def _sample_n(self, n, seed=None):
sample_shape = _concat_vectors(
distribution_util.pick_vector(self._needs_rotation, self._empty, [n]),
self._override_batch_shape,
self._override_event_shape,
distribution_util.pick_vector(self._needs_rotation, [n], self._empty))
x = self.distribution.sample(sample_shape=sample_shape, seed=seed)
x = self._maybe_rotate_dims(x)
# We'll apply the bijector in the `_call_sample_n` function.
return x
def _sample_n(self, n, seed=None):
sample_shape = _concat_vectors(
distribution_util.pick_vector(self._needs_rotation, self._empty, [n]),
self._override_batch_shape,
self._override_event_shape,
distribution_util.pick_vector(self._needs_rotation, [n], self._empty))
x = self.distribution.sample(sample_shape=sample_shape, seed=seed)
x = self._maybe_rotate_dims(x)
# We'll apply the bijector in the `_call_sample_n` function.
return x
def _sample_n(self, n, seed=None, **distribution_kwargs):
sample_shape = prefer_static.concat([
distribution_util.pick_vector(self._needs_rotation, self._empty, [n]),
self._override_batch_shape,
self._override_event_shape,
distribution_util.pick_vector(self._needs_rotation, [n], self._empty),
], axis=0)
x = self.distribution.sample(sample_shape=sample_shape, seed=seed,
**distribution_kwargs)
x = self._maybe_rotate_dims(x)
# We'll apply the bijector in the `_call_sample_n` function.
return x
def testCorrectlyPicksVector(self):
x = np.arange(10, 12)
y = np.arange(15, 18)
self.assertAllEqual(
x, self.evaluate(distribution_util.pick_vector(tf.less(0, 5), x, y)))
self.assertAllEqual(
y, self.evaluate(distribution_util.pick_vector(tf.less(5, 0), x, y)))
self.assertAllEqual(x,
distribution_util.pick_vector(
tf.constant(True), x, y)) # No eval.
self.assertAllEqual(y,
distribution_util.pick_vector(
tf.constant(False), x, y)) # No eval.
def _make_columnar(self, x):
"""Ensures non-scalar input has at least one column.
Example:
If `x = [1, 2, 3]` then the output is `[[1], [2], [3]]`.
If `x = [[1, 2, 3], [4, 5, 6]]` then the output is unchanged.
If `x = 1` then the output is unchanged.
Args:
x: `Tensor`.
Returns:
columnar_x: `Tensor` with at least two dimensions.
"""
if x.shape.ndims is not None:
if x.shape.ndims == 1:
x = x[tf.newaxis, :]
return x
shape = tf.shape(x)
maybe_expanded_shape = tf.concat([
shape[:-1],
distribution_util.pick_vector(
tf.equal(tf.rank(x), 1), [1], np.array([], dtype=np.int32)),
shape[-1:],
], 0)
return tf.reshape(x, maybe_expanded_shape)
def _expand_sample_shape_to_vector(self, x, name):
"""Helper to `sample` which ensures input is 1D."""
x_static_val = tensor_util.constant_value(x)
if x_static_val is None:
prod = tf.reduce_prod(x)
else:
prod = np.prod(x_static_val, dtype=x.dtype.as_numpy_dtype())
ndims = x.get_shape().ndims # != sample_ndims
if ndims is None:
# Maybe expand_dims.
ndims = tf.rank(x)
expanded_shape = util.pick_vector(tf.equal(ndims, 0),
np.array([1], dtype=np.int32),
tf.shape(x))
x = tf.reshape(x, expanded_shape)
elif ndims == 0:
# Definitely expand_dims.
if x_static_val is not None:
x = tf.convert_to_tensor(np.array(
[x_static_val], dtype=x.dtype.as_numpy_dtype()),
name=name)
else:
x = tf.reshape(x, [1])
elif ndims != 1:
raise ValueError("Input is neither scalar nor vector.")
return x, prod
def _batch_shape_tensor(self,
override_batch_shape=None,
base_batch_shape_tensor=None):
override_batch_shape = (tf.convert_to_tensor(
self._override_batch_shape) if override_batch_shape is None else
override_batch_shape)
base_batch_shape_tensor = (self.distribution.batch_shape_tensor()
if base_batch_shape_tensor is None else
base_batch_shape_tensor)
# The `batch_shape_tensor` of the transformed distribution is the same as
# that of the base distribution in all cases except when the following are
# both true:
# - the base distribution is joint with structured `batch_shape_tensor`
# - the transformed distribution is not joint.
# In this case, the components of the base distribution's
# `batch_shape_tensor` are broadcast to obtain the `batch_shape_tensor` of
# the transformed distribution. Non-broadcasting components are not
# supported. (Note that joint distributions may either have a single
# `batch_shape_tensor` for all components, or a component-wise
# `batch_shape_tensor` with the same nested structure as the distribution's
# dtype.)
if tf.nest.is_nested(base_batch_shape_tensor):
if self._is_joint:
return base_batch_shape_tensor
base_batch_shape_tensor = functools.reduce(
prefer_static.broadcast_shape,
tf.nest.flatten(base_batch_shape_tensor))
# If the batch shape has been overridden, return the override batch shape
# instead.
return distribution_util.pick_vector(
self._has_nonzero_rank(override_batch_shape), override_batch_shape,
base_batch_shape_tensor)
def _make_columnar(self, x):
"""Ensures non-scalar input has at least one column.
Example:
If `x = [1, 2, 3]` then the output is `[[1], [2], [3]]`.
