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Bijector that approximates clipping as a continuous, differentiable map.
Inherits From: AutoCompositeTensorBijector
, Bijector
tfp.substrates.numpy.bijectors.SoftClip(
low=None,
high=None,
hinge_softness=None,
validate_args=False,
name='soft_clip'
)
The forward
method takes unconstrained scalar x
to a value y
in
[low, high]
. For values within the interval and far from the bounds
(low << x << high
), this mapping is approximately the identity mapping.
b = tfb.SoftClip(low=-10., high=10.)
b.forward([-15., -7., 1., 9., 20.])
# => [-9.993284, -6.951412, 0.9998932, 8.686738, 9.999954 ]
The softness of the clipping can be adjusted via the hinge_softness
parameter. A sharp constraint (hinge_softness < 1.0
) will approximate
the identity mapping very well across almost all of its range, but may
be numerically ill-conditioned at the boundaries. A soft constraint
(hinge_softness > 1.0
) corresponds to a smoother, better-conditioned
mapping, but creates a larger distortion of its inputs.
b_hard = SoftClip(low=-5, high=5., hinge_softness=0.1)
b_soft.forward([-15., -7., 1., 9., 20.])
# => [-10., -7., 1., 8.999995, 10.]
b_soft = SoftClip(low=-5, high=5., hinge_softness=10.0)
b_soft.forward([-15., -7., 1., 9., 20.])
# => [-6.1985435, -3.369276, 0.16719627, 3.6655345, 7.1750355]
Note that the outputs are always in the interval [low, high]
, regardless
of the hinge_softness
.
Example use
A trivial application of this bijector is to constrain the values sampled from a distribution:
dist = tfd.TransformedDistribution(
distribution=tfd.Normal(loc=0., scale=1.),
bijector=tfb.SoftClip(low=-5., high=5.))
samples = dist.sample(100) # => samples guaranteed in [-10., 10.]
A more useful application is to constrain the values considered
during inference, preventing an inference algorithm from proposing values
that cause numerical issues. For example, this model will return a log_prob
of NaN
when z
is outside of the range [-5., 5.]
:
dist = tfd.JointDistributionNamed({
'z': tfd.Normal(0., 1.0)
'x': lambda z: tfd.Normal(
loc=tf.log(25 - z**2), # Breaks if z >= 5 or z <= -5.
scale=1.)})
Using SoftClip allows us to keep an inference algorithm in the feasible region without distorting the inference geometry by very much:
target_log_prob_fn = lambda z: dist.log_prob(z=z, x=3.) # Condition on x==3.
# Use SoftClip to ensure sampler stays within the numerically valid region.
mcmc_samples = tfp.mcmc.sample_chain(
kernel=tfp.mcmc.TransformedTransitionKernel(
tfp.mcmc.HamiltonianMonteCarlo(
target_log_prob_fn=target_log_prob_fn,
num_leapfrog_steps=2,
step_size=0.1),
bijector=tfb.SoftClip(-5., 5.)),
trace_fn=None,
current_state=0.,
num_results=100)
Mathematical Details
The constraint is built by using softplus(x) = log(1 + exp(x))
as a smooth
approximation to max(x, 0)
. In combination with affine transformations, this
can implement a constraint to any scalar interval.
In particular, translating softplus
gives a generic lower bound constraint:
max(x, low) = max(x - low, 0) + low
~= softplus(x - low) + low
:= softlower(x)
Note that this quantity is always greater than low
because softplus
is
positive-valued. We can also implement a soft upper bound:
min(x, high) = min(x - high, 0) + high
= -max(high - x, 0) + high
~= -softplus(high - x) + high
:= softupper(x)
which, similarly, is always less than high
.
Composing these bounds as softupper(softlower(x))
gives a quantity bounded
above by high
, and bounded below by softupper(low)
(because softupper
is monotonic and its input is bounded below by low
). In general, we will
have softupper(low) < low
, so we need to shrink the interval slightly
(by (high - low) / (high - softupper(low))
) to preserve the lower bound.
The two-sided constraint is therefore:
softclip(x) := (softupper(softlower(x)) - high) *
(high - low) / (high - softupper(low)) + high
= -softplus(high - low - softplus(x - low)) *
(high - low) / (softplus(high-low)) + high
Due to this rescaling, the bijector can be mildly asymmetric. Values of equal distance from the endpoints are mapped to values with slightly unequal distance from the endpoints; for example,
b = SoftConstrain(-1., 1.)
b.forward([-0.5., 0.5.])
