def __init__(self,
loc=None,
scale_tril_log_diag=None,
validate_args=False,
allow_nan_stats=True,
name="MultivariateNormalTriL"):
parameters = dict(locals())
def _convert_to_tensor(x, name, dtype):
return None if x is None else tf.convert_to_tensor(
x, name=name, dtype=dtype)
if loc is None and scale_tril_log_diag is None:
raise ValueError(
"Must specify one or both of `loc`, `scale_tril`.")
with tf.name_scope(name) as name:
with tf.name_scope("init", values=[loc, scale_tril_log_diag]):
dtype = dtype_util.common_dtype([loc, scale_tril_log_diag],
tf.float32)
loc = _convert_to_tensor(loc, name="loc", dtype=dtype)
scale_tril_log_diag = _convert_to_tensor(scale_tril_log_diag,
name="scale_tril",
dtype=dtype)
if scale_tril_log_diag is None:
scale = custom_lin_op.LinearOperatorLogIdentity(
num_rows=distribution_util.dimension_size(loc, -1),
dtype=loc.dtype,
is_self_adjoint=True,
is_positive_definite=True,
assert_proper_shapes=validate_args)
else:
# No need to validate that scale_tril is non-singular.
# LinearOperatorLowerTriangular has an assert_non_singular
# method that is called by the Bijector.
scale = custom_lin_op.LinearOperatorLowerTriangularLogDiagonal(
scale_tril_log_diag,
is_non_singular=True,
is_self_adjoint=False,
is_positive_definite=False)
super(MultivariateNormalTriLLogDiagonal,
self).__init__(loc=loc,
scale=scale,
validate_args=validate_args,
allow_nan_stats=allow_nan_stats,
name=name)
self._parameters = parameters
def __init__(self,
loc=None,
scale_diag=None,
scale_perturb_factor=None,
scale_perturb_diag=None,
validate_args=False,
allow_nan_stats=True,
name='MultivariateNormalDiagPlusLowRank'):
"""Construct Multivariate Normal distribution on `R^k`.
The `batch_shape` is the broadcast shape between `loc` and `scale`
arguments.
The `event_shape` is given by last dimension of the matrix implied by
`scale`. The last dimension of `loc` (if provided) must broadcast with this.
Recall that `covariance = scale @ scale.T`. A (non-batch) `scale` matrix is:
```none
scale = diag(scale_diag) +
scale_perturb_factor @ diag(scale_perturb_diag) @ scale_perturb_factor.T
```
where:
* `scale_diag.shape = [k]`,
* `scale_perturb_factor.shape = [k, r]`, typically `k >> r`, and,
* `scale_perturb_diag.shape = [r]`.
Additional leading dimensions (if any) will index batches.
Args:
loc: Floating-point `Tensor`. If this is set to `None`, `loc` is
implicitly `0`. When specified, must have shape `[B1, ..., Bb, k]` where
`b >= 0` and `k` is the event size.
scale_diag: Floating-point `Tensor` representing a non-singular diagonal
matrix added to `scale`. Must have shape `[B1, ..., Bb, k]`, `b >= 0`,
and characterizes `b`-batches of `k x k` diagonal matrices added to
`scale`. When `scale_diag` is `None` it defaults to the `Identity`
matrix.
scale_perturb_factor: Floating-point `Tensor` representing a rank-`r`
perturbation added to `scale`. Must have shape `[B1, ..., Bb, k, r]`,
`b >= 0`, and characterizes `b`-batches of rank-`r` updates to `scale`.
When `None`, no rank-`r` update is added to `scale`.
scale_perturb_diag: Floating-point `Tensor` representing a non-singular
diagonal matrix inside the rank-`r` perturbation added to `scale`. Must
have shape `[B1, ..., Bb, r]`, `b >= 0`, and characterizes `b`-batches
of `r x r` diagonal matrices inside the perturbation added to `scale`.
When `None`, an identity matrix is used inside the perturbation. Can
only be specified if `scale_perturb_factor` is also specified.
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 at most `scale_identity_multiplier` is specified.
