contrib.distributions.bijectors.AffineLinearOperator
tf.contrib.distributions.bijectors.AffineLinearOperator
class tf.contrib.distributions.bijectors.AffineLinearOperator
Defined in tensorflow/contrib/distributions/python/ops/bijectors/affine_linear_operator_impl.py
.
See the guide: Random variable transformations (contrib) > Bijectors
Compute Y = g(X; shift, scale) = scale @ X + shift
.
shift
is a numeric Tensor
and scale
is a LinearOperator
.
If X
is a scalar then the forward transformation is: scale * X + shift
where *
denotes the scalar product.
Note: we don't always simply transposeX
(but write it this way for brevity). Actually the inputX
undergoes the following transformation before being premultiplied byscale
:
- If there are no sample dims, we call
X = tf.expand_dims(X, 0)
, i.e.,new_sample_shape = [1]
. Otherwise do nothing. - The sample shape is flattened to have one dimension, i.e.,
new_sample_shape = [n]
wheren = tf.reduce_prod(old_sample_shape)
. - The sample dim is cyclically rotated left by 1, i.e.,
new_shape = [B1,...,Bb, k, n]
wheren
is as above,k
is the event_shape, andB1,...,Bb
are the batch shapes for each ofb
batch dimensions.
(For more details see shape.make_batch_of_event_sample_matrices
.)
The result of the above transformation is that X
can be regarded as a batch of matrices where each column is a draw from the distribution. After premultiplying by scale
, we take the inverse of this procedure. The input Y
also undergoes the same transformation before/after premultiplying by inv(scale)
.
Example Use:
linalg = tf.contrib.linalg x = [1., 2, 3] shift = [-1., 0., 1] diag = [1., 2, 3] scale = linalg.LinearOperatorDiag(diag) affine = AffineLinearOperator(shift, scale) # In this case, `forward` is equivalent to: # y = scale @ x + shift y = affine.forward(x) # [0., 4, 10] shift = [2., 3, 1] tril = [[1., 0, 0], [2, 1, 0], [3, 2, 1]] scale = linalg.LinearOperatorTriL(tril) affine = AffineLinearOperator(shift, scale) # In this case, `forward` is equivalent to: # np.squeeze(np.matmul(tril, np.expand_dims(x, -1)), -1) + shift y = affine.forward(x) # [3., 7, 11]
Properties
dtype
dtype of Tensor
s 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
: Pythonbool
.
name
Returns the string name of this Bijector
.
scale
The scale
LinearOperator
in Y = scale @ X + shift
.
shift
The shift
Tensor
in Y = scale @ X + shift
.
validate_args
Returns True if Tensor arguments will be validated.
Methods
__init__
__init__( shift=None, scale=None, event_ndims=1, validate_args=False, name='affine_linear_operator' )
Instantiates the AffineLinearOperator
bijector.
Args:
-
shift
: Floating-pointTensor
. -
scale
: Subclass ofLinearOperator
. Represents the (batch) positive definite matrixM
inR^{k x k}
. -
event_ndims
: Scalarinteger
Tensor
indicating the number of dimensions associated with a particular draw from the distribution. Must be 0 or 1. -
validate_args
: Pythonbool
indicating whether arguments should be checked for correctness. -
name
: Pythonstr
name given to ops managed by this object.
Raises:
-
ValueError
: ifevent_ndims
is not 0 or 1. -
TypeError
: ifscale
is not aLinearOperator
. -
TypeError
: ifshift.dtype
does not matchscale.dtype
. -
ValueError
: if notscale.is_non_singular
.
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/AffineLinearOperator