def testAssertPositive(self):
with self.test_session():
with self.assertRaisesOpError("diagonal part must be positive"):
scale = distribution_util.make_diag_scale(
scale_diag=[[-1., 1], [1., 1.]],
validate_args=True,
assert_positive=True)
scale.to_dense().eval()
def _testLegalInputs(
self, loc=None, shape_hint=None, scale_params=None):
for args in _powerset(scale_params.items()):
with self.test_session():
args = dict(args)
scale_args = dict({
"loc": loc,
"shape_hint": shape_hint}, **args)
expected_scale = _make_diag_scale(**scale_args)
if expected_scale is None:
# Not enough shape information was specified.
with self.assertRaisesRegexp(ValueError, ("is specified.")):
scale = distribution_util.make_diag_scale(**scale_args)
scale.to_dense().eval()
else:
scale = distribution_util.make_diag_scale(**scale_args)
self.assertAllClose(expected_scale, scale.to_dense().eval())
def testAssertPositive(self):
with self.cached_session():
with self.assertRaisesOpError("diagonal part must be positive"):
scale = distribution_util.make_diag_scale(scale_diag=[[-1., 1],
[1.,
1.]],
validate_args=True,
assert_positive=True)
scale.to_dense().eval()
def _testLegalInputs(self, loc=None, shape_hint=None, scale_params=None):
for args in _powerset(scale_params.items()):
with self.test_session():
args = dict(args)
scale_args = dict({
"loc": loc,
"shape_hint": shape_hint
}, **args)
expected_scale = _make_diag_scale(**scale_args)
if expected_scale is None:
# Not enough shape information was specified.
with self.assertRaisesRegexp(ValueError,
("is specified.")):
scale = distribution_util.make_diag_scale(**scale_args)
scale.to_dense().eval()
else:
scale = distribution_util.make_diag_scale(**scale_args)
self.assertAllClose(expected_scale,
scale.to_dense().eval())
def _create_dist(self):
scale_diag = tf.nn.softplus(self._scale_variable) if self._softplus_scale \
else self._scale_variable
scale = distribution_util.make_diag_scale(loc=self._loc_variable,
scale_diag=scale_diag,
validate_args=False,
assert_positive=False)
batch_shape, event_shape = distribution_util.shapes_from_loc_and_scale(
self._loc_variable, scale)
return tfp.TransformedDistribution(
distribution=tfp.Cauchy(loc=tf.zeros([], dtype=scale.dtype),
scale=tf.ones([], dtype=scale.dtype)),
bijector=bijectors.AffineLinearOperator(shift=self._loc_variable,
scale=scale),
batch_shape=batch_shape,
event_shape=event_shape,
name="MultivariateCauchyDiag" +
("SoftplusScale" if self._softplus_scale else ""))
def __init__(self,
loc=None,
scale_diag=None,
scale_identity_multiplier=None,
validate_args=False,
allow_nan_stats=True,
name="VectorExponentialDiag"):
"""Construct Vector Exponential distribution supported on a subset of `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`.
```none
scale = diag(scale_diag + scale_identity_multiplier * ones(k))
```
where:
* `scale_diag.shape = [k]`, and,
* `scale_identity_multiplier.shape = []`.
Additional leading dimensions (if any) will index batches.
If both `scale_diag` and `scale_identity_multiplier` are `None`, then
`scale` is the Identity matrix.
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_diag: Non-zero, floating-point `Tensor` representing a diagonal
matrix added to `scale`. May have shape `[B1, ..., Bb, k]`, `b >= 0`,
and characterizes `b`-batches of `k x k` diagonal matrices added to
`scale`. When both `scale_identity_multiplier` and `scale_diag` are
`None` then `scale` is the `Identity`.
scale_identity_multiplier: Non-zero, floating-point `Tensor` representing
a scaled-identity-matrix added to `scale`. May have shape
`[B1, ..., Bb]`, `b >= 0`, and characterizes `b`-batches of scaled
`k x k` identity matrices added to `scale`. When both
`scale_identity_multiplier` and `scale_diag` are `None` then `scale` is
the `Identity`.