If `x = [[1, 2, 3], [4, 5, 6]]` then the output is unchanged.
If `x = 1` then the output is unchanged.
Args:
x: `Tensor`.
Returns:
columnar_x: `Tensor` with at least two dimensions.
"""
if tensorshape_util.rank(x.shape) is not None:
if tensorshape_util.rank(x.shape) == 1:
x = x[tf.newaxis, :]
return x
shape = tf.shape(x)
maybe_expanded_shape = tf.concat([
shape[:-1],
distribution_util.pick_vector(
tf.equal(tf.rank(x), 1), [1], np.array([], dtype=np.int32)),
shape[-1:],
], 0)
return tf.reshape(x, maybe_expanded_shape)
def _expand_sample_shape_to_vector(self, x, name):
"""Helper to `sample` which ensures input is 1D."""
x_static_val = tf.contrib.util.constant_value(x)
if x_static_val is None:
prod = tf.reduce_prod(x)
else:
prod = np.prod(x_static_val, dtype=x.dtype.as_numpy_dtype())
ndims = x.shape.ndims # != sample_ndims
if ndims is None:
# Maybe expand_dims.
ndims = tf.rank(x)
expanded_shape = util.pick_vector(
tf.equal(ndims, 0),
np.array([1], dtype=np.int32), tf.shape(x))
x = tf.reshape(x, expanded_shape)
elif ndims == 0:
# Definitely expand_dims.
if x_static_val is not None:
x = tf.convert_to_tensor(
np.array([x_static_val], dtype=x.dtype.as_numpy_dtype()),
name=name)
else:
x = tf.reshape(x, [1])
elif ndims != 1:
raise ValueError("Input is neither scalar nor vector.")
return x, prod
def _sample_n(self, n, seed=None):
# Get ids as a [n, batch_size]-shaped matrix, unless batch_shape=[] then get
# ids as a [n]-shaped vector.
distributions = self.poisson_and_mixture_distributions()
dist, mixture_dist = distributions
batch_size = tensorshape_util.num_elements(self.batch_shape)
if batch_size is None:
batch_size = tf.reduce_prod(
self._batch_shape_tensor(distributions=distributions))
# We need to 'sample extra' from the mixture distribution if it doesn't
# already specify a probs vector for each batch coordinate.
# We only support this kind of reduced broadcasting, i.e., there is exactly
# one probs vector for all batch dims or one for each.
mixture_seed, poisson_seed = samplers.split_seed(
seed, salt='PoissonLogNormalQuadratureCompound')
ids = mixture_dist.sample(
sample_shape=concat_vectors(
[n],
distribution_util.pick_vector(
mixture_dist.is_scalar_batch(),
[batch_size],
np.int32([]))),
seed=mixture_seed)
# We need to flatten batch dims in case mixture_dist has its own
# batch dims.
ids = tf.reshape(
ids,
shape=concat_vectors([n],
distribution_util.pick_vector(
self.is_scalar_batch(), np.int32([]),
np.int32([-1]))))
# Stride `quadrature_size` for `batch_size` number of times.
offset = tf.range(
start=0,
limit=batch_size * self._quadrature_size,
delta=self._quadrature_size,
dtype=ids.dtype)
ids = ids + offset
rate = tf.gather(tf.reshape(dist.rate_parameter(), shape=[-1]), ids)
rate = tf.reshape(
rate, shape=concat_vectors([n], self._batch_shape_tensor(
distributions=distributions)))
return samplers.poisson(
shape=[], lam=rate, dtype=self.dtype, seed=poisson_seed)
def _batch_shape_tensor(self,
override_batch_shape=None,
base_batch_shape_tensor=None):
override_batch_shape = (tf.convert_to_tensor(
self._override_batch_shape) if override_batch_shape is None else
override_batch_shape)
base_batch_shape_tensor = (self.distribution.batch_shape_tensor()
if base_batch_shape_tensor is None else
base_batch_shape_tensor)
return distribution_util.pick_vector(
self._has_nonzero_rank(override_batch_shape), override_batch_shape,
base_batch_shape_tensor)
def _sample_n(self, n, seed=None):
# Get ids as a [n, batch_size]-shaped matrix, unless batch_shape=[] then get
# ids as a [n]-shaped vector.
batch_size = self.batch_shape.num_elements()
if batch_size is None:
batch_size = tf.reduce_prod(self.batch_shape_tensor())
# We need to "sample extra" from the mixture distribution if it doesn't
# already specify a probs vector for each batch coordinate.
# We only support this kind of reduced broadcasting, i.e., there is exactly
# one probs vector for all batch dims or one for each.
stream = seed_stream.SeedStream(
seed, salt="PoissonLogNormalQuadratureCompound")
ids = self._mixture_distribution.sample(
sample_shape=concat_vectors(
[n],
distribution_util.pick_vector(
self.mixture_distribution.is_scalar_batch(),
[batch_size],
np.int32([]))),
seed=stream())
# We need to flatten batch dims in case mixture_distribution has its own
# batch dims.
ids = tf.reshape(
ids,
shape=concat_vectors([n],
distribution_util.pick_vector(
self.is_scalar_batch(), np.int32([]),
np.int32([-1]))))
# Stride `quadrature_size` for `batch_size` number of times.
offset = tf.range(
start=0,
limit=batch_size * self._quadrature_size,
delta=self._quadrature_size,
dtype=ids.dtype)
ids += offset
rate = tf.gather(tf.reshape(self.distribution.rate, shape=[-1]), ids)
rate = tf.reshape(
rate, shape=concat_vectors([n], self.batch_shape_tensor()))
return tf.random_poisson(lam=rate, shape=[], dtype=self.dtype, seed=seed)
def _sample_n(self, n, seed=None):
# Get ids as a [n, batch_size]-shaped matrix, unless batch_shape=[] then get
# ids as a [n]-shaped vector.
batch_size = self.batch_shape.num_elements()
if batch_size is None:
batch_size = tf.reduce_prod(input_tensor=self.batch_shape_tensor())
