Bijector which computes Y = g(X) = Log[1 + exp(X)]
.
Inherits From: Bijector
tf.contrib.distributions.bijectors.Softplus( hinge_softness=None, validate_args=False, name='softplus' )
The softplus Bijector
has the following two useful properties:
softplus(x) approx x
, for large x
, so it does not overflow as easily as the Exp
Bijector
.The optional nonzero hinge_softness
parameter changes the transition at zero. With hinge_softness = c
, the bijector is:
For large x >> 1
, c * Log[1 + exp(x / c)] approx c * Log[exp(x / c)] = x
, so the behavior for large x
is the same as the standard softplus.
As c > 0
approaches 0 from the right, f_c(x)
becomes less and less soft, approaching max(0, x)
.
c = 1
is the default.c > 0
but small means f(x) approx ReLu(x) = max(0, x)
.c < 0
flips sign and reflects around the y-axis
: f_{-c}(x) = -f_c(-x)
.c = 0
results in a non-bijective transformation and triggers an exception.
Example Use:
# Create the Y=g(X)=softplus(X) transform which works only on Tensors with 1 # batch ndim and 2 event ndims (i.e., vector of matrices). softplus = Softplus() x = [[[1., 2], [3, 4]], [[5, 6], [7, 8]]] log(1 + exp(x)) == softplus.forward(x) log(exp(x) - 1) == softplus.inverse(x)
Note: log(.) and exp(.) are applied element-wise but the Jacobian is a reduction over the event space.
Attributes | |
---|---|
dtype | dtype of Tensor s 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. |
hinge_softness | |
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 . |
validate_args | Returns True if Tensor arguments will be validated. |
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, 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
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, 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. |
© 2020 The TensorFlow Authors. All rights reserved.
Licensed under the Creative Commons Attribution License 3.0.
Code samples licensed under the Apache 2.0 License.
https://www.tensorflow.org/versions/r1.15/api_docs/python/tf/contrib/distributions/bijectors/Softplus