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 = locals()
with ops.name_scope(name):
with ops.name_scope("init", values=[
loc, scale_diag, scale_identity_multiplier]):
# No need to validate_args while making diag_scale. The returned
# LinearOperatorDiag has an assert_non_singular method that is called by
# the Bijector.
scale = distribution_util.make_diag_scale(
loc=loc,
scale_diag=scale_diag,
scale_identity_multiplier=scale_identity_multiplier,
validate_args=False,
assert_positive=False)
super(VectorExponentialDiag, 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_identity_multiplier=None,
skewness=None,
tailweight=None,
distribution=None,
validate_args=False,
allow_nan_stats=True,
name="MultivariateNormalLinearOperator"):
"""Construct VectorSinhArcsinhDiag distribution on `R^k`.
The arguments `scale_diag` and `scale_identity_multiplier` combine to
define the diagonal `scale` referred to in this class docstring:
```none
scale = diag(scale_diag + scale_identity_multiplier * ones(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
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_diag: Non-zero, floating-point `Tensor` representing a diagonal
matrix added to `scale`. May have shape `[B1, ..., Bb, k]`, `b >= 0`,
and characterizes `b`-batches of `k x k` diagonal matrices added to
`scale`. When both `scale_identity_multiplier` and `scale_diag` are
`None` then `scale` is the `Identity`.
scale_identity_multiplier: Non-zero, floating-point `Tensor` representing
a scale-identity-matrix added to `scale`. May have shape
`[B1, ..., Bb]`, `b >= 0`, and characterizes `b`-batches of scale
`k x k` identity matrices added to `scale`. When both
`scale_identity_multiplier` and `scale_diag` are `None` then `scale`
is the `Identity`.
skewness: Skewness parameter. floating-point `Tensor` with shape
broadcastable with `event_shape`.
tailweight: Tailweight parameter. floating-point `Tensor` with shape
broadcastable with `event_shape`.
distribution: `tf.Distribution`-like instance. Distribution from which `k`
iid samples are used as input to transformation `F`. Default is
`tf.distributions.Normal(loc=0., scale=1.)`.
Must be a scalar-batch, scalar-event distribution. Typically
`distribution.reparameterization_type = FULLY_REPARAMETERIZED` or it is
a function of non-trainable parameters. WARNING: If you backprop through
a VectorSinhArcsinhDiag sample and `distribution` is not
`FULLY_REPARAMETERIZED` yet is a function of trainable variables, then
the gradient will be incorrect!
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())
with ops.name_scope(
name,
values=[
loc, scale_diag, scale_identity_multiplier, skewness, tailweight
]) as name:
loc = ops.convert_to_tensor(loc, name="loc") if loc is not None else loc
tailweight = 1. if tailweight is None else tailweight
has_default_skewness = skewness is None
skewness = 0. if skewness is None else skewness
# Recall, with Z a random variable,
# Y := loc + C * F(Z),
# F(Z) := Sinh( (Arcsinh(Z) + skewness) * tailweight )
# F_0(Z) := Sinh( Arcsinh(Z) * tailweight )
# C := 2 * scale / F_0(2)
# Construct shapes and 'scale' out of the scale_* and loc kwargs.
# scale_linop is only an intermediary to:
# 1. get shapes from looking at loc and the two scale args.
# 2. combine scale_diag with scale_identity_multiplier, which gives us
# 'scale', which in turn gives us 'C'.
scale_linop = distribution_util.make_diag_scale(
loc=loc,
scale_diag=scale_diag,
scale_identity_multiplier=scale_identity_multiplier,
validate_args=False,
assert_positive=False)
batch_shape, event_shape = distribution_util.shapes_from_loc_and_scale(
loc, scale_linop)
# scale_linop.diag_part() is efficient since it is a diag type linop.
scale_diag_part = scale_linop.diag_part()
dtype = scale_diag_part.dtype
if distribution is None:
distribution = normal.Normal(
loc=array_ops.zeros([], dtype=dtype),
scale=array_ops.ones([], dtype=dtype),
allow_nan_stats=allow_nan_stats)
else:
asserts = distribution_util.maybe_check_scalar_distribution(
distribution, dtype, validate_args)
if asserts:
scale_diag_part = control_flow_ops.with_dependencies(
asserts, scale_diag_part)
# Make the SAS bijector, 'F'.
skewness = ops.convert_to_tensor(skewness, dtype=dtype, name="skewness")
tailweight = ops.convert_to_tensor(
tailweight, dtype=dtype, name="tailweight")
f = bijectors.SinhArcsinh(
skewness=skewness, tailweight=tailweight)
if has_default_skewness:
f_noskew = f
else:
f_noskew = bijectors.SinhArcsinh(
skewness=skewness.dtype.as_numpy_dtype(0.),
tailweight=tailweight)
