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)
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.
Attributes
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.
name
Returns the string name of this Bijector.
validate_args
Returns True if Tensor arguments will be validated.
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.
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.
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