# We need to "sample extra" from the mixture distribution if it doesn't
# already specify a probs vector for each batch coordinate.
# We only support this kind of reduced broadcasting, i.e., there is exactly
# one probs vector for all batch dims or one for each.
stream = seed_stream.SeedStream(
seed, salt="PoissonLogNormalQuadratureCompound")
ids = self._mixture_distribution.sample(sample_shape=concat_vectors(
[n],
distribution_util.pick_vector(
self.mixture_distribution.is_scalar_batch(), [batch_size],
np.int32([]))),
seed=stream())
# We need to flatten batch dims in case mixture_distribution has its own
# batch dims.
ids = tf.reshape(ids,
shape=concat_vectors([n],
distribution_util.pick_vector(
self.is_scalar_batch(),
np.int32([]),
np.int32([-1]))))
# Stride `quadrature_size` for `batch_size` number of times.
offset = tf.range(start=0,
limit=batch_size * self._quadrature_size,
delta=self._quadrature_size,
dtype=ids.dtype)
ids += offset
rate = tf.gather(tf.reshape(self.distribution.rate, shape=[-1]), ids)
rate = tf.reshape(rate,
shape=concat_vectors([n], self.batch_shape_tensor()))
return tf.random.poisson(lam=rate,
shape=[],
dtype=self.dtype,
seed=seed)
def _event_shape_tensor(self,
override_event_shape=None,
base_event_shape_tensor=None):
override_event_shape = (tf.convert_to_tensor(
self._override_event_shape) if override_event_shape is None else
override_event_shape)
base_event_shape_tensor = (self.distribution.event_shape_tensor()
if base_event_shape_tensor is None else
base_event_shape_tensor)
return self.bijector.forward_event_shape_tensor(
distribution_util.pick_vector(
self._has_nonzero_rank(override_event_shape),
override_event_shape, base_event_shape_tensor))
def _sample_n(self, n, seed=None, **distribution_kwargs):
override_event_shape = tf.convert_to_tensor(self._override_event_shape)
override_batch_shape = tf.convert_to_tensor(self._override_batch_shape)
base_is_scalar_batch = self.distribution.is_scalar_batch()
needs_rotation = self._needs_rotation(override_event_shape,
override_batch_shape,
base_is_scalar_batch)
sample_shape = prefer_static.concat([
distribution_util.pick_vector(needs_rotation, self._empty, [n]),
override_batch_shape,
override_event_shape,
distribution_util.pick_vector(needs_rotation, [n], self._empty),
],
axis=0)
x = self.distribution.sample(sample_shape=sample_shape,
seed=seed,
**distribution_kwargs)
x = self._maybe_rotate_dims(x, override_event_shape,
override_batch_shape, base_is_scalar_batch)
# We'll apply the bijector in the `_call_sample_n` function.
return x
def make_batch_of_event_sample_matrices(
self,
x,
expand_batch_dim=True,
name="make_batch_of_event_sample_matrices"):
"""Reshapes/transposes `Distribution` `Tensor` from S+B+E to B_+E_+S_.
Where:
- `B_ = B if B or not expand_batch_dim else [1]`,
- `E_ = E if E else [1]`,
- `S_ = [tf.reduce_prod(S)]`.
Args:
x: `Tensor`.
expand_batch_dim: Python `bool`. If `True` the batch dims will be expanded
such that `batch_ndims >= 1`.
name: Python `str`. The name to give this op.
Returns:
x: `Tensor`. Input transposed/reshaped to `B_+E_+S_`.
sample_shape: `Tensor` (1D, `int32`).
"""
with self._name_scope(name, values=[x]):
x = tf.convert_to_tensor(x, name="x")
# x.shape: S+B+E
sample_shape, batch_shape, event_shape = self.get_shape(x)
event_shape = distribution_util.pick_vector(
self._event_ndims_is_0, [1], event_shape)
if expand_batch_dim:
batch_shape = distribution_util.pick_vector(
self._batch_ndims_is_0, [1], batch_shape)
new_shape = tf.concat([[-1], batch_shape, event_shape], 0)
x = tf.reshape(x, shape=new_shape)
# x.shape: [prod(S)]+B_+E_
x = distribution_util.rotate_transpose(x, shift=-1)
# x.shape: B_+E_+[prod(S)]
return x, sample_shape
def _event_shape_tensor(self,
override_event_shape=None,
base_event_shape_tensor=None):
override_event_shape = (tf.convert_to_tensor(
self._override_event_shape) if override_event_shape is None else
override_event_shape)
base_event_shape_tensor = (self.distribution.event_shape_tensor()
if base_event_shape_tensor is None else
base_event_shape_tensor)
# If the base distribution is not joint, use the base event shape override,
# if any.
if not self._base_is_joint:
base_event_shape_tensor = distribution_util.pick_vector(
self._has_nonzero_rank(override_event_shape),
override_event_shape, base_event_shape_tensor)
return self.bijector.forward_event_shape_tensor(
base_event_shape_tensor)
def __init__(self,
df,
loc=None,
scale_identity_multiplier=None,
scale_diag=None,
scale_tril=None,
scale_perturb_factor=None,
scale_perturb_diag=None,
validate_args=False,
allow_nan_stats=True,
name="VectorStudentT"):
"""Instantiates the vector Student's t-distributions on `R^k`.
