tf.contrib.distributions.bijectors.AbsoluteValue

Class AbsoluteValue

Inherits From: Bijector

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

Computes Y = g(X) = Abs(X), element-wise.

This non-injective bijector allows for transformations of scalar distributions with the absolute value function, which maps (-inf, inf) to [0, inf).

• For y in (0, inf), AbsoluteValue.inverse(y) returns the set inverse {x in (-inf, inf) : |x| = y} as a tuple, -y, y.
• AbsoluteValue.inverse(0) returns 0, 0, which is not the set inverse (the set inverse is the singleton {0}), but "works" in conjunction with TransformedDistribution to produce a left semi-continuous pdf.
• For y < 0, AbsoluteValue.inverse(y) happily returns the wrong thing, -y, y. This is done for efficiency. If validate_args == True, y < 0 will raise an exception.

tfd = tf.contrib.distributions

abs = tfd.bijectors.AbsoluteValue()

abs.forward([-1., 0., 1.])
==> [1., 0.,  1.]

abs.inverse(1.)
==> [-1., 1.]

# The |dX/dY| is constant, == 1.  So Log|dX/dY| == 0.
abs.inverse_log_det_jacobian(1.)
==> [0., 0.]

# Special case handling of 0.
abs.inverse(0.)
==> [0., 0.]

abs.inverse_log_det_jacobian(0.)
==> [0., 0.]

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.

validate_args

Returns True if Tensor arguments will be validated.

Methods

__init__

__init__(
    event_ndims=0,
    validate_args=False,
    name='absolute_value'
)

Instantiates the AbsoluteValue bijector.

Args:

• event_ndims: Python scalar indicating the number of dimensions associated with a particular draw from the distribution. Currently only zero is supported.
• validate_args: Python bool indicating whether arguments should be checked for correctness, in particular whether inputs to inverse and inverse_log_det_jacobian are non-negative.
• name: Python str name given to ops managed by this object.

Raises:

• ValueError: If event_ndims is not zero.

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.