# => [-0.2527727 , 0.19739306]
The degree of the asymmetry is proportional to the size of the rescaling
correction, i.e., the extent to which softupper
fails to be the identity
map at the lower end of the interval. This is maximized when the upper and
lower bounds are very close together relative to the hinge softness, as in
the example above. Conversely, when the interval is wide, the required
correction and asymmetry are very small.
Methods
copy
copy(
**override_parameters_kwargs
)
Creates a copy of the bijector.
Args | |
---|---|
**override_parameters_kwargs
|
String/value dictionary of initialization arguments to override with new values. |
Returns | |
---|---|
bijector
|
A new instance of type(self) initialized from the union
of self.parameters and override_parameters_kwargs, i.e.,
dict(self.parameters, **override_parameters_kwargs) .
|
experimental_batch_shape
experimental_batch_shape(
x_event_ndims=None, y_event_ndims=None
)
Returns the batch shape of this bijector for inputs of the given rank.
The batch shape of a bijector decribes the set of distinct
transformations it represents on events of a given size. For example: the
bijector tfb.Scale([1., 2.])
has batch shape [2]
for scalar events
(event_ndims = 0
), because applying it to a scalar event produces
two scalar outputs, the result of two different scaling transformations.
The same bijector has batch shape []
for vector events, because applying
it to a vector produces (via elementwise multiplication) a single vector
output.
Bijectors that operate independently on multiple state parts, such as
tfb.JointMap
, must broadcast to a coherent batch shape. Some events may
not be valid: for example, the bijector
tfd.JointMap([tfb.Scale([1., 2.]), tfb.Scale([1., 2., 3.])])
does not
produce a valid batch shape when event_ndims = [0, 0]
, since the batch
shapes of the two parts are inconsistent. The same bijector
does define valid batch shapes of []
, [2]
, and [3]
if event_ndims
is [1, 1]
, [0, 1]
, or [1, 0]
, respectively.
Since transforming a single event produces a scalar log-det-Jacobian, the
batch shape of a bijector with non-constant Jacobian is expected to equal
the shape of forward_log_det_jacobian(x, event_ndims=x_event_ndims)
or inverse_log_det_jacobian(y, event_ndims=y_event_ndims)
, for x
or y
of the specified ndims
.
Args | |
---|---|
x_event_ndims
|
Optional Python int (structure) number of dimensions in
a probabilistic event passed to forward ; this must be greater than
or equal to self.forward_min_event_ndims . If None , defaults to
self.forward_min_event_ndims . Mutually exclusive with y_event_ndims .
Default value: None .
|
y_event_ndims
|
Optional Python int (structure) number of dimensions in
a probabilistic event passed to inverse ; this must be greater than
or equal to self.inverse_min_event_ndims . Mutually exclusive with
x_event_ndims .
Default value: None .
|
Returns | |
---|---|
batch_shape
|
TensorShape batch shape of this bijector for a
value with the given event rank. May be unknown or partially defined.
|
experimental_batch_shape_tensor
experimental_batch_shape_tensor(
x_event_ndims=None, y_event_ndims=None
)
Returns the batch shape of this bijector for inputs of the given rank.
The batch shape of a bijector decribes the set of distinct
transformations it represents on events of a given size. For example: the
bijector tfb.Scale([1., 2.])
has batch shape [2]
for scalar events
(event_ndims = 0
), because applying it to a scalar event produces
two scalar outputs, the result of two different scaling transformations.
The same bijector has batch shape []
for vector events, because applying
it to a vector produces (via elementwise multiplication) a single vector
output.
Bijectors that operate independently on multiple state parts, such as
tfb.JointMap
, must broadcast to a coherent batch shape. Some events may
not be valid: for example, the bijector
tfd.JointMap([tfb.Scale([1., 2.]), tfb.Scale([1., 2., 3.])])
does not
produce a valid batch shape when event_ndims = [0, 0]
, since the batch
shapes of the two parts are inconsistent. The same bijector
does define valid batch shapes of []
, [2]
, and [3]
if event_ndims
is [1, 1]
, [0, 1]
, or [1, 0]
, respectively.
Since transforming a single event produces a scalar log-det-Jacobian, the
batch shape of a bijector with non-constant Jacobian is expected to equal
the shape of forward_log_det_jacobian(x, event_ndims=x_event_ndims)
or inverse_log_det_jacobian(y, event_ndims=y_event_ndims)
, for x
or y
of the specified ndims
.