The `batch_shape` is the broadcast between `df.batch_shape` and
`Affine.batch_shape` where `Affine` is constructed from `loc` and
`scale_*` arguments.
The `event_shape` is the event shape of `Affine.event_shape`.
Args:
df: Floating-point `Tensor`. The degrees of freedom of the
distribution(s). `df` must contain only positive values. Must be
scalar if `loc`, `scale_*` imply non-scalar batch_shape or must have the
same `batch_shape` implied by `loc`, `scale_*`.
loc: Floating-point `Tensor`. If this is set to `None`, no `loc` is
applied.
scale_identity_multiplier: floating point rank 0 `Tensor` representing a
scaling done to the identity matrix. When `scale_identity_multiplier =
scale_diag=scale_tril = None` then `scale += IdentityMatrix`. Otherwise
no scaled-identity-matrix is added to `scale`.
scale_diag: Floating-point `Tensor` representing the diagonal matrix.
`scale_diag` has shape [N1, N2, ..., k], which represents a k x k
diagonal matrix. When `None` no diagonal term is added to `scale`.
scale_tril: Floating-point `Tensor` representing the diagonal matrix.
`scale_diag` has shape [N1, N2, ..., k, k], which represents a k x k
lower triangular matrix. When `None` no `scale_tril` term is added to
`scale`. The upper triangular elements above the diagonal are ignored.
scale_perturb_factor: Floating-point `Tensor` representing factor matrix
with last two dimensions of shape `(k, r)`. When `None`, no rank-r
update is added to `scale`.
scale_perturb_diag: Floating-point `Tensor` representing the diagonal
matrix. `scale_perturb_diag` has shape [N1, N2, ..., r], which
represents an r x r Diagonal matrix. When `None` low rank updates will
take the form `scale_perturb_factor * scale_perturb_factor.T`.
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.
"""
parameters = dict(locals())
graph_parents = [df, loc, scale_identity_multiplier, scale_diag,
scale_tril, scale_perturb_factor, scale_perturb_diag]
with tf.name_scope(name) as name:
with tf.name_scope("init", values=graph_parents):
# The shape of the _VectorStudentT distribution is governed by the
# relationship between df.batch_shape and affine.batch_shape. In
# pseudocode the basic procedure is:
# if df.batch_shape is scalar:
# if affine.batch_shape is not scalar:
# # broadcast distribution.sample so
# # it has affine.batch_shape.
# self.batch_shape = affine.batch_shape
# else:
# if affine.batch_shape is scalar:
# # let affine broadcasting do its thing.
# self.batch_shape = df.batch_shape
# All of the above magic is actually handled by TransformedDistribution.
# Here we really only need to collect the affine.batch_shape and decide
# what we're going to pass in to TransformedDistribution's
# (override) batch_shape arg.
affine = bijectors.Affine(
shift=loc,
scale_identity_multiplier=scale_identity_multiplier,
scale_diag=scale_diag,
scale_tril=scale_tril,
scale_perturb_factor=scale_perturb_factor,
scale_perturb_diag=scale_perturb_diag,
validate_args=validate_args)
distribution = student_t.StudentT(
df=df,
loc=tf.zeros([], dtype=affine.dtype),
scale=tf.ones([], dtype=affine.dtype))
batch_shape, override_event_shape = (
distribution_util.shapes_from_loc_and_scale(
affine.shift, affine.scale))
override_batch_shape = distribution_util.pick_vector(
distribution.is_scalar_batch(), batch_shape,
tf.constant([], dtype=tf.int32))
super(_VectorStudentT, self).__init__(
distribution=distribution,
bijector=affine,
batch_shape=override_batch_shape,
event_shape=override_event_shape,
validate_args=validate_args,
name=name)
self._parameters = parameters
def __init__(self,
mixture_distribution,
components_distribution,
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.
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 mixture_distribution.dtype.is_integer`.
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.
