tf.contrib.distributions.bijectors.SinhArcsinh

Compute Y = g(X) = Sinh( (Arcsinh(X) + skewness) * tailweight ).

Inherits From: Bijector

tf.contrib.distributions.bijectors.SinhArcsinh(
    skewness=None, tailweight=None, validate_args=False, name='SinhArcsinh'
)

For skewness in (-inf, inf) and tailweight in (0, inf), this transformation is a diffeomorphism of the real line (-inf, inf). The inverse transform is X = g^{-1}(Y) = Sinh( ArcSinh(Y) / tailweight - skewness ).

The SinhArcsinh transformation of the Normal is described in Sinh-arcsinh distributions This Bijector allows a similar transformation of any distribution supported on (-inf, inf).

Meaning of the parameters

• If skewness = 0 and tailweight = 1, this transform is the identity.
• Positive (negative) skewness leads to positive (negative) skew.
  • positive skew means, for unimodal X centered at zero, the mode of Y is "tilted" to the right.
  • positive skew means positive values of Y become more likely, and negative values become less likely.
• Larger (smaller) tailweight leads to fatter (thinner) tails.
  • Fatter tails mean larger values of |Y| become more likely.
  • If X is a unit Normal, tailweight < 1 leads to a distribution that is "flat" around Y = 0, and a very steep drop-off in the tails.
  • If X is a unit Normal, tailweight > 1 leads to a distribution more peaked at the mode with heavier tails.

To see the argument about the tails, note that for |X| >> 1 and |X| >> (|skewness| * tailweight)**tailweight, we have Y approx 0.5 X**tailweight e**(sign(X) skewness * tailweight).

Args
skewness	Skewness parameter. Float-type Tensor. Default is 0 of type float32.
tailweight	Tailweight parameter. Positive Tensor of same dtype as skewness and broadcastable shape. Default is 1 of type float32.
validate_args	Python bool indicating whether arguments should be checked for correctness.
name	Python str name given to ops managed by this object.

Attributes
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. Note: Jacobian matrix is either constant for both forward and inverse or neither.
name	Returns the string name of this Bijector.
skewness	The skewness in: Y = Sinh((Arcsinh(X) + skewness) * tailweight).
tailweight	The tailweight in: Y = Sinh((Arcsinh(X) + skewness) * tailweight).
validate_args	Returns True if Tensor arguments will be validated.

Methods

forward

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forward(
    x, name='forward'
)

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.

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

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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

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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

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

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 x.shape.ndims - event_ndims dimensions.
name	The name to give this op.

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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inverse(
    y, name='inverse'
)

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.

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

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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

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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

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inverse_log_det_jacobian(
    y, event_ndims, name='inverse_log_det_jacobian'
)

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 y.shape.ndims - event_ndims dimensions.
name	The name to give this op.

Returns
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.