Class AffineLinearOperator
Inherits From: Bijector
Defined in tensorflow/contrib/distributions/python/ops/bijectors/affine_linear_operator.py
.
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.
- 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.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.LinearOperatorLowerTriangular(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]
__init__
__init__(
shift=None,
scale=None,
validate_args=False,
name='affine_linear_operator'
)
Instantiates the AffineLinearOperator
bijector. (deprecated)
Args:
shift
: Floating-pointTensor
.scale
: Subclass ofLinearOperator
. Represents the (batch) positive definite matrixM
inR^{k x k}
.validate_args
: Pythonbool
indicating whether arguments should be checked for correctness.name
: Pythonstr
name given to ops managed by this object.
Raises:
TypeError
: ifscale
is not aLinearOperator
.TypeError
: ifshift.dtype
does not matchscale.dtype
.ValueError
: if notscale.is_non_singular
.
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.
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
.
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
tf.contrib.distributions.bijectors.AffineLinearOperator.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.AffineLinearOperator.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.AffineLinearOperator.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.AffineLinearOperator.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.AffineLinearOperator.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.AffineLinearOperator.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.AffineLinearOperator.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.AffineLinearOperator.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.