"""
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 = (
s.shape[0].value if s.shape.with_rank_at_least(1)[0].value is not None
else tf.shape(s)[0])
if not mixture_distribution.dtype.is_integer:
raise ValueError(
"`mixture_distribution.dtype` ({}) is not over integers".format(
mixture_distribution.dtype.name))
if (mixture_distribution.event_shape.ndims is not None
and mixture_distribution.event_shape.ndims != 0):
raise ValueError("`mixture_distribution` must have scalar `event_dim`s")
elif validate_args:
self._runtime_assertions += [
tf.assert_rank(
mixture_distribution.event_shape_tensor(), 0,
message="`mixture_distribution` must have scalar `event_dim`s"),
]
mdbs = mixture_distribution.batch_shape
cdbs = components_distribution.batch_shape.with_rank_at_least(1)[:-1]
if mdbs.is_fully_defined() and cdbs.is_fully_defined():
if mdbs.ndims != 0 and mdbs != cdbs:
raise ValueError(
"`mixture_distribution.batch_shape` (`{}`) is not "
"compatible with `components_distribution.batch_shape` "
"(`{}`)".format(mdbs.as_list(), cdbs.as_list()))
elif validate_args:
mdbs = mixture_distribution.batch_shape_tensor()
cdbs = components_distribution.batch_shape_tensor()[:-1]
self._runtime_assertions += [
tf.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 = mixture_distribution.logits.shape.with_rank_at_least(1)[-1].value
kc = components_distribution.batch_shape.with_rank_at_least(1)[-1].value
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(mixture_distribution.logits)[-1]
kc = components_distribution.batch_shape_tensor()[-1]
self._runtime_assertions += [
tf.assert_equal(
km, kc,
message=("`mixture_distribution components` does not equal "
"`components_distribution.batch_shape[-1:]`")),
]
elif km is None:
km = tf.shape(mixture_distribution.logits)[-1]
self._num_components = km
super(MixtureSameFamily, self).__init__(
dtype=self._components_distribution.dtype,
reparameterization_type=reparameterization.NOT_REPARAMETERIZED,
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 _sample_n(self, n, seed=None):
stream = seed_stream.SeedStream(seed, salt="VectorDiffeomixture")
x = self.distribution.sample(
sample_shape=concat_vectors(
[n],
self.batch_shape_tensor(),
self.event_shape_tensor()),
seed=stream()) # shape: [n, B, e]
x = [aff.forward(x) for aff in self.endpoint_affine]
# Get ids as a [n, batch_size]-shaped matrix, unless batch_shape=[] then get
# ids as a [n]-shaped vector.
batch_size = self.batch_shape.num_elements()
if batch_size is None:
batch_size = tf.reduce_prod(self.batch_shape_tensor())
mix_batch_size = self.mixture_distribution.batch_shape.num_elements()
if mix_batch_size is None:
mix_batch_size = tf.reduce_prod(
self.mixture_distribution.batch_shape_tensor())
ids = self.mixture_distribution.sample(
sample_shape=concat_vectors(
[n],
distribution_util.pick_vector(
self.is_scalar_batch(),
np.int32([]),
[batch_size // mix_batch_size])),
seed=stream())
# We need to flatten batch dims in case mixture_distribution has its own
# batch dims.
ids = tf.reshape(
ids,
shape=concat_vectors([n],
distribution_util.pick_vector(
self.is_scalar_batch(), np.int32([]),
np.int32([-1]))))
# Stride `components * quadrature_size` for `batch_size` number of times.
stride = self.grid.shape.with_rank_at_least(
2)[-2:].num_elements()
if stride is None:
stride = tf.reduce_prod(tf.shape(self.grid)[-2:])
offset = tf.range(
start=0, limit=batch_size * stride, delta=stride, dtype=ids.dtype)
weight = tf.gather(tf.reshape(self.grid, shape=[-1]), ids + offset)
# At this point, weight flattened all batch dims into one.
# We also need to append a singleton to broadcast with event dims.
if self.batch_shape.is_fully_defined():
new_shape = [-1] + self.batch_shape.as_list() + [1]
else:
new_shape = tf.concat(([-1], self.batch_shape_tensor(), [1]), axis=0)
weight = tf.reshape(weight, shape=new_shape)
if len(x) != 2:
# We actually should have already triggered this exception. However as a
# policy we're putting this exception wherever we exploit the bimixture
# assumption.
raise NotImplementedError("Currently only bimixtures are supported; "
"len(scale)={} is not 2.".format(len(x)))
# Alternatively:
# x = weight * x[0] + (1. - weight) * x[1]
x = weight * (x[0] - x[1]) + x[1]
return x
def _sample_n(self, n, seed=None):
stream = seed_stream.SeedStream(seed, salt="VectorDiffeomixture")
x = self.distribution.sample(sample_shape=concat_vectors(
[n], self.batch_shape_tensor(), self.event_shape_tensor()),
seed=stream()) # shape: [n, B, e]
x = [aff.forward(x) for aff in self.endpoint_affine]
# Get ids as a [n, batch_size]-shaped matrix, unless batch_shape=[] then get
# ids as a [n]-shaped vector.
batch_size = tensorshape_util.num_elements(self.batch_shape)
if batch_size is None:
batch_size = tf.reduce_prod(input_tensor=self.batch_shape_tensor())
mix_batch_size = tensorshape_util.num_elements(
self.mixture_distribution.batch_shape)
if mix_batch_size is None:
mix_batch_size = tf.reduce_prod(
input_tensor=self.mixture_distribution.batch_shape_tensor())
ids = self.mixture_distribution.sample(sample_shape=concat_vectors(
[n],
distribution_util.pick_vector(self.is_scalar_batch(), np.int32([]),
[batch_size // mix_batch_size])),
seed=stream())
# We need to flatten batch dims in case mixture_distribution has its own
# batch dims.
ids = tf.reshape(ids,
shape=concat_vectors([n],
distribution_util.pick_vector(
self.is_scalar_batch(),
np.int32([]),
np.int32([-1]))))
# Stride `components * quadrature_size` for `batch_size` number of times.
stride = tensorshape_util.num_elements(
tensorshape_util.with_rank_at_least(self.grid.shape, 2)[-2:])
if stride is None:
stride = tf.reduce_prod(input_tensor=tf.shape(
input=self.grid)[-2:])
offset = tf.range(start=0,
limit=batch_size * stride,
delta=stride,
dtype=ids.dtype)
weight = tf.gather(tf.reshape(self.grid, shape=[-1]), ids + offset)
# At this point, weight flattened all batch dims into one.
# We also need to append a singleton to broadcast with event dims.
if tensorshape_util.is_fully_defined(self.batch_shape):
new_shape = [-1] + tensorshape_util.as_list(self.batch_shape) + [1]
else:
new_shape = tf.concat(([-1], self.batch_shape_tensor(), [1]),
axis=0)
weight = tf.reshape(weight, shape=new_shape)
if len(x) != 2:
# We actually should have already triggered this exception. However as a
# policy we're putting this exception wherever we exploit the bimixture
# assumption.
raise NotImplementedError(
"Currently only bimixtures are supported; "
"len(scale)={} is not 2.".format(len(x)))
# Alternatively:
# x = weight * x[0] + (1. - weight) * x[1]
x = weight * (x[0] - x[1]) + x[1]
return x
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 mixture_distribution.dtype.is_integer`.
