contrib.distributions.bijectors.Affine
tf.contrib.distributions.bijectors.Affine
class tf.contrib.distributions.bijectors.Affine
Defined in tensorflow/contrib/distributions/python/ops/bijectors/affine_impl.py
.
See the guide: Random variable transformations (contrib) > Bijectors
Compute Y = g(X; shift, scale) = scale @ X + shift
.
Here scale = c * I + diag(D1) + tril(L) + V @ diag(D2) @ V.T
.
In TF parlance, the scale
term is logically equivalent to:
scale = ( scale_identity_multiplier * tf.diag(tf.ones(d)) + tf.diag(scale_diag) + scale_tril + scale_perturb_factor @ diag(scale_perturb_diag) @ tf.transpose([scale_perturb_factor]) )
The scale
term is applied without necessarily materializing constituent matrices, i.e., the matmul is matrix-free when possible.
Examples:
# Y = X b = Affine() # Y = X + shift b = Affine(shift=[1., 2, 3]) # Y = 2 * I @ X.T + shift b = Affine(shift=[1., 2, 3], scale_identity_multiplier=2.) # Y = tf.diag(d1) @ X.T + shift b = Affine(shift=[1., 2, 3], scale_diag=[-1., 2, 1]) # Implicitly 3x3. # Y = (I + v * v.T) @ X.T + shift b = Affine(shift=[1., 2, 3], scale_perturb_factor=[[1., 0], [0, 1], [1, 1]]) # Y = (diag(d1) + v * diag(d2) * v.T) @ X.T + shift b = Affine(shift=[1., 2, 3], scale_diag=[1., 3, 3], # Implicitly 3x3. scale_perturb_diag=[2., 1], # Implicitly 2x2. scale_perturb_factor=[[1., 0], [0, 1], [1, 1]])
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_identity_multiplier=None, scale_diag=None, scale_tril=None, scale_perturb_factor=None, scale_perturb_diag=None, event_ndims=1, validate_args=False, name='affine' )
Instantiates the Affine
bijector.
This Bijector
is initialized with shift
Tensor
and scale
arguments, giving the forward operation:
Y = g(X) = scale @ X + shift
where the scale
term is logically equivalent to:
scale = ( scale_identity_multiplier * tf.diag(tf.ones(d)) + tf.diag(scale_diag) + scale_tril + scale_perturb_factor @ diag(scale_perturb_diag) @ tf.transpose([scale_perturb_factor]) )
If none of scale_identity_multiplier
, scale_diag
, or scale_tril
are specified then scale += IdentityMatrix
. Otherwise specifying a scale
argument has the semantics of scale += Expand(arg)
, i.e., scale_diag != None
means scale += tf.diag(scale_diag)
.
Args:
-
shift
: Floating-pointTensor
. If this is set toNone
, no shift is applied. -
scale_identity_multiplier
: floating point rank 0Tensor
representing a scaling done to the identity matrix. Whenscale_identity_multiplier = scale_diag = scale_tril = None
thenscale += IdentityMatrix
. Otherwise no scaled-identity-matrix is added toscale
. -
scale_diag
: Floating-pointTensor
representing the diagonal matrix.scale_diag
has shape [N1, N2, ... k], which represents a k x k diagonal matrix. WhenNone
no diagonal term is added toscale
. -
scale_tril
: Floating-pointTensor
representing the diagonal matrix.scale_diag
has shape [N1, N2, ... k, k], which represents a k x k lower triangular matrix. WhenNone
noscale_tril
term is added toscale
. The upper triangular elements above the diagonal are ignored. -
scale_perturb_factor
: Floating-pointTensor
representing factor matrix with last two dimensions of shape(k, r)
. WhenNone
, no rank-r update is added toscale
. -
scale_perturb_diag
: Floating-pointTensor
representing the diagonal matrix.scale_perturb_diag
has shape [N1, N2, ... r], which represents anr x r
diagonal matrix. WhenNone
low rank updates will take the formscale_perturb_factor * scale_perturb_factor.T
. -
event_ndims
: Scalarint32
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
: ifperturb_diag
is specified but notperturb_factor
. -
TypeError
: ifshift
has differentdtype
fromscale
arguments.
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/Affine