tfp.experimental.substrates.numpy.bijectors.SoftClip

Bijector that approximates clipping as a continuous, differentiable map.

Inherits From: Bijector

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 dtype of Tensors transformable by this distribution.
forward_min_event_ndims Returns the minimal number of dimensions bijector.forward operates on.
graph_parents Returns this Bijector's graph_parents as a Python list.
high

hinge_softness

inverse_min_event_ndims Returns the minimal number of dimensions bijector.inverse operates on.
is_constant_jacobian Returns true iff the Jacobian matrix is not a function of x.

low

name Returns the string name of this Bijector.
parameters Dictionary of parameters used to instantiate this Bijector.
trainable_variables

validate_args Returns True if Tensor arguments will be validated.
variables

Methods

forward

View source

Returns the forward Bijector evaluation, i.e., X = g(Y).

Args
x Tensor. The input to the 'forward' evaluation.
name The name to give this op.
**kwargs Named arguments forwarded to subclass implementation.

Returns
Tensor.

Raises
TypeError if self.dtype is specified and x.dtype is not self.dtype.
NotImplementedError if _forward is not implemented.

forward_dtype

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Returns the dtype of the output of the forward transformation.

Args
dtype tf.dtype, or nested structure of tf.dtypes, of the input to forward.
name The name to give this op.
**kwargs Named arguments forwarded to subclass implementation.

Returns
tf.dtype or nested structure of tf.dtypes of the output of 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 indicating event-portion shape passed into forward function.

Returns
forward_event_shape_tensor TensorShape 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 indicating event-portion shape passed into forward function.
name name to give to the op

Returns
forward_event_shape_tensor Tensor, int32 vector indicating event-portion shape after applying forward.

forward_log_det_jacobian

View source

Returns both the forward_log_det_jacobian.

Args
x Tensor. The input to the 'forward' Jacobian determinant evaluation.
event_ndims Number of dimensions in the probabilistic events being transformed. Must be greater than or equal to self.forward_min_event_ndims. The result is summed over the final dimensions to produce a scalar Jacobian determinant for each event, i.e. it has shape rank(x) - event_ndims dimensions.
name The name to give this op.
**kwargs Named arguments forwarded to subclass implementation.

Returns
Tensor, if this bijector is injective. If not injective this is not implemented.

Raises
TypeError if self.dtype is specified and y.dtype is not self.dtype.
NotImplementedError if neither _forward_log_det_jacobian nor {_inverse, _inverse_log_det_jacobian} are implemented, or this is a non-injective bijector.

inverse

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Returns the inverse Bijector evaluation, i.e., X = g^{-1}(Y).

Args
y Tensor. The input to the 'inverse' evaluation.
name The name to give this op.
**kwargs Named arguments forwarded to subclass implementation.

Returns
Tensor, 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 self.dtype is specified and y.dtype is not self.dtype.
NotImplementedError if _inverse is not implemented.

inverse_dtype

View source

Returns the dtype of the output of the inverse transformation.

Args
dtype tf.dtype, or nested structure of tf.dtypes, of the input to inverse.
name The name to give this op.
**kwargs Named arguments forwarded to subclass implementation.

Returns
tf.dtype or nested structure of tf.dtypes of the output of 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 indicating event-portion shape passed into inverse function.

Returns
inverse_event_shape_tensor TensorShape 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 indicating event-portion shape passed into inverse function.
name name to give to the op

Returns
inverse_event_shape_tensor Tensor, int32 vector 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. The input to the 'inverse' Jacobian determinant evaluation.
event_ndims Number of dimensions in the probabilistic events being transformed. Must be greater than or equal to self.inverse_min_event_ndims. The result is summed over the final dimensions to produce a scalar Jacobian determinant for each event, i.e. it has shape rank(y) - event_ndims dimensions.
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 self.dtype is specified and y.dtype is not self.dtype.
NotImplementedError if _inverse_log_det_jacobian is not implemented.

__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 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 Tensor computed by self.forward.

Examples

sigmoid = tfb.Reciprocal()(
    tfb.AffineScalar(shift=1.)(
      tfb.Exp()(
        tfb.AffineScalar(scale=-1.))))
# ==> `tfb.Chain([
#         tfb.Reciprocal(),
#         tfb.AffineScalar(shift=1.),
#         tfb.Exp(),
#         tfb.AffineScalar(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.])