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 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 = ops.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 = array_ops.concat([[-1], batch_shape, event_shape], 0)
x = array_ops.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 _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)
return self.bijector.forward(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)
return self.bijector.forward(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 _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.get_shape().ndims is not None:
if x.get_shape().ndims == 1:
x = x[array_ops.newaxis, :]
return x
shape = array_ops.shape(x)
maybe_expanded_shape = array_ops.concat([
shape[:-1],
distribution_util.pick_vector(
math_ops.equal(array_ops.rank(x), 1),
[1], np.array([], dtype=np.int32)),
shape[-1:],
], 0)
return array_ops.reshape(x, maybe_expanded_shape)
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 = (np.prod(self.batch_shape.as_list(), dtype=np.int32)
if self.batch_shape.is_fully_defined() else
math_ops.reduce_prod(self.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])),
seed=distribution_util.gen_new_seed(
seed, "poisson_lognormal_quadrature_compound"))
# Stride `quadrature_polynomial_degree` for `batch_size` number of times.
offset = math_ops.range(start=0,
limit=batch_size * self._degree,
delta=self._degree,
dtype=ids.dtype)
ids += offset
rate = array_ops.gather(
array_ops.reshape(self.distribution.rate, shape=[-1]), ids)
rate = array_ops.reshape(rate,
shape=concat_vectors(
[n], self.batch_shape_tensor()))
return random_ops.random_poisson(lam=rate,
shape=[],
dtype=self.dtype,
seed=seed)
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.get_shape().ndims is not None:
if x.get_shape().ndims == 1:
x = x[array_ops.newaxis, :]
return x
shape = array_ops.shape(x)
maybe_expanded_shape = array_ops.concat([
shape[:-1],
distribution_util.pick_vector(math_ops.equal(array_ops.rank(x), 1),
[1], np.array([], dtype=np.int32)),
shape[-1:],
], 0)
return array_ops.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 = math_ops.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 = array_ops.rank(x)
expanded_shape = util.pick_vector(
math_ops.equal(ndims, 0),
np.array([1], dtype=np.int32), array_ops.shape(x))
x = array_ops.reshape(x, expanded_shape)
elif ndims == 0:
# Definitely expand_dims.
if x_static_val is not None:
x = ops.convert_to_tensor(
np.array([x_static_val], dtype=x.dtype.as_numpy_dtype()),
name=name)
else:
x = array_ops.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.
batch_size = (np.prod(self.batch_shape.as_list(), dtype=np.int32)
if self.batch_shape.is_fully_defined()
else math_ops.reduce_prod(self.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])),
seed=distribution_util.gen_new_seed(
seed, "poisson_lognormal_quadrature_compound"))
# Stride `quadrature_degree` for `batch_size` number of times.
offset = math_ops.range(start=0,
limit=batch_size * len(self.quadrature_probs),
delta=len(self.quadrature_probs),
dtype=ids.dtype)
ids += offset
rate = array_ops.gather(
array_ops.reshape(self.distribution.rate, shape=[-1]), ids)
rate = array_ops.reshape(
rate, shape=concat_vectors([n], self.batch_shape_tensor()))
return random_ops.random_poisson(
lam=rate, shape=[], dtype=self.dtype, seed=seed)
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 = math_ops.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 = array_ops.rank(x)
expanded_shape = util.pick_vector(math_ops.equal(ndims, 0),
np.array([1], dtype=np.int32),
array_ops.shape(x))
x = array_ops.reshape(x, expanded_shape)
elif ndims == 0:
# Definitely expand_dims.
if x_static_val is not None:
x = ops.convert_to_tensor(np.array(
[x_static_val], dtype=x.dtype.as_numpy_dtype()),
name=name)
else:
x = array_ops.reshape(x, [1])
elif ndims != 1:
raise ValueError("Input is neither scalar nor vector.")
return x, prod
def testCorrectlyPicksVector(self):
with self.test_session():
x = np.arange(10, 12)
y = np.arange(15, 18)
self.assertAllEqual(
x,
distribution_util.pick_vector(math_ops.less(0, 5), x,
y).eval())
self.assertAllEqual(
y,
distribution_util.pick_vector(math_ops.less(5, 0), x,
y).eval())
self.assertAllEqual(x,
distribution_util.pick_vector(
constant_op.constant(True), x,
y)) # No eval.
self.assertAllEqual(y,
distribution_util.pick_vector(
constant_op.constant(False), x,
y)) # No eval.
