tfp.bijectors.SoftClip

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Class 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=tfd.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(
  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.))
  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.

__init__

View source

__init__(
    low=None,
    high=None,
    hinge_softness=None,
    validate_args=False,
    name='soft_clip'
)

Instantiates the SoftClip bijector.

Args:

  • 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.

Properties

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.

Returns:

  • is_constant_jacobian: Python bool.

low

name

Returns the string name of this Bijector.

name_scope

Returns a tf.name_scope instance for this class.

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 

Returns:

A sequence of all submodules.

trainable_variables

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

Returns:

A sequence of variables for the current module (sorted by attribute name) followed by variables from all submodules recursively (breadth first).

validate_args

Returns True if Tensor arguments will be validated.

variables

Sequence of variables owned by this module and its submodules.

Returns:

A sequence of variables for the current module (sorted by attribute name) followed by variables from all submodules recursively (breadth first).

Methods

__call__

View source

__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:

  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.])

forward

View source

forward(
    x,
    name='forward',
    **kwargs
)

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_event_shape

View source

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 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

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 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

forward_log_det_jacobian(
    x,
    event_ndims,
    name='forward_log_det_jacobian',
    **kwargs
)

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

View source

inverse(
    y,
    name='inverse',
    **kwargs
)

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_event_shape

View source

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 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

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 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

inverse_log_det_jacobian(
    y,
    event_ndims,
    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. 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.

with_name_scope

@classmethod
with_name_scope(
    cls,
    method
)

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.Variables and tf.Tensors 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.