# Make the Affine bijector, Z --> loc + C * Z.
c = 2 * scale_diag_part / f_noskew.forward(
ops.convert_to_tensor(2, dtype=dtype))
affine = bijectors.Affine(
shift=loc, scale_diag=c, validate_args=validate_args)
bijector = bijectors.Chain([affine, f])
super(VectorSinhArcsinhDiag, self).__init__(
distribution=distribution,
bijector=bijector,
batch_shape=batch_shape,
event_shape=event_shape,
validate_args=validate_args,
name=name)
self._parameters = parameters
self._loc = loc
self._scale = scale_linop
self._tailweight = tailweight
self._skewness = skewness
def __init__(self,
loc=None,
scale_diag=None,
scale_identity_multiplier=None,
validate_args=False,
allow_nan_stats=True,
name="MultivariateNormalDiag"):
"""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 the last dimension of `loc` or the last
dimension of the matrix implied by `scale`.
Recall that `covariance = scale @ scale.T`. A (non-batch) `scale` matrix is:
```none
scale = diag(scale_diag + scale_identity_multiplier * ones(k))
```
where:
* `scale_diag.shape = [k]`, and,
* `scale_identity_multiplier.shape = []`.
Additional leading dimensions (if any) will index batches.
If both `scale_diag` and `scale_identity_multiplier` are `None`, then
`scale` is the Identity matrix.
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_diag: Non-zero, floating-point `Tensor` representing a diagonal
matrix added to `scale`. May have shape `[B1, ..., Bb, k]`, `b >= 0`,
and characterizes `b`-batches of `k x k` diagonal matrices added to
`scale`. When both `scale_identity_multiplier` and `scale_diag` are
`None` then `scale` is the `Identity`.
scale_identity_multiplier: Non-zero, floating-point `Tensor` representing
a scaled-identity-matrix added to `scale`. May have shape
`[B1, ..., Bb]`, `b >= 0`, and characterizes `b`-batches of scaled
`k x k` identity matrices added to `scale`. When both
`scale_identity_multiplier` and `scale_diag` are `None` then `scale` is
the `Identity`.
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 = locals()
with ops.name_scope(name) as ns:
with ops.name_scope("init",
values=[
loc, scale_diag, scale_identity_multiplier
]):
scale = distribution_util.make_diag_scale(
loc=loc,
scale_diag=scale_diag,
scale_identity_multiplier=scale_identity_multiplier,
validate_args=validate_args,
assert_positive=False)
super(MultivariateNormalDiag,
self).__init__(loc=loc,
scale=scale,
validate_args=validate_args,
allow_nan_stats=allow_nan_stats,
name=ns)
self._parameters = parameters
def __init__(self,
loc=None,
scale_diag=None,
scale_identity_multiplier=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_identity_multiplier ones(k)) +
scale_perturb_factor @ diag(scale_perturb_diag) @ scale_perturb_factor.T
```
where:
* `scale_diag.shape = [k]`,
* `scale_identity_multiplier.shape = []`,
* `scale_perturb_factor.shape = [k, r]`, typically `k >> r`, and,
* `scale_perturb_diag.shape = [r]`.
Additional leading dimensions (if any) will index batches.
If both `scale_diag` and `scale_identity_multiplier` are `None`, then
`scale` is the Identity matrix.
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_diag: Non-zero, floating-point `Tensor` representing a diagonal
matrix added to `scale`. May have shape `[B1, ..., Bb, k]`, `b >= 0`,
and characterizes `b`-batches of `k x k` diagonal matrices added to
`scale`. When both `scale_identity_multiplier` and `scale_diag` are
`None` then `scale` is the `Identity`.
scale_identity_multiplier: Non-zero, floating-point `Tensor` representing
a scaled-identity-matrix added to `scale`. May have shape
`[B1, ..., Bb]`, `b >= 0`, and characterizes `b`-batches of scaled
`k x k` identity matrices added to `scale`. When both
`scale_identity_multiplier` and `scale_diag` are `None` then `scale` is
the `Identity`.