Args | |
---|---|
x_event_ndims
|
Optional Python int (structure) number of dimensions in
a probabilistic event passed to forward ; this must be greater than
or equal to self.forward_min_event_ndims . If None , defaults to
self.forward_min_event_ndims . Mutually exclusive with y_event_ndims .
Default value: None .
|
y_event_ndims
|
Optional Python int (structure) number of dimensions in
a probabilistic event passed to inverse ; this must be greater than
or equal to self.inverse_min_event_ndims . Mutually exclusive with
x_event_ndims .
Default value: None .
|
Returns | |
---|---|
batch_shape_tensor
|
integer Tensor batch shape of this bijector for a
value with the given event rank.
|
experimental_compute_density_correction
experimental_compute_density_correction(
x, tangent_space, backward_compat=False, **kwargs
)
Density correction for this transformation wrt the tangent space, at x.
Subclasses of Bijector may call the most specific applicable
method of TangentSpace
, based on whether the transformation is
dimension-preserving, coordinate-wise, a projection, or something
more general. The backward-compatible assumption is that the
transformation is dimension-preserving (goes from R^n to R^n).
Args | |
---|---|
x
|
Tensor (structure). The point at which to calculate the density.
|
tangent_space
|
TangentSpace or one of its subclasses. The tangent to
the support manifold at x .
|
backward_compat
|
bool specifying whether to assume that the Bijector
is dimension-preserving.
|
**kwargs
|
Optional keyword arguments forwarded to tangent space methods. |
Returns | |
---|---|
density_correction
|
Tensor representing the density correction---in log
space---under the transformation that this Bijector denotes.
|
Raises | |
---|---|
TypeError if backward_compat is False but no method of
TangentSpace has been called explicitly.
|
forward
forward(
x, name='forward', **kwargs
)
Returns the forward Bijector
evaluation, i.e., X = g(Y).
Args | |
---|---|
x
|
Tensor (structure). The input to the 'forward' evaluation.
|
name
|
The name to give this op. |
**kwargs
|
Named arguments forwarded to subclass implementation. |
Returns | |
---|---|
Tensor (structure).
|
Raises | |
---|---|
TypeError
|
if self.dtype is specified and x.dtype is not
self.dtype .
|
NotImplementedError
|
if _forward is not implemented.
|
forward_dtype
forward_dtype(
dtype=UNSPECIFIED, name='forward_dtype', **kwargs
)
Returns the dtype returned by forward
for the provided input.
forward_event_ndims
forward_event_ndims(
event_ndims, **kwargs
)
Returns the number of event dimensions produced by forward
.
Args | |
---|---|
event_ndims
|
Structure of Python and/or Tensor int s, and/or None
values. The structure should match that of
self.forward_min_event_ndims , and all non-None values must be
greater than or equal to the corresponding value in
self.forward_min_event_ndims .
|
**kwargs
|
Optional keyword arguments forwarded to nested bijectors. |
Returns | |
---|---|
forward_event_ndims
|
Structure of integers and/or None values matching
self.inverse_min_event_ndims . These are computed using 'prefer static'
semantics: if any inputs are None , some or all of the outputs may be
None , indicating that the output dimension could not be inferred
(conversely, if all inputs are non-None , all outputs will be
non-None ). If all input event_ndims are Python int s, all of the
(non-None ) outputs will be Python int s; otherwise, some or
all of the outputs may be Tensor int s.
|
forward_event_shape
forward_event_shape(
input_shape
)
Shape of a single sample from a single batch as a TensorShape
.
Same meaning as forward_event_shape_tensor
. May be only partially defined.
Args | |
---|---|
input_shape
|
TensorShape (structure) indicating event-portion shape
passed into forward function.
|
Returns | |
---|---|
forward_event_shape_tensor
|
TensorShape (structure) indicating
event-portion shape after applying forward . Possibly unknown.
|
forward_event_shape_tensor
forward_event_shape_tensor(
input_shape, name='forward_event_shape_tensor'
)
Shape of a single sample from a single batch as an int32
1D Tensor
.
