Missed TensorFlow Dev Summit? Check out the video playlist. Watch recordings

tfp.bijectors.LambertWTail

View source on GitHub

LambertWTail transformation for heavy-tail Lambert W x F random variables.

Inherits From: Chain

tfp.bijectors.LambertWTail(
    shift, scale, tailweight, validate_args=False, name='lambertw_tail'
)

A random variable Y has a Lambert W x F distribution if W_tau(Y) = X has distribution F, where tau = (shift, scale, tail) parameterizes the inverse transformation.

This bijector defines the transformation underlying Lambert W x F distributions that transform an input random variable to an output random variable with heavier tails. It is defined as

Y = (U * exp(0.5 * tail * U^2)) * scale + shift, tail >= 0

where U = (X - shift) / scale is a shifted/scaled input random variable, and tail >= 0 is the tail parameter.

Args:

  • shift: Floating point tensor; the shift for centering (uncentering) the input (output) random variable(s).
  • scale: Floating point tensor; the scaling (unscaling) of the input (output) random variable(s). Must contain only positive values.
  • tailweight: Floating point tensor; the tail behaviors of the output random variable(s). Must contain only non-negative values.
  • 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.
  • name: Python str name prefixed to Ops created by this class.

Attributes:

  • shift: shift to center (uncenter) the input data.
  • scale: scale to normalize (de-normalize) the input data.
  • tailweight: Tail parameter delta of heavy-tail transformation; must be >= 0.* bijectors
  • 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.
  • 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.

  • 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 
     
  • 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.

Raises:

  • TypeError: if shift and scale and tail have different dtype.

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_dtype

View source

forward_dtype(
    dtype, name='forward_dtype', **kwargs
)

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

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_dtype

View source

inverse_dtype(
    dtype, name='inverse_dtype', **kwargs
)

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

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.