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 mixture_distribution.dtype.is_integer:
raise ValueError(
"`mixture_distribution.dtype` ({}) is not over integers".
format(mixture_distribution.dtype.name))
if (mixture_distribution.event_shape.ndims is not None
and mixture_distribution.event_shape.ndims != 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 = components_distribution.batch_shape.with_rank_at_least(
1)[:-1]
if mdbs.is_fully_defined() and cdbs.is_fully_defined():
if mdbs.ndims != 0 and mdbs != cdbs:
raise ValueError(
"`mixture_distribution.batch_shape` (`{}`) is not "
"compatible with `components_distribution.batch_shape` "
"(`{}`)".format(mdbs.as_list(), cdbs.as_list()))
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(
mixture_distribution.logits.shape.with_rank_at_least(1)[-1])
kc = tf.compat.dimension_value(
components_distribution.batch_shape.with_rank_at_least(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 _event_shape_tensor(self):
return self.bijector.forward_event_shape_tensor(
distribution_util.pick_vector(
self._is_event_override,
self._override_event_shape,
self.distribution.event_shape_tensor()))
def _forward_log_det_jacobian(self, x):
# Let Y be a symmetric, positive definite matrix and write:
# Y = X X.T
# where X is lower-triangular.
#
# Observe that,
# dY[i,j]/dX[a,b]
# = d/dX[a,b] { X[i,:] X[j,:] }
# = sum_{d=1}^p { I[i=a] I[d=b] X[j,d] + I[j=a] I[d=b] X[i,d] }
#
# To compute the Jacobian dX/dY we must represent X,Y as vectors. Since Y is
# symmetric and X is lower-triangular, we need vectors of dimension:
# d = p (p + 1) / 2
# where X, Y are p x p matrices, p > 0. We use a row-major mapping, i.e.,
# k = { i (i + 1) / 2 + j i>=j
# { undef i<j
# and assume zero-based indexes. When k is undef, the element is dropped.
# Example:
# j k
# 0 1 2 3 /
# 0 [ 0 . . . ]
# i 1 [ 1 2 . . ]
# 2 [ 3 4 5 . ]
# 3 [ 6 7 8 9 ]
# Write vec[.] to indicate transforming a matrix to vector via k(i,j). (With
# slight abuse: k(i,j)=undef means the element is dropped.)
#
# We now show d vec[Y] / d vec[X] is lower triangular. Assuming both are
# defined, observe that k(i,j) < k(a,b) iff (1) i<a or (2) i=a and j<b.
# In both cases dvec[Y]/dvec[X]@[k(i,j),k(a,b)] = 0 since:
# (1) j<=i<a thus i,j!=a.
# (2) i=a>j thus i,j!=a.
#
# Since the Jacobian is lower-triangular, we need only compute the product
# of diagonal elements:
# d vec[Y] / d vec[X] @[k(i,j), k(i,j)]
# = X[j,j] + I[i=j] X[i,j]
# = 2 X[j,j].
# Since there is a 2 X[j,j] term for every lower-triangular element of X we
# conclude:
# |Jac(d vec[Y]/d vec[X])| = 2^p prod_{j=0}^{p-1} X[j,j]^{p-j}.
diag = tf.linalg.diag_part(x)
# We now ensure diag is columnar. Eg, if `diag = [1, 2, 3]` then the output
# is `[[1], [2], [3]]` and if `diag = [[1, 2, 3], [4, 5, 6]]` then the
# output is unchanged.
diag = self._make_columnar(diag)
with tf.control_dependencies(self._assertions(x)):
# Create a vector equal to: [p, p-1, ..., 2, 1].
if tf.compat.dimension_value(x.shape[-1]) is None:
p_int = tf.shape(x)[-1]
p_float = tf.cast(p_int, dtype=x.dtype)
else:
p_int = tf.compat.dimension_value(x.shape[-1])
p_float = dtype_util.as_numpy_dtype(x.dtype)(p_int)
exponents = tf.linspace(p_float, 1., p_int)
sum_weighted_log_diag = tf.squeeze(
tf.matmul(tf.math.log(diag), exponents[..., tf.newaxis]), axis=-1)
fldj = p_float * np.log(2.) + sum_weighted_log_diag
# We finally need to undo adding an extra column in non-scalar cases
# where there is a single matrix as input.
if tensorshape_util.rank(x.shape) is not None:
if tensorshape_util.rank(x.shape) == 2:
fldj = tf.squeeze(fldj, axis=-1)
return fldj
shape = tf.shape(fldj)
maybe_squeeze_shape = tf.concat([
shape[:-1],
distribution_util.pick_vector(
tf.equal(tf.rank(x), 2),
np.array([], dtype=np.int32), shape[-1:])], 0)
return tf.reshape(fldj, maybe_squeeze_shape)
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,
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.
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 mixture_distribution.dtype.is_integer`.
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.