Args | |
---|---|
input_shape
|
Tensor , int32 vector (structure) indicating event-portion
shape passed into forward function.
|
name
|
name to give to the op |
Returns | |
---|---|
forward_event_shape_tensor
|
Tensor , int32 vector (structure)
indicating event-portion shape after applying forward .
|
forward_log_det_jacobian
forward_log_det_jacobian(
x, event_ndims=None, name='forward_log_det_jacobian', **kwargs
)
Returns both the forward_log_det_jacobian.
Args | |
---|---|
x
|
Tensor (structure). The input to the 'forward' Jacobian determinant
evaluation.
|
event_ndims
|
Optional number of dimensions in the probabilistic events
being transformed; this must be greater than or equal to
self.forward_min_event_ndims . If event_ndims is specified, the
log Jacobian determinant is summed to produce a
scalar log-determinant for each event. Otherwise
(if event_ndims is None ), no reduction is performed.
Multipart bijectors require structured event_ndims, such that the
batch rank rank(y[i]) - event_ndims[i] is the same for all
elements i of the structured input. In most cases (with the
exception of tfb.JointMap ) they further require that
event_ndims[i] - self.inverse_min_event_ndims[i] is the same for
all elements i of the structured input.
Default value: None (equivalent to self.forward_min_event_ndims ).
|
name
|
The name to give this op. |
**kwargs
|
Named arguments forwarded to subclass implementation. |
Returns | |
---|---|
Tensor (structure), if this bijector is injective.
If not injective this is not implemented.
|
Raises | |
---|---|
TypeError
|
if y 's dtype is incompatible with the expected output dtype.
|
NotImplementedError
|
if neither _forward_log_det_jacobian
nor {_inverse , _inverse_log_det_jacobian } are implemented, or
this is a non-injective bijector.
|
ValueError
|
if the value of event_ndims is not valid for this bijector.
|
inverse
inverse(
y, name='inverse', **kwargs
)
Returns the inverse Bijector
evaluation, i.e., X = g^{-1}(Y).
Args | |
---|---|
y
|
Tensor (structure). The input to the 'inverse' evaluation.
|
name
|
The name to give this op. |
**kwargs
|
Named arguments forwarded to subclass implementation. |
Returns | |
---|---|
Tensor (structure), if this bijector is injective.
If not injective, returns the k-tuple containing the unique
k points (x1, ..., xk) such that g(xi) = y .
|
Raises | |
---|---|
TypeError
|
if y 's structured dtype is incompatible with the expected
output dtype.
|
NotImplementedError
|
if _inverse is not implemented.
|
inverse_dtype
inverse_dtype(
dtype=UNSPECIFIED, name='inverse_dtype', **kwargs
)
Returns the dtype returned by inverse
for the provided input.
inverse_event_ndims
inverse_event_ndims(
event_ndims, **kwargs
)
Returns the number of event dimensions produced by inverse
.
Args | |
---|---|
event_ndims
|
Structure of Python and/or Tensor int s, and/or None
values. The structure should match that of
self.inverse_min_event_ndims , and all non-None values must be
greater than or equal to the corresponding value in
self.inverse_min_event_ndims .
|
**kwargs
|
Optional keyword arguments forwarded to nested bijectors. |
Returns | |
---|---|
inverse_event_ndims
|
Structure of integers and/or None values matching
self.forward_min_event_ndims . These are computed using 'prefer static'
semantics: if any inputs are None , some or all of the outputs may be
None , indicating that the output dimension could not be inferred
(conversely, if all inputs are non-None , all outputs will be
non-None ). If all input event_ndims are Python int s, all of the
(non-None ) outputs will be Python int s; otherwise, some or
all of the outputs may be Tensor int s.
|
inverse_event_shape
inverse_event_shape(
output_shape
)
Shape of a single sample from a single batch as a TensorShape
.
Same meaning as inverse_event_shape_tensor
. May be only partially defined.
Args | |
---|---|
output_shape
|
TensorShape (structure) indicating event-portion shape
passed into inverse function.
|
Returns | |
---|---|
inverse_event_shape_tensor
|
TensorShape (structure) indicating
event-portion shape after applying inverse . Possibly unknown.
|
inverse_event_shape_tensor
inverse_event_shape_tensor(
output_shape, name='inverse_event_shape_tensor'
)
Shape of a single sample from a single batch as an int32
1D Tensor
.
