tf.contrib.distributions.bijectors.SinhArcsinh

Class SinhArcsinh

Inherits From: Bijector

Defined in tensorflow/contrib/distributions/python/ops/bijectors/sinh_arcsinh.py.

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

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).

Properties

dtype

dtype of Tensors transformable by this distribution.

event_ndims

Returns then number of event dimensions this bijector operates on.

graph_parents

Returns this Bijector's graph_parents as a Python list.

is_constant_jacobian

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

Note: Jacobian is either constant for both forward and inverse or neither.

Returns:

• is_constant_jacobian: Python bool.

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

__init__

__init__(
    skewness=None,
    tailweight=None,
    event_ndims=0,
    validate_args=False,
    name='SinhArcsinh'
)

Instantiates the SinhArcsinh bijector.

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.
• event_ndims: Python scalar indicating the number of dimensions associated with a particular draw from the distribution.
• validate_args: Python bool indicating whether arguments should be checked for correctness.
• name: Python str name given to ops managed by this object.

forward

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

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

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

forward_log_det_jacobian(
    x,
    name='forward_log_det_jacobian'
)

Returns both the forward_log_det_jacobian.

Args:

• x: Tensor. The input to the "forward" Jacobian evaluation.
• 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

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

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

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

inverse_log_det_jacobian(
    y,
    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 evaluation.
• 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.