tf.contrib.distributions.bijectors.SoftmaxCentered

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Bijector which computes Y = g(X) = exp([X 0]) / sum(exp([X 0])).

Inherits From: Bijector

tf.contrib.distributions.bijectors.SoftmaxCentered(
    validate_args=False, name='softmax_centered'
)

To implement softmax as a bijection, the forward transformation appends a value to the input and the inverse removes this coordinate. The appended coordinate represents a pivot, e.g., softmax(x) = exp(x-c) / sum(exp(x-c)) where c is the implicit last coordinate.

Example Use:

bijector.SoftmaxCentered().forward(tf.math.log([2, 3, 4]))
# Result: [0.2, 0.3, 0.4, 0.1]
# Extra result: 0.1

bijector.SoftmaxCentered().inverse([0.2, 0.3, 0.4, 0.1])
# Result: tf.math.log([2, 3, 4])
# Extra coordinate removed.

At first blush it may seem like the Invariance of domain theorem implies this implementation is not a bijection. However, the appended dimension makes the (forward) image non-open and the theorem does not directly apply.

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.
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.