scale_perturb_factor: Floating-point `Tensor` representing a rank-`r`
perturbation added to `scale`. May 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 diagonal matrix
inside the rank-`r` perturbation added to `scale`. May 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())
def _convert_to_tensor(x, name):
return None if x is None else ops.convert_to_tensor(x, name=name)
with ops.name_scope(name) as name:
with ops.name_scope("init",
values=[
loc, scale_diag, scale_identity_multiplier,
scale_perturb_factor, scale_perturb_diag
]):
has_low_rank = (scale_perturb_factor is not None
or scale_perturb_diag is not None)
scale = distribution_util.make_diag_scale(
loc=loc,
scale_diag=scale_diag,
scale_identity_multiplier=scale_identity_multiplier,
validate_args=validate_args,
assert_positive=has_low_rank)
scale_perturb_factor = _convert_to_tensor(
scale_perturb_factor, name="scale_perturb_factor")
scale_perturb_diag = _convert_to_tensor(
scale_perturb_diag, name="scale_perturb_diag")
if has_low_rank:
scale = linalg.LinearOperatorLowRankUpdate(
scale,
u=scale_perturb_factor,
diag_update=scale_perturb_diag,
is_diag_update_positive=scale_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)
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_diag=None,
scale_identity_multiplier=None,
skewness=None,
tailweight=None,
distribution=None,
validate_args=False,
allow_nan_stats=True,
name="MultivariateNormalLinearOperator"):
"""Construct VectorSinhArcsinhDiag distribution on `R^k`.
The arguments `scale_diag` and `scale_identity_multiplier` combine to
define the diagonal `scale` referred to in this class docstring:
```none
scale = diag(scale_diag + scale_identity_multiplier * ones(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
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_diag: Non-zero, floating-point `Tensor` representing a diagonal
matrix added to `scale`. May have shape `[B1, ..., Bb, k]`, `b >= 0`,
and characterizes `b`-batches of `k x k` diagonal matrices added to
`scale`. When both `scale_identity_multiplier` and `scale_diag` are
`None` then `scale` is the `Identity`.
scale_identity_multiplier: Non-zero, floating-point `Tensor` representing
a scale-identity-matrix added to `scale`. May have shape
`[B1, ..., Bb]`, `b >= 0`, and characterizes `b`-batches of scale
`k x k` identity matrices added to `scale`. When both
`scale_identity_multiplier` and `scale_diag` are `None` then `scale`
is the `Identity`.
skewness: Skewness parameter. floating-point `Tensor` with shape
broadcastable with `event_shape`.
tailweight: Tailweight parameter. floating-point `Tensor` with shape
broadcastable with `event_shape`.
distribution: `tf.Distribution`-like instance. Distribution from which `k`
iid samples are used as input to transformation `F`. Default is
`ds.Normal(0., 1.)`.
Must be a scalar-batch, scalar-event distribution. Typically
`distribution.reparameterization_type = FULLY_REPARAMETERIZED` or it is
a function of non-trainable parameters. WARNING: If you backprop through
a VectorSinhArcsinhDiag sample and `distribution` is not
`FULLY_REPARAMETERIZED` yet is a function of trainable variables, then
the gradient will be incorrect!
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 = locals()
with ops.name_scope(name,
values=[
loc, scale_diag, scale_identity_multiplier,
skewness, tailweight
]):
loc = ops.convert_to_tensor(loc,
name="loc") if loc is not None else loc
tailweight = 1. if tailweight is None else tailweight
skewness = 0. if skewness is None else skewness
# Recall, with Z ~ Normal(0, 1),
# Y := loc + C * F(Z),
# F(Z) := Sinh( (Arcsinh(Z) + skewness) * tailweight )
# C := 2 * scale / F(2)
# Construct shapes and 'scale' out of the scale_* and loc kwargs.
# scale_linop is only an intermediary to:
# 1. get shapes from looking at loc and the two scale args.
# 2. combine scale_diag with scale_identity_multiplier, which gives us
# 'scale', which in turn gives us 'C'.
scale_linop = distribution_util.make_diag_scale(
loc=loc,
scale_diag=scale_diag,
scale_identity_multiplier=scale_identity_multiplier,
validate_args=False,
assert_positive=False)
batch_shape, event_shape = distribution_util.shapes_from_loc_and_scale(
loc, scale_linop)
