Class Softplus
Inherits From: Bijector
Defined in tensorflow/contrib/distributions/python/ops/bijectors/softplus.py
.
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() 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. 2 id="__init__"><code>__init__</code></h2>
__init__( hinge_softness=None, validate_args=False, name='softplus' )
DEPRECATED FUNCTION
kwargs
:
hinge_softness
: Nonzero floating pointTensor
. Controls the softness of what would otherwise be a kink at the origin. Default is 1.0
Properties
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.
Returns:
is_constant_jacobian
: Pythonbool
.
name
Returns the string name of this Bijector
.
validate_args
Returns True if Tensor arguments will be validated.
Methods
tf.contrib.distributions.bijectors.Softplus.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.
tf.contrib.distributions.bijectors.Softplus.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.
tf.contrib.distributions.bijectors.Softplus.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
.
tf.contrib.distributions.bijectors.Softplus.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 toself.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 shapex.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
: ifself.dtype
is specified andy.dtype
is notself.dtype
.NotImplementedError
: if neither_forward_log_det_jacobian
nor {_inverse
,_inverse_log_det_jacobian
} are implemented, or this is a non-injective bijector.
tf.contrib.distributions.bijectors.Softplus.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
: ifself.dtype
is specified andy.dtype
is notself.dtype
.NotImplementedError
: if_inverse
is not implemented.
tf.contrib.distributions.bijectors.Softplus.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.
tf.contrib.distributions.bijectors.Softplus.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
.
tf.contrib.distributions.bijectors.Softplus.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 toself.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 shapey.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
: ifself.dtype
is specified andy.dtype
is notself.dtype
.NotImplementedError
: if_inverse_log_det_jacobian
is not implemented.