Args | |
---|---|
output_shape
|
Tensor , int32 vector (structure) indicating
event-portion shape passed into inverse function.
|
name
|
name to give to the op |
Returns | |
---|---|
inverse_event_shape_tensor
|
Tensor , int32 vector (structure)
indicating event-portion shape after applying inverse .
|
inverse_log_det_jacobian
inverse_log_det_jacobian(
y, event_ndims=None, name='inverse_log_det_jacobian', **kwargs
)
Returns the (log o det o Jacobian o inverse)(y).
Mathematically, returns: log(det(dX/dY))(Y)
. (Recall that: X=g^{-1}(Y)
.)
Note that forward_log_det_jacobian
is the negative of this function,
evaluated at g^{-1}(y)
.
Args | |
---|---|
y
|
Tensor (structure). The input to the 'inverse' Jacobian determinant
evaluation.
|
event_ndims
|
Optional number of dimensions in the probabilistic events
being transformed; this must be greater than or equal to
self.inverse_min_event_ndims . If event_ndims is specified, the
log Jacobian determinant is summed to produce a
scalar log-determinant for each event. Otherwise
(if event_ndims is None ), no reduction is performed.
Multipart bijectors require structured event_ndims, such that the
batch rank rank(y[i]) - event_ndims[i] is the same for all
elements i of the structured input. In most cases (with the
exception of tfb.JointMap ) they further require that
event_ndims[i] - self.inverse_min_event_ndims[i] is the same for
all elements i of the structured input.
Default value: None (equivalent to self.inverse_min_event_ndims ).
|
name
|
The name to give this op. |
**kwargs
|
Named arguments forwarded to subclass implementation. |
Returns | |
---|---|
ildj
|
Tensor , if this bijector is injective.
If not injective, returns the tuple of local log det
Jacobians, log(det(Dg_i^{-1}(y))) , where g_i is the restriction
of g to the ith partition Di .
|
Raises | |
---|---|
TypeError
|
if x 's dtype is incompatible with the expected inverse-dtype.
|
NotImplementedError
|
if _inverse_log_det_jacobian is not implemented.
|
ValueError
|
if the value of event_ndims is not valid for this bijector.
|
parameter_properties
@classmethod
parameter_properties( dtype=tf.float32 )
Returns a dict mapping constructor arg names to property annotations.
This dict should include an entry for each of the bijector's
Tensor
-valued constructor arguments.
Args | |
---|---|
dtype
|
Optional float dtype to assume for continuous-valued parameters.
Some constraining bijectors require advance knowledge of the dtype
because certain constants (e.g., tfb.Softplus.low ) must be
instantiated with the same dtype as the values to be transformed.
|
Returns | |
---|---|
parameter_properties
|
A
str -> tfp.python.internal.parameter_properties.ParameterPropertiesdict mapping constructor argument names to ParameterProperties`
instances.
|
__call__
__call__(
value, name=None, **kwargs
)
Applies or composes the Bijector
, depending on input type.
This is a convenience function which applies the Bijector
instance in
three different ways, depending on the input:
- If the input is a
tfd.Distribution
instance, returntfd.TransformedDistribution(distribution=input, bijector=self)
. - If the input is a
tfb.Bijector
instance, returntfb.Chain([self, input])
. - Otherwise, return
self.forward(input)
Args | |
---|---|
value
|
A tfd.Distribution , tfb.Bijector , or a (structure of) Tensor .
|
name
|
Python str name given to ops created by this function.
|
**kwargs
|
Additional keyword arguments passed into the created
tfd.TransformedDistribution , tfb.Bijector , or self.forward .
|
Returns | |
---|---|
composition
|
A tfd.TransformedDistribution if the input was a
tfd.Distribution , a tfb.Chain if the input was a tfb.Bijector , or
a (structure of) Tensor computed by self.forward .
|
Examples
sigmoid = tfb.Reciprocal()(
tfb.Shift(shift=1.)(
tfb.Exp()(
tfb.Scale(scale=-1.))))
# ==> `tfb.Chain([
# tfb.Reciprocal(),
# tfb.Shift(shift=1.),
# tfb.Exp(),
# tfb.Scale(scale=-1.),
# ])` # ie, `tfb.Sigmoid()`
log_normal = tfb.Exp()(tfd.Normal(0, 1))
# ==> `tfd.TransformedDistribution(tfd.Normal(0, 1), tfb.Exp())`
tfb.Exp()([-1., 0., 1.])
# ==> tf.exp([-1., 0., 1.])
__eq__
__eq__(
other
)
Return self==value.
__getitem__
__getitem__(
slices
)
__iter__
__iter__()