"""
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 = (s.shape[0].value
if s.shape.with_rank_at_least(1)[0].value
is not None else tf.shape(s)[0])
if not mixture_distribution.dtype.is_integer:
raise ValueError(
"`mixture_distribution.dtype` ({}) is not over integers".
format(mixture_distribution.dtype.name))
if (mixture_distribution.event_shape.ndims is not None
and mixture_distribution.event_shape.ndims != 0):
raise ValueError(
"`mixture_distribution` must have scalar `event_dim`s")
elif validate_args:
self._runtime_assertions += [
control_flow_ops.assert_has_rank(
mixture_distribution.event_shape_tensor(),
0,
message=
"`mixture_distribution` must have scalar `event_dim`s"
),
]
mdbs = mixture_distribution.batch_shape
cdbs = components_distribution.batch_shape.with_rank_at_least(
1)[:-1]
if mdbs.is_fully_defined() and cdbs.is_fully_defined():
if mdbs.ndims != 0 and mdbs != cdbs:
raise ValueError(
"`mixture_distribution.batch_shape` (`{}`) is not "
"compatible with `components_distribution.batch_shape` "
"(`{}`)".format(mdbs.as_list(), cdbs.as_list()))
elif validate_args:
mdbs = mixture_distribution.batch_shape_tensor()
cdbs = components_distribution.batch_shape_tensor()[:-1]
self._runtime_assertions += [
control_flow_ops.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 = mixture_distribution.logits.shape.with_rank_at_least(
1)[-1].value
kc = components_distribution.batch_shape.with_rank_at_least(
1)[-1].value
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(mixture_distribution.logits)[-1]
kc = components_distribution.batch_shape_tensor()[-1]
self._runtime_assertions += [
control_flow_ops.assert_equal(
km,
kc,
message=(
"`mixture_distribution components` does not equal "
"`components_distribution.batch_shape[-1:]`")),
]
elif km is None:
km = tf.shape(mixture_distribution.logits)[-1]
self._num_components = km
super(MixtureSameFamily, self).__init__(
dtype=self._components_distribution.dtype,
reparameterization_type=reparameterization.NOT_REPARAMETERIZED,
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 _batch_shape_tensor(self):
return distribution_util.pick_vector(
self._is_batch_override,
self._override_batch_shape,
self.distribution.batch_shape_tensor())
def _forward_log_det_jacobian(self, x):
# Let Y be a symmetric, positive definite matrix and write:
# Y = X X.T
# where X is lower-triangular.
#
# Observe that,
# dY[i,j]/dX[a,b]
# = d/dX[a,b] { X[i,:] X[j,:] }
# = sum_{d=1}^p { I[i=a] I[d=b] X[j,d] + I[j=a] I[d=b] X[i,d] }
#
# To compute the Jacobian dX/dY we must represent X,Y as vectors. Since Y is
# symmetric and X is lower-triangular, we need vectors of dimension:
# d = p (p + 1) / 2
# where X, Y are p x p matrices, p > 0. We use a row-major mapping, i.e.,
# k = { i (i + 1) / 2 + j i>=j
# { undef i<j
# and assume zero-based indexes. When k is undef, the element is dropped.
# Example:
# j k
# 0 1 2 3 /
# 0 [ 0 . . . ]
# i 1 [ 1 2 . . ]
# 2 [ 3 4 5 . ]
# 3 [ 6 7 8 9 ]
# Write vec[.] to indicate transforming a matrix to vector via k(i,j). (With
# slight abuse: k(i,j)=undef means the element is dropped.)
#
# We now show d vec[Y] / d vec[X] is lower triangular. Assuming both are
# defined, observe that k(i,j) < k(a,b) iff (1) i<a or (2) i=a and j<b.
# In both cases dvec[Y]/dvec[X]@[k(i,j),k(a,b)] = 0 since:
# (1) j<=i<a thus i,j!=a.
# (2) i=a>j thus i,j!=a.
#
# Since the Jacobian is lower-triangular, we need only compute the product
# of diagonal elements:
# d vec[Y] / d vec[X] @[k(i,j), k(i,j)]
# = X[j,j] + I[i=j] X[i,j]
# = 2 X[j,j].
# Since there is a 2 X[j,j] term for every lower-triangular element of X we
# conclude:
# |Jac(d vec[Y]/d vec[X])| = 2^p prod_{j=0}^{p-1} X[j,j]^{p-j}.
diag = tf.matrix_diag_part(x)
# We now ensure diag is columnar. Eg, if `diag = [1, 2, 3]` then the output
# is `[[1], [2], [3]]` and if `diag = [[1, 2, 3], [4, 5, 6]]` then the
# output is unchanged.
diag = self._make_columnar(diag)
if self.validate_args:
is_matrix = tf.assert_rank_at_least(
x, 2, message="Input must be a (batch of) matrix.")
shape = tf.shape(x)
is_square = tf.assert_equal(
shape[-2],
shape[-1],
message="Input must be a (batch of) square matrix.")
