tf.contrib.distributions.bijectors.ScaleTriL

Class ScaleTriL

Inherits From: Chain

Defined in tensorflow/contrib/distributions/python/ops/bijectors/scale_tril.py.

Transforms unconstrained vectors to TriL matrices with positive diagonal.

This is implemented as a simple tfb.Chain of tfb.FillTriangular followed by tfb.TransformDiagonal, and provided mostly as a convenience. The default setup is somewhat opinionated, using a Softplus transformation followed by a small shift (1e-5) which attempts to avoid numerical issues from zeros on the diagonal.

Examples

import tensorflow_probability as tfp
tfd = tfp.distributions
tfb = tfp.bijectors

b = tfb.ScaleTriL(
     diag_bijector=tfb.Exp(),
     diag_shift=None)
b.forward(x=[0., 0., 0.])
# Result: [[1., 0.],
#          [0., 1.]]
b.inverse(y=[[1., 0],
             [.5, 2]])
# Result: [log(2), .5, log(1)]

# Define a distribution over PSD matrices of shape `[3, 3]`,
# with `1 + 2 + 3 = 6` degrees of freedom.
dist = tfd.TransformedDistribution(
        tfd.Normal(tf.zeros(6), tf.ones(6)),
        tfb.Chain([tfb.CholeskyOuterProduct(), tfb.ScaleTriL()]))

# Using an identity transformation, ScaleTriL is equivalent to
# tfb.FillTriangular.
b = tfb.ScaleTriL(
     diag_bijector=tfb.Identity(),
     diag_shift=None)

# For greater control over initialization, one can manually encode
# pre- and post- shifts inside of `diag_bijector`.
b = tfb.ScaleTriL(
     diag_bijector=tfb.Chain([
       tfb.AffineScalar(shift=1e-3),
       tfb.Softplus(),
       tfb.AffineScalar(shift=0.5413)]),  # softplus_inverse(1.)
                                          #  = log(expm1(1.)) = 0.5413
     diag_shift=None)

__init__

__init__(
    diag_bijector=None,
    diag_shift=1e-05,
    validate_args=False,
    name='scale_tril'
)

Instantiates the ScaleTriL bijector. (deprecated)

Args:

  • diag_bijector: Bijector instance, used to transform the output diagonal to be positive. Default value: None (i.e., tfb.Softplus()).
  • diag_shift: Float value broadcastable and added to all diagonal entries after applying the diag_bijector. Setting a positive value forces the output diagonal entries to be positive, but prevents inverting the transformation for matrices with diagonal entries less than this value. Default value: 1e-5 (i.e., no shift is applied).
  • validate_args: Python bool indicating whether arguments should be checked for correctness. Default value: False (i.e., arguments are not validated).
  • name: Python str name given to ops managed by this object. Default value: scale_tril.

Properties

bijectors

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.

Returns:

  • is_constant_jacobian: Python bool.

name

Returns the string name of this Bijector.

validate_args

Returns True if Tensor arguments will be validated.

Methods

tf.contrib.distributions.bijectors.ScaleTriL.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.

tf.contrib.distributions.bijectors.ScaleTriL.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.

tf.contrib.distributions.bijectors.ScaleTriL.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.

tf.contrib.distributions.bijectors.ScaleTriL.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 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.

tf.contrib.distributions.bijectors.ScaleTriL.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.

tf.contrib.distributions.bijectors.ScaleTriL.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.

tf.contrib.distributions.bijectors.ScaleTriL.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.

tf.contrib.distributions.bijectors.ScaleTriL.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 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.