def _pad_mix_dims(self, x):
with ops.name_scope("pad_mix_dims", values=[x]):
def _get_ndims(d):
if d.batch_shape.ndims is not None:
return d.batch_shape.ndims
return array_ops.shape(d.batch_shape_tensor())[0]
dist_batch_ndims = _get_ndims(self)
cat_batch_ndims = _get_ndims(self.mixture_distribution)
bnd = distribution_util.pick_vector(
self.mixture_distribution.is_scalar_batch(),
[dist_batch_ndims], [cat_batch_ndims])[0]
s = array_ops.shape(x)
x = array_ops.reshape(x, shape=array_ops.concat([
s[:-1],
array_ops.ones([bnd], dtype=dtypes.int32),
s[-1:],
array_ops.ones([self._event_ndims], dtype=dtypes.int32),
], axis=0))
return x
def _pad_mix_dims(self, x):
with ops.name_scope("pad_mix_dims", values=[x]):
def _get_ndims(d):
if d.batch_shape.ndims is not None:
return d.batch_shape.ndims
return array_ops.shape(d.batch_shape_tensor())[0]
dist_batch_ndims = _get_ndims(self)
cat_batch_ndims = _get_ndims(self.mixture_distribution)
bnd = distribution_util.pick_vector(
self.mixture_distribution.is_scalar_batch(),
[dist_batch_ndims], [cat_batch_ndims])[0]
s = array_ops.shape(x)
x = array_ops.reshape(x, shape=array_ops.concat([
s[:-1],
array_ops.ones([bnd], dtype=dtypes.int32),
s[-1:],
array_ops.ones([self._event_ndims], dtype=dtypes.int32),
], axis=0))
return x
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 = array_ops.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 = check_ops.assert_rank_at_least(
x, 2, message="Input must be a (batch of) matrix.")
shape = array_ops.shape(x)
is_square = check_ops.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 = check_ops.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.get_shape().ndims is None or x.get_shape().dims[-1].value is None:
p_int = array_ops.shape(x)[-1]
p_float = math_ops.cast(p_int, dtype=x.dtype)
else:
p_int = x.get_shape().dims[-1].value
p_float = np.array(p_int, dtype=x.dtype.as_numpy_dtype)
exponents = math_ops.linspace(p_float, 1., p_int)
sum_weighted_log_diag = array_ops.squeeze(math_ops.matmul(
math_ops.log(diag), exponents[..., array_ops.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.get_shape().ndims is not None:
if x.get_shape().ndims == 2:
fldj = array_ops.squeeze(fldj, axis=-1)
return fldj
shape = array_ops.shape(fldj)
maybe_squeeze_shape = array_ops.concat([
shape[:-1],
distribution_util.pick_vector(math_ops.equal(array_ops.rank(x), 2),
np.array([], dtype=np.int32),
shape[-1:])
], 0)
return array_ops.reshape(fldj, maybe_squeeze_shape)
def _batch_shape_tensor(self):
return distribution_util.pick_vector(
self._is_batch_override, self._override_batch_shape,
self.distribution.batch_shape_tensor())
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.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.get_shape().ndims is None or x.get_shape()[-1].value is None:
p_int = tf.shape(x)[-1]
p_float = tf.cast(p_int, dtype=x.dtype)
else:
p_int = x.get_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.get_shape().ndims is not None:
if x.get_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 = locals()
graph_parents = [df, loc, scale_identity_multiplier, scale_diag,
scale_tril, scale_perturb_factor, scale_perturb_diag]
with ops.name_scope(name):
with ops.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=array_ops.zeros([], dtype=affine.dtype),
scale=array_ops.ones([], dtype=affine.dtype))
batch_shape, override_event_shape = _infer_shapes(
affine.scale, affine.shift)
override_batch_shape = distribution_util.pick_vector(
distribution.is_scalar_batch(),
batch_shape,
constant_op.constant([], dtype=dtypes.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 _batch_shape_tensor(self):
return distribution_util.pick_vector(
self._is_batch_override,
self._override_batch_shape,
self.distribution.batch_shape_tensor())
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 __init__(self,
mixture_distribution,
components_distribution,
validate_args=False,
allow_nan_stats=True,
name="MixtureSameFamily"):
"""Construct a `MixtureSameFamily` distribution.
Args:
mixture_distribution: `tf.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: `tf.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 = distribution_util.parent_frame_arguments()
with ops.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 array_ops.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_util.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 = array_ops.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 = array_ops.shape(mixture_distribution.logits)[-1]
self._num_components = km
super(MixtureSameFamily, self).__init__(
dtype=self._components_distribution.dtype,
reparameterization_type=distribution.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 __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 = locals()
graph_parents = [df, loc, scale_identity_multiplier, scale_diag,
scale_tril, scale_perturb_factor, scale_perturb_diag]
with ops.name_scope(name):
with ops.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=array_ops.zeros([], dtype=affine.dtype),
scale=array_ops.ones([], dtype=affine.dtype))
batch_shape, override_event_shape = _infer_shapes(
affine.scale, affine.shift)
override_batch_shape = distribution_util.pick_vector(
distribution.is_scalar_batch(),
batch_shape,
constant_op.constant([], dtype=dtypes.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: `tf.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: `tf.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_util.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=tf.distributions.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)