"""
parameters = dict(locals())
if all(x is None for x in [loc, scale_diag, scale_perturb_factor]):
raise ValueError('At least one of `loc`, `scale_diag`, or '
'`scale_perturb_factor` required.')
if scale_perturb_diag is not None and scale_perturb_factor is None:
raise ValueError('`scale_perturb_diag` should be set only if '
'`scale_perturb_factor` is also set.')
with tf.name_scope(name) as name:
dtype = dtype_util.common_dtype(
[loc, scale_diag, scale_perturb_factor, scale_perturb_diag],
tf.float32)
loc = tensor_util.convert_nonref_to_tensor(loc,
dtype=dtype,
name='loc')
scale_diag = tensor_util.convert_nonref_to_tensor(
scale_diag, dtype=dtype, name='scale_diag')
scale_perturb_factor = tensor_util.convert_nonref_to_tensor(
scale_perturb_factor, dtype=dtype, name='scale_perturb_factor')
scale_perturb_diag = tensor_util.convert_nonref_to_tensor(
scale_perturb_diag, dtype=dtype, name='scale_perturb_diag')
if scale_diag is not None:
scale = tf.linalg.LinearOperatorDiag(
diag=scale_diag,
is_non_singular=True,
is_self_adjoint=True,
is_positive_definite=False)
else:
# This might not be tape-safe if shape unknown and assigned to later.
if loc is not None:
num_rows = distribution_util.dimension_size(loc, -1)
else:
num_rows = distribution_util.dimension_size(
scale_perturb_factor, -2)
scale = tf.linalg.LinearOperatorIdentity(
num_rows=num_rows,
dtype=dtype,
is_self_adjoint=True,
is_positive_definite=True,
assert_proper_shapes=validate_args)
if scale_perturb_factor is not None:
scale = tf.linalg.LinearOperatorLowRankUpdate(
scale,
u=scale_perturb_factor,
diag_update=scale_perturb_diag,
is_diag_update_positive=scale_perturb_diag is None,
is_self_adjoint=True,
is_non_singular=True,
is_square=True)
super(MultivariateNormalDiagPlusLowRank,
self).__init__(loc=loc,
scale=scale,
validate_args=validate_args,
allow_nan_stats=allow_nan_stats,
name=name)
self._parameters = parameters
def __init__(self,
loc=None,
scale_tril=None,
validate_args=False,
allow_nan_stats=True,
name='MultivariateNormalTriL'):
"""Construct Multivariate Normal distribution on `R^k`.
The `batch_shape` is the broadcast shape between `loc` and `scale`
arguments.
The `event_shape` is given by last dimension of the matrix implied by
`scale`. The last dimension of `loc` (if provided) must broadcast with this.
Recall that `covariance = scale @ scale.T`. A (non-batch) `scale` matrix is:
```none
scale = scale_tril
```
where `scale_tril` is lower-triangular `k x k` matrix with non-zero
diagonal, i.e., `tf.diag_part(scale_tril) != 0`.
Additional leading dimensions (if any) will index batches.
Args:
loc: Floating-point `Tensor`. If this is set to `None`, `loc` is
implicitly `0`. When specified, may have shape `[B1, ..., Bb, k]` where
`b >= 0` and `k` is the event size.
scale_tril: Floating-point, lower-triangular `Tensor` with non-zero
diagonal elements. `scale_tril` has shape `[B1, ..., Bb, k, k]` where
`b >= 0` and `k` is the event size.
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 neither `loc` nor `scale_tril` are specified.
"""
parameters = dict(locals())
if loc is None and scale_tril is None:
raise ValueError(
'Must specify one or both of `loc`, `scale_tril`.')
with tf.name_scope(name) as name:
dtype = dtype_util.common_dtype([loc, scale_tril], tf.float32)
loc = tensor_util.convert_nonref_to_tensor(loc,
name='loc',
dtype=dtype)
scale_tril = tensor_util.convert_nonref_to_tensor(
scale_tril, name='scale_tril', dtype=dtype)
self._scale_tril = scale_tril
if scale_tril is None:
scale = tf.linalg.LinearOperatorIdentity(
num_rows=distribution_util.dimension_size(loc, -1),
dtype=loc.dtype,
is_self_adjoint=True,
is_positive_definite=True,
assert_proper_shapes=validate_args)
else:
# No need to validate that scale_tril is non-singular.
# LinearOperatorLowerTriangular has an assert_non_singular
# method that is called by the Bijector.
scale = tf.linalg.LinearOperatorLowerTriangular(
scale_tril,
is_non_singular=True,
is_self_adjoint=False,
is_positive_definite=False)
super(MultivariateNormalTriL,
self).__init__(loc=loc,
scale=scale,
validate_args=validate_args,
allow_nan_stats=allow_nan_stats,
name=name)
self._parameters = parameters
def _create_scale_operator(self, identity_multiplier, diag, tril,
perturb_diag, perturb_factor, shift,
validate_args, dtype):
"""Construct `scale` from various components.
