tf.contrib.distributions.bijectors.Affine

Class Affine

Inherits From: Bijector

Defined in tensorflow/contrib/distributions/python/ops/bijectors/affine.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 Tensors 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: Python bool.

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,
    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-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.

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: if self.dtype is specified and x.dtype is not self.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 into forward function.

Returns:

• forward_event_shape_tensor: TensorShape indicating event-portion shape after applying forward. 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 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

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, 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

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

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

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

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, evaluated at g^{-1}(y).

Args:

• y: Tensor. The input to the "inverse" Jacobian evaluation.
• 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.