# Assuming lower-triangular means we only need check diag>0.
is_positive_definite = tf.assert_positive(
diag, message="Input must be positive definite.")
x = control_flow_ops.with_dependencies(
[is_matrix, is_square, is_positive_definite], x)
# Create a vector equal to: [p, p-1, ..., 2, 1].
if x.shape.ndims is None or x.shape[-1].value is None:
p_int = tf.shape(x)[-1]
p_float = tf.cast(p_int, dtype=x.dtype)
else:
p_int = x.shape[-1].value
p_float = np.array(p_int, dtype=x.dtype.as_numpy_dtype)
exponents = tf.linspace(p_float, 1., p_int)
sum_weighted_log_diag = tf.squeeze(
tf.matmul(tf.log(diag), exponents[..., tf.newaxis]), axis=-1)
fldj = p_float * np.log(2.) + sum_weighted_log_diag
# We finally need to undo adding an extra column in non-scalar cases
# where there is a single matrix as input.
if x.shape.ndims is not None:
if x.shape.ndims == 2:
fldj = tf.squeeze(fldj, axis=-1)
return fldj
shape = tf.shape(fldj)
maybe_squeeze_shape = tf.concat([
shape[:-1],
distribution_util.pick_vector(
tf.equal(tf.rank(x), 2),
np.array([], dtype=np.int32), shape[-1:])], 0)
return tf.reshape(fldj, maybe_squeeze_shape)
def __init__(self,
df,
loc=None,
scale_identity_multiplier=None,
scale_diag=None,
scale_tril=None,
scale_perturb_factor=None,
scale_perturb_diag=None,
validate_args=False,
allow_nan_stats=True,
name="VectorStudentT"):
"""Instantiates the vector Student's t-distributions on `R^k`.
The `batch_shape` is the broadcast between `df.batch_shape` and
`Affine.batch_shape` where `Affine` is constructed from `loc` and
`scale_*` arguments.
The `event_shape` is the event shape of `Affine.event_shape`.
Args:
df: Floating-point `Tensor`. The degrees of freedom of the
distribution(s). `df` must contain only positive values. Must be
scalar if `loc`, `scale_*` imply non-scalar batch_shape or must have the
same `batch_shape` implied by `loc`, `scale_*`.
loc: Floating-point `Tensor`. If this is set to `None`, no `loc` is
applied.
scale_identity_multiplier: floating point rank 0 `Tensor` representing a
scaling done to the identity matrix. When `scale_identity_multiplier =
scale_diag=scale_tril = None` then `scale += IdentityMatrix`. Otherwise
no scaled-identity-matrix is added to `scale`.
scale_diag: Floating-point `Tensor` representing the diagonal matrix.
`scale_diag` has shape [N1, N2, ..., k], which represents a k x k
diagonal matrix. When `None` no diagonal term is added to `scale`.
scale_tril: Floating-point `Tensor` representing the diagonal matrix.
`scale_diag` has shape [N1, N2, ..., k, k], which represents a k x k
lower triangular matrix. When `None` no `scale_tril` term is added to
`scale`. The upper triangular elements above the diagonal are ignored.
scale_perturb_factor: Floating-point `Tensor` representing factor matrix
with last two dimensions of shape `(k, r)`. When `None`, no rank-r
update is added to `scale`.
scale_perturb_diag: Floating-point `Tensor` representing the diagonal
matrix. `scale_perturb_diag` has shape [N1, N2, ..., r], which
represents an r x r Diagonal matrix. When `None` low rank updates will
take the form `scale_perturb_factor * scale_perturb_factor.T`.
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.
"""
parameters = dict(locals())
graph_parents = [
df, loc, scale_identity_multiplier, scale_diag, scale_tril,
scale_perturb_factor, scale_perturb_diag
]
with tf.name_scope(name) as name:
with tf.name_scope("init"):
dtype = dtype_util.common_dtype(graph_parents, tf.float32)
df = tf.convert_to_tensor(value=df, name="df", dtype=dtype)
# The shape of the _VectorStudentT distribution is governed by the
# relationship between df.batch_shape and affine.batch_shape. In
# pseudocode the basic procedure is:
# if df.batch_shape is scalar:
# if affine.batch_shape is not scalar:
# # broadcast distribution.sample so
# # it has affine.batch_shape.
# self.batch_shape = affine.batch_shape
# else:
# if affine.batch_shape is scalar:
# # let affine broadcasting do its thing.
# self.batch_shape = df.batch_shape
# All of the above magic is actually handled by TransformedDistribution.
# Here we really only need to collect the affine.batch_shape and decide
# what we're going to pass in to TransformedDistribution's
# (override) batch_shape arg.
affine = affine_bijector.Affine(
shift=loc,
scale_identity_multiplier=scale_identity_multiplier,
scale_diag=scale_diag,
scale_tril=scale_tril,
scale_perturb_factor=scale_perturb_factor,
scale_perturb_diag=scale_perturb_diag,
validate_args=validate_args,
dtype=dtype)
distribution = student_t.StudentT(
df=df,
loc=tf.zeros([], dtype=affine.dtype),
scale=tf.ones([], dtype=affine.dtype))
batch_shape, override_event_shape = (
distribution_util.shapes_from_loc_and_scale(
affine.shift, affine.scale))
override_batch_shape = distribution_util.pick_vector(
distribution.is_scalar_batch(), batch_shape,
tf.constant([], dtype=tf.int32))
super(_VectorStudentT,
self).__init__(distribution=distribution,
bijector=affine,
batch_shape=override_batch_shape,
event_shape=override_event_shape,
validate_args=validate_args,
name=name)
self._parameters = parameters
def _event_shape_tensor(self):
return self.bijector.forward_event_shape_tensor(
distribution_util.pick_vector(
self._is_event_override,
self._override_event_shape,
self.distribution.event_shape_tensor()))
def _batch_shape_tensor(self):
return distribution_util.pick_vector(
self._is_batch_override,
self._override_batch_shape,
self.distribution.batch_shape_tensor())
