contrib.distributions.bijectors.Softplus
tf.contrib.distributions.bijectors.Softplus
class tf.contrib.distributions.bijectors.Softplus
Defined in tensorflow/contrib/distributions/python/ops/bijectors/softplus_impl.py
.
See the guide: Random variable transformations (contrib) > Bijectors
Bijector which computes Y = g(X) = Log[1 + exp(X)]
.
The softplus Bijector
has the following two useful properties:
- The domain is the positive real numbers
-
softplus(x) approx x
, for largex
, so it does not overflow as easily as theExp
Bijector
.
The optional nonzero hinge_softness
parameter changes the transition at zero. With hinge_softness = c
, the bijector is:
r large `x >> 1`, `c * Log[1 + exp(x / c)] approx c * Log[exp(x / c)] = x`, the behavior for large `x` is the same as the standard softplus. `c > 0` approaches 0 from the right, `f_c(x)` becomes less and less soft, proaching `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(event_ndims=2) 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. Properties 3 id="dtype"><code>dtype</code></h3> ype of `Tensor`s transformable by this distribution. 3 id="event_ndims"><code>event_ndims</code></h3> turns then number of event dimensions this bijector operates on. 3 id="graph_parents"><code>graph_parents</code></h3> turns this `Bijector`'s graph_parents as a Python list. 3 id="hinge_softness"><code>hinge_softness</code></h3> 3 id="is_constant_jacobian"><code>is_constant_jacobian</code></h3> turns true iff the Jacobian is not a function of x. te: Jacobian is either constant for both forward and inverse or neither. ## Returns: <b>`is_constant_jacobian`</b>: Python `bool`. 3 id="name"><code>name</code></h3> turns the string name of this `Bijector`. 3 id="validate_args"><code>validate_args</code></h3> turns True if Tensor arguments will be validated. Methods 3 id="__init__"><code>__init__</code></h3>
__init__( *args, **kwargs )
kwargs
:
-
hinge_softness
: Nonzero floating pointTensor
. Controls the softness of what would otherwise be a kink at the origin. Default is 1.0
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
: ifself.dtype
is specified andx.dtype
is notself.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 intoforward
function.
Returns:
-
forward_event_shape_tensor
:TensorShape
indicating event-portion shape after applyingforward
. 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 intoforward
function. -
name
: name to give to the op
Returns:
-
forward_event_shape_tensor
:Tensor
,int32
vector indicating event-portion shape after applyingforward
.
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
.
Raises:
-
TypeError
: ifself.dtype
is specified andy.dtype
is notself.dtype
. -
NotImplementedError
: if neither_forward_log_det_jacobian
nor {_inverse
,_inverse_log_det_jacobian
} are implemented.
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
.
Raises:
-
TypeError
: ifself.dtype
is specified andy.dtype
is notself.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 intoinverse
function.
Returns:
-
inverse_event_shape_tensor
:TensorShape
indicating event-portion shape after applyinginverse
. 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 intoinverse
function. -
name
: name to give to the op
Returns:
-
inverse_event_shape_tensor
:Tensor
,int32
vector indicating event-portion shape after applyinginverse
.
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.
Args:
-
y
:Tensor
. The input to the "inverse" Jacobian evaluation. -
name
: The name to give this op.
Returns:
Tensor
.
Raises:
-
TypeError
: ifself.dtype
is specified andy.dtype
is notself.dtype
. -
NotImplementedError
: if_inverse_log_det_jacobian
is not implemented.
© 2017 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/api_docs/python/tf/contrib/distributions/bijectors/Softplus