Args:
identity_multiplier: floating point rank 0 `Tensor` representing a scaling
done to the identity matrix.
diag: Floating-point `Tensor` representing the diagonal matrix.`diag` has
shape `[N1, N2, ... k]`, which represents a k x k diagonal matrix.
tril: Floating-point `Tensor` representing the lower triangular matrix.
`tril` has shape `[N1, N2, ... k, k]`, which represents a k x k lower
triangular matrix.
perturb_diag: Floating-point `Tensor` representing the diagonal matrix of
the low rank update.
perturb_factor: Floating-point `Tensor` representing factor matrix.
shift: Floating-point `Tensor` representing `shift in `scale @ X + shift`.
validate_args: Python `bool` indicating whether arguments should be
checked for correctness.
dtype: `DType` for arg `Tensor` conversions.
Returns:
scale. In the case of scaling by a constant, scale is a
floating point `Tensor`. Otherwise, scale is a `LinearOperator`.
Raises:
ValueError: if all of `tril`, `diag` and `identity_multiplier` are `None`.
"""
identity_multiplier = _as_tensor(identity_multiplier,
"identity_multiplier", dtype)
diag = _as_tensor(diag, "diag", dtype)
tril = _as_tensor(tril, "tril", dtype)
perturb_diag = _as_tensor(perturb_diag, "perturb_diag", dtype)
perturb_factor = _as_tensor(perturb_factor, "perturb_factor", dtype)
# If possible, use the low rank update to infer the shape of
# the identity matrix, when scale represents a scaled identity matrix
# with a low rank update.
shape_hint = None
if perturb_factor is not None:
shape_hint = distribution_util.dimension_size(perturb_factor,
axis=-2)
if self._is_only_identity_multiplier:
if validate_args:
return distribution_util.with_dependencies([
assert_util.assert_none_equal(
identity_multiplier,
tf.zeros([], identity_multiplier.dtype),
["identity_multiplier should be non-zero."])
], identity_multiplier)
return identity_multiplier
scale = _make_tril_scale(loc=shift,
scale_tril=tril,
scale_diag=diag,
scale_identity_multiplier=identity_multiplier,
validate_args=validate_args,
assert_positive=False,
shape_hint=shape_hint)
if perturb_factor is not None:
return tf.linalg.LinearOperatorLowRankUpdate(
scale,
u=perturb_factor,
diag_update=perturb_diag,
is_diag_update_positive=perturb_diag is None,
is_non_singular=True, # Implied by is_positive_definite=True.
is_self_adjoint=True,
is_positive_definite=True,
is_square=True)
return scale
def __init__(self,
loc=None,
scale_tril=None,
validate_args=False,
allow_nan_stats=True,
name="MultivariateNormalTriL"):
"""Construct Multivariate Normal distribution on `R^k`.
The `batch_shape` is the broadcast shape between `loc` and `scale`
arguments.
The `event_shape` is given by last dimension of the matrix implied by
`scale`. The last dimension of `loc` (if provided) must broadcast with this.
Recall that `covariance = scale @ scale.T`. A (non-batch) `scale` matrix is:
```none
scale = scale_tril
```
where `scale_tril` is lower-triangular `k x k` matrix with non-zero
diagonal, i.e., `tf.diag_part(scale_tril) != 0`.
Additional leading dimensions (if any) will index batches.
Args:
loc: Floating-point `Tensor`. If this is set to `None`, `loc` is
implicitly `0`. When specified, may have shape `[B1, ..., Bb, k]` where
`b >= 0` and `k` is the event size.
scale_tril: Floating-point, lower-triangular `Tensor` with non-zero
diagonal elements. `scale_tril` has shape `[B1, ..., Bb, k, k]` where
`b >= 0` and `k` is the event size.