# scale_linop.diag_part() is efficient since it is a diag type linop.
scale_diag_part = scale_linop.diag_part()
dtype = scale_diag_part.dtype
if distribution is None:
distribution = normal.Normal(loc=array_ops.zeros([],
dtype=dtype),
scale=array_ops.ones([],
dtype=dtype),
allow_nan_stats=allow_nan_stats)
else:
asserts = distribution_util.maybe_check_scalar_distribution(
distribution, dtype, validate_args)
if asserts:
scale_diag_part = control_flow_ops.with_dependencies(
asserts, scale_diag_part)
# Make the SAS bijector, 'F'.
skewness = ops.convert_to_tensor(skewness,
dtype=dtype,
name="skewness")
tailweight = ops.convert_to_tensor(tailweight,
dtype=dtype,
name="tailweight")
f = bijectors.SinhArcsinh(skewness=skewness,
tailweight=tailweight,
event_ndims=1)
# Make the Affine bijector, Z --> loc + C * Z.
c = 2 * scale_diag_part / f.forward(
ops.convert_to_tensor(2, dtype=dtype))
affine = bijectors.Affine(shift=loc,
scale_diag=c,
validate_args=validate_args,
event_ndims=1)
bijector = bijectors.Chain([affine, f])
super(VectorSinhArcsinhDiag,
self).__init__(distribution=distribution,
bijector=bijector,
batch_shape=batch_shape,
event_shape=event_shape,
validate_args=validate_args,
name=name)
self._parameters = parameters
self._loc = loc
self._scale = scale_linop
self._tailweight = tailweight
self._skewness = skewness
def __init__(self,
loc=None,
scale_diag=None,
scale_identity_multiplier=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_identity_multiplier ones(k)) +
scale_perturb_factor @ diag(scale_perturb_diag) @ scale_perturb_factor.T
```
where:
* `scale_diag.shape = [k]`,
* `scale_identity_multiplier.shape = []`,
* `scale_perturb_factor.shape = [k, r]`, typically `k >> r`, and,
* `scale_perturb_diag.shape = [r]`.
Additional leading dimensions (if any) will index batches.
If both `scale_diag` and `scale_identity_multiplier` are `None`, then
`scale` is the Identity matrix.
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_diag: Non-zero, floating-point `Tensor` representing a diagonal
matrix added to `scale`. May have shape `[B1, ..., Bb, k]`, `b >= 0`,
and characterizes `b`-batches of `k x k` diagonal matrices added to
`scale`. When both `scale_identity_multiplier` and `scale_diag` are
`None` then `scale` is the `Identity`.
scale_identity_multiplier: Non-zero, floating-point `Tensor` representing
a scaled-identity-matrix added to `scale`. May have shape
`[B1, ..., Bb]`, `b >= 0`, and characterizes `b`-batches of scaled
`k x k` identity matrices added to `scale`. When both
`scale_identity_multiplier` and `scale_diag` are `None` then `scale` is
the `Identity`.
scale_perturb_factor: Floating-point `Tensor` representing a rank-`r`
perturbation added to `scale`. May 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 diagonal matrix
inside the rank-`r` perturbation added to `scale`. May 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())
def _convert_to_tensor(x, name):
return None if x is None else ops.convert_to_tensor(x, name=name)
with ops.name_scope(name) as name:
with ops.name_scope("init", values=[
loc, scale_diag, scale_identity_multiplier, scale_perturb_factor,
scale_perturb_diag]):
has_low_rank = (scale_perturb_factor is not None or
scale_perturb_diag is not None)
scale = distribution_util.make_diag_scale(
loc=loc,
scale_diag=scale_diag,
scale_identity_multiplier=scale_identity_multiplier,
validate_args=validate_args,
assert_positive=has_low_rank)
scale_perturb_factor = _convert_to_tensor(
scale_perturb_factor,
name="scale_perturb_factor")
scale_perturb_diag = _convert_to_tensor(
scale_perturb_diag,
name="scale_perturb_diag")
if has_low_rank:
scale = linalg.LinearOperatorLowRankUpdate(
scale,
u=scale_perturb_factor,
diag_update=scale_perturb_diag,
is_diag_update_positive=scale_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)
super(MultivariateNormalDiagPlusLowRank, self).__init__(
loc=loc,
scale=scale,
validate_args=validate_args,
allow_nan_stats=allow_nan_stats,
name=name)
self._parameters = parameters
def testValidateArgs(self):
with self.test_session():
with self.assertRaisesOpError("diagonal part must be non-zero"):
scale = distribution_util.make_diag_scale(
scale_diag=[[0., 1], [1., 1.]], validate_args=True)
scale.to_dense().eval()
