tf.contrib.distributions.bijectors.Affine

Compute Y = g(X; shift, scale) = scale @ X + shift.

Inherits From: Bijector

tf.contrib.distributions.bijectors.Affine(
    shift=None, scale_identity_multiplier=None, scale_diag=None, scale_tril=None,
    scale_perturb_factor=None, scale_perturb_diag=None, validate_args=False,
    name='affine'
)

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.linalg.tensor_diag(tf.ones(d)) +
  tf.linalg.tensor_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.linalg.tensor_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]])

Args
shift	Floating-point Tensor. If this is set to None, no shift is applied.
scale_identity_multiplier	floating point rank 0 Tensor representing a scaling done to the identity matrix. When scale_identity_multiplier = scale_diag = scale_tril = None then scale += IdentityMatrix. Otherwise no scaled-identity-matrix is added to scale.
scale_diag	Floating-point Tensor representing the diagonal matrix. scale_diag has shape [N1, N2, ... k], which represents a k x k diagonal matrix. When None no diagonal term is added to scale.
scale_tril	Floating-point Tensor representing the diagonal matrix. scale_diag has shape [N1, N2, ... k, k], which represents a k x k lower triangular matrix. When None no scale_tril term is added to scale. The upper triangular elements above the diagonal are ignored.
scale_perturb_factor	Floating-point Tensor representing factor matrix with last two dimensions of shape (k, r). When None, no rank-r update is added to scale.
scale_perturb_diag	Floating-point Tensor representing the diagonal matrix. scale_perturb_diag has shape [N1, N2, ... r], which represents an r x r diagonal matrix. When None low rank updates will take the form scale_perturb_factor * scale_perturb_factor.T.
validate_args	Python bool indicating whether arguments should be checked for correctness.
name	Python str name given to ops managed by this object.

Raises
ValueError	if perturb_diag is specified but not perturb_factor.
TypeError	if shift has different dtype from scale arguments.

Attributes
dtype	dtype of Tensors 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. Note: Jacobian matrix is either constant for both forward and inverse or neither.
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

forward

View source

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	if self.dtype is specified and x.dtype is not self.dtype.
NotImplementedError	if _forward is not implemented.

forward_event_shape

View source

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 into forward function.

Returns
forward_event_shape_tensor	TensorShape indicating event-portion shape after applying forward. Possibly unknown.

forward_event_shape_tensor

View source

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 into forward function.
name	name to give to the op

Returns
forward_event_shape_tensor	Tensor, int32 vector indicating event-portion shape after applying forward.

forward_log_det_jacobian

View source

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 to self.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 shape x.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	if self.dtype is specified and y.dtype is not self.dtype.
NotImplementedError	if neither _forward_log_det_jacobian nor {_inverse, _inverse_log_det_jacobian} are implemented, or this is a non-injective bijector.

inverse

View source

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	if self.dtype is specified and y.dtype is not self.dtype.
NotImplementedError	if _inverse is not implemented.

inverse_event_shape

View source

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 into inverse function.

Returns
inverse_event_shape_tensor	TensorShape indicating event-portion shape after applying inverse. Possibly unknown.

inverse_event_shape_tensor

View source

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 into inverse function.
name	name to give to the op

Returns
inverse_event_shape_tensor	Tensor, int32 vector indicating event-portion shape after applying inverse.

inverse_log_det_jacobian

View source

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 to self.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 shape y.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	if self.dtype is specified and y.dtype is not self.dtype.
NotImplementedError	if _inverse_log_det_jacobian is not implemented.