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 neither `loc` nor `scale_tril` are specified.
"""
parameters = dict(locals())
def _convert_to_tensor(x, name, dtype):
return None if x is None else tf.convert_to_tensor(
x, name=name, dtype=dtype)
if loc is None and scale_tril is None:
raise ValueError("Must specify one or both of `loc`, `scale_tril`.")
with tf.name_scope(name) as name:
with tf.name_scope("init", values=[loc, scale_tril]):
dtype = dtype_util.common_dtype([loc, scale_tril], tf.float32)
loc = _convert_to_tensor(loc, name="loc", dtype=dtype)
scale_tril = _convert_to_tensor(
scale_tril, name="scale_tril", dtype=dtype)
if scale_tril is None:
scale = tf.linalg.LinearOperatorIdentity(
num_rows=distribution_util.dimension_size(loc, -1),
dtype=loc.dtype,
is_self_adjoint=True,
is_positive_definite=True,
assert_proper_shapes=validate_args)
else:
# No need to validate that scale_tril is non-singular.
# LinearOperatorLowerTriangular has an assert_non_singular
# method that is called by the Bijector.
scale = tf.linalg.LinearOperatorLowerTriangular(
scale_tril,
is_non_singular=True,
is_self_adjoint=False,
is_positive_definite=False)
super(MultivariateNormalTriL, self).__init__(
loc=loc,
scale=scale,
validate_args=validate_args,
allow_nan_stats=allow_nan_stats,
name=name)
self._parameters = parameters
def _create_scale_operator(self, identity_multiplier, diag, tril,
perturb_diag, perturb_factor, shift,
validate_args):
"""Construct `scale` from various components.
Args:
identity_multiplier: floating point rank 0 `Tensor` representing a scaling
done to the identity matrix.
diag: Floating-point `Tensor` representing the diagonal matrix.
`scale_diag` has shape [N1, N2, ... k], which represents a k x k
diagonal matrix.
tril: Floating-point `Tensor` representing the diagonal matrix.
`scale_tril` has shape [N1, N2, ... k], which represents a k x k lower
triangular matrix.
perturb_diag: Floating-point `Tensor` representing the diagonal matrix of
the low rank update.
perturb_factor: Floating-point `Tensor` representing factor matrix.
shift: Floating-point `Tensor` representing `shift in `scale @ X + shift`.
validate_args: Python `bool` indicating whether arguments should be
checked for correctness.
Returns:
scale. In the case of scaling by a constant, scale is a
floating point `Tensor`. Otherwise, scale is a `LinearOperator`.
Raises:
ValueError: if all of `tril`, `diag` and `identity_multiplier` are `None`.
"""
identity_multiplier = _as_tensor(identity_multiplier, "identity_multiplier")
diag = _as_tensor(diag, "diag")
tril = _as_tensor(tril, "tril")
perturb_diag = _as_tensor(perturb_diag, "perturb_diag")
perturb_factor = _as_tensor(perturb_factor, "perturb_factor")
# If possible, use the low rank update to infer the shape of
# the identity matrix, when scale represents a scaled identity matrix
# with a low rank update.
shape_hint = None
if perturb_factor is not None:
shape_hint = distribution_util.dimension_size(perturb_factor, axis=-2)
if self._is_only_identity_multiplier:
if validate_args:
return control_flow_ops.with_dependencies([
tf.assert_none_equal(identity_multiplier,
tf.zeros([], identity_multiplier.dtype),
["identity_multiplier should be non-zero."])
], identity_multiplier)
return identity_multiplier
scale = distribution_util.make_tril_scale(
loc=shift,
scale_tril=tril,
scale_diag=diag,
scale_identity_multiplier=identity_multiplier,
validate_args=validate_args,
assert_positive=False,
shape_hint=shape_hint)
if perturb_factor is not None:
return tf.linalg.LinearOperatorLowRankUpdate(
scale,
u=perturb_factor,
diag_update=perturb_diag,
is_diag_update_positive=perturb_diag is None,
is_non_singular=True, # Implied by is_positive_definite=True.
is_self_adjoint=True,
is_positive_definite=True,
is_square=True)
return scale
