# tfp.bijectors.SoftClip

Bijector that approximates clipping as a continuous, differentiable map.

Inherits From: `AutoCompositeTensorBijector`

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.

`low` Optional float `Tensor` lower bound. If `None`, the lower-bound constraint is omitted. Default value: `None`.
`high` Optional float `Tensor` upper bound. If `None`, the upper-bound constraint is omitted. Default value: `None`.
`hinge_softness` Optional nonzero float `Tensor`. Controls the softness of the constraint at the boundaries; values outside of the constraint set are mapped into intervals of width approximately `log(2) * hinge_softness` on the interior of each boundary. High softness reserves more space for values outside of the constraint set, leading to greater distortion of inputs within the constraint set, but improved numerical stability near the boundaries. Default value: `None` (`1.0`).
`validate_args` Python `bool` indicating whether arguments should be checked for correctness.
`name` Python `str` name given to ops managed by this object.

`dtype`

`forward_min_event_ndims` Returns the minimal number of dimensions bijector.forward operates on.

Multipart bijectors return structured `ndims`, which indicates the expected structure of their inputs. Some multipart bijectors, notably Composites, may return structures of `None`.

`graph_parents` Returns this `Bijector`'s graph_parents as a Python list.
`has_static_min_event_ndims` Returns True if the bijector has statically-known `min_event_ndims`. (deprecated)

`high`

`hinge_softness`

`inverse_min_event_ndims` Returns the minimal number of dimensions bijector.inverse operates on.

Multipart bijectors return structured `event_ndims`, which indicates the expected structure of their outputs. Some multipart bijectors, notably Composites, may return structures of `None`.

`is_constant_jacobian` Returns true iff the Jacobian matrix is not a function of x.

`low`

`name` Returns the string name of this `Bijector`.
`name_scope` Returns a `tf.name_scope` instance for this class.
`non_trainable_variables` Sequence of non-trainable variables owned by this module and its submodules.

`parameters` Dictionary of parameters used to instantiate this `Bijector`.
`submodules` Sequence of all sub-modules.

Submodules are modules which are properties of this module, or found as properties of modules which are properties of this module (and so on).

````a = tf.Module()`
`b = tf.Module()`
`c = tf.Module()`
`a.b = b`
`b.c = c`
`list(a.submodules) == [b, c]`
`True`
`list(b.submodules) == [c]`
`True`
`list(c.submodules) == []`
`True`
```

`trainable_variables` Sequence of trainable variables owned by this module and its submodules.

`validate_args` Returns True if Tensor arguments will be validated.
`variables` Sequence of variables owned by this module and its submodules.

## Methods

### `forward`

View source

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`

View source

Returns the dtype returned by `forward` for the provided input.

### `forward_event_ndims`

View source

Returns the number of event dimensions produced by `forward`.

### `forward_event_shape`

View source

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`

View source

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`

View source

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`

View source

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`

View source

Returns the dtype returned by `inverse` for the provided input.

### `inverse_event_ndims`

View source

Returns the number of event dimensions produced by `inverse`.

### `inverse_event_shape`

View source

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`

View source

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`

View source

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`

View source

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.ParameterProperties`dict mapping constructor argument names to`ParameterProperties` instances.

### `with_name_scope`

Decorator to automatically enter the module name scope.

````class MyModule(tf.Module):`
`  @tf.Module.with_name_scope`
`  def __call__(self, x):`
`    if not hasattr(self, 'w'):`
`      self.w = tf.Variable(tf.random.normal([x.shape[1], 3]))`
`    return tf.matmul(x, self.w)`
```

Using the above module would produce `tf.Variable`s and `tf.Tensor`s whose names included the module name:

````mod = MyModule()`
`mod(tf.ones([1, 2]))`
`<tf.Tensor: shape=(1, 3), dtype=float32, numpy=..., dtype=float32)>`
`mod.w`
`<tf.Variable 'my_module/Variable:0' shape=(2, 3) dtype=float32,`
`numpy=..., dtype=float32)>`
```

Args
`method` The method to wrap.

Returns
The original method wrapped such that it enters the module's name scope.

### `__call__`

View source

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:

1. If the input is a `tfd.Distribution` instance, return `tfd.TransformedDistribution(distribution=input, bijector=self)`.
2. If the input is a `tfb.Bijector` instance, return `tfb.Chain([self, input])`.
3. 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__`

View source

Return self==value.

[{ "type": "thumb-down", "id": "missingTheInformationINeed", "label":"必要な情報がない" },{ "type": "thumb-down", "id": "tooComplicatedTooManySteps", "label":"複雑すぎる / 手順が多すぎる" },{ "type": "thumb-down", "id": "outOfDate", "label":"最新ではない" },{ "type": "thumb-down", "id": "samplesCodeIssue", "label":"Samples / code issue" },{ "type": "thumb-down", "id": "otherDown", "label":"その他" }]
[{ "type": "thumb-up", "id": "easyToUnderstand", "label":"わかりやすい" },{ "type": "thumb-up", "id": "solvedMyProblem", "label":"問題の解決に役立った" },{ "type": "thumb-up", "id": "otherUp", "label":"その他" }]