
'Must provide at least 4 samples when splitting chains. '
'Found {}'.format(n_samples_))
if not split_chains and n_samples_ < 2:
raise ValueError(
'Must provide at least 2 samples. Found {}'.format(
n_samples_))
elif validate_args:
if split_chains:
assertions = [
assert_util.assert_greater(
ps.shape(state)[0],
4,
message=
'Must provide at least 4 samples when splitting chains.'
)
]
with tf.control_dependencies(assertions):
state = tf.identity(state)
else:
assertions = [
assert_util.assert_greater(
ps.shape(state)[0],
2,
message='Must provide at least 2 samples.')
]
with tf.control_dependencies(assertions):
state = tf.identity(state)
# Define so it's not a magic number.
# Warning! `if split_chains` logic assumes this is 1!
sample_ndims = 1
if split_chains:
# Split the sample dimension in half, doubling the number of
# independent chains.
# For odd number of samples, keep all but the last sample.
state_shape = ps.shape(state)
n_samples = state_shape[0]
state = state[:n_samples - n_samples % 2]
# Suppose state = [0, 1, 2, 3, 4, 5]
# Step 1: reshape into [[0, 1, 2], [3, 4, 5]]
# E.g. reshape states of shape [a, b] into [2, a//2, b].
state = tf.reshape(
state, ps.concat([[2, n_samples // 2], state_shape[1:]],
axis=0))
# Step 2: Put the size `2` dimension in the right place to be treated as a
# chain, changing [[0, 1, 2], [3, 4, 5]] into [[0, 3], [1, 4], [2, 5]],
# reshaping [2, a//2, b] into [a//2, 2, b].
state = tf.transpose(
a=state,
perm=ps.concat([[1, 0], tf.range(2, tf.rank(state))], axis=0))
# We're treating the new dim as indexing 2 chains, so increment.
independent_chain_ndims += 1
sample_axis = tf.range(0, sample_ndims)
chain_axis = tf.range(sample_ndims,
sample_ndims + independent_chain_ndims)
sample_and_chain_axis = tf.range(
0, sample_ndims + independent_chain_ndims)
n = _axis_size(state, sample_axis)
m = _axis_size(state, chain_axis)
# In the language of Brooks and Gelman (1998),
# B / n is the between chain variance, the variance of the chain means.
# W is the within sequence variance, the mean of the chain variances.
b_div_n = _reduce_variance(tf.reduce_mean(state,
axis=sample_axis,
keepdims=True),
sample_and_chain_axis,
biased=False)
w = tf.reduce_mean(_reduce_variance(state,
sample_axis,
keepdims=True,
biased=False),
axis=sample_and_chain_axis)
# sigma^2_+ is an estimate of the true variance, which would be unbiased if
# each chain was drawn from the target. c.f. "law of total variance."
sigma_2_plus = ((n - 1) / n) * w + b_div_n
return ((m + 1.) / m) * sigma_2_plus / w - (n - 1.) / (m * n)
