View source on GitHub |
Affine MaskedAutoregressiveFlow bijector.
Inherits From: Bijector
tfp.substrates.jax.bijectors.MaskedAutoregressiveFlow(
shift_and_log_scale_fn=None,
bijector_fn=None,
is_constant_jacobian=False,
validate_args=False,
unroll_loop=False,
event_ndims=1,
name=None
)
The affine autoregressive flow [(Papamakarios et al., 2016)][3] provides a relatively simple framework for user-specified (deep) architectures to learn a distribution over continuous events. Regarding terminology,
'Autoregressive models decompose the joint density as a product of conditionals, and model each conditional in turn. Normalizing flows transform a base density (e.g. a standard Gaussian) into the target density by an invertible transformation with tractable Jacobian.' [(Papamakarios et al., 2016)][3]
In other words, the 'autoregressive property' is equivalent to the
decomposition, p(x) = prod{ p(x[perm[i]] | x[perm[0:i]]) : i=0, ..., d }
where perm
is some permutation of {0, ..., d}
. In the simple case where
the permutation is identity this reduces to:
p(x) = prod{ p(x[i] | x[0:i]) : i=0, ..., d }
.
In TensorFlow Probability, 'normalizing flows' are implemented as
tfp.bijectors.Bijector
s. The forward
'autoregression' is implemented
using a tf.while_loop
and a deep neural network (DNN) with masked weights
such that the autoregressive property is automatically met in the inverse
.
A TransformedDistribution
using MaskedAutoregressiveFlow(...)
uses the
(expensive) forward-mode calculation to draw samples and the (cheap)
reverse-mode calculation to compute log-probabilities. Conversely, a
TransformedDistribution
using Invert(MaskedAutoregressiveFlow(...))
uses
the (expensive) forward-mode calculation to compute log-probabilities and the
(cheap) reverse-mode calculation to compute samples. See 'Example Use'
[below] for more details.
Given a shift_and_log_scale_fn
, the forward and inverse transformations are
(a sequence of) affine transformations. A 'valid' shift_and_log_scale_fn
must compute each shift
(aka loc
or 'mu' in [Germain et al. (2015)][1])
and log(scale)
(aka 'alpha' in [Germain et al. (2015)][1]) such that each
are broadcastable with the arguments to forward
and inverse
, i.e., such
that the calculations in forward
, inverse
[below] are possible.
For convenience, tfp.bijectors.AutoregressiveNetwork
is offered as a
possible shift_and_log_scale_fn
function. It implements the MADE
architecture [(Germain et al., 2015)][1]. MADE is a feed-forward network that
computes a shift
and log(scale)
using masked dense layers in a deep
neural network. Weights are masked to ensure the autoregressive property. It
is possible that this architecture is suboptimal for your task. To build
alternative networks, either change the arguments to
tfp.bijectors.AutoregressiveNetwork
or use some other architecture, e.g.,
using tf.keras.layers
.
Assuming shift_and_log_scale_fn
has valid shape and autoregressive
semantics, the forward transformation is
def forward(x):
y = zeros_like(x)
event_size = x.shape[-event_dims:].num_elements()
for _ in range(event_size):
shift, log_scale = shift_and_log_scale_fn(y)
y = x * tf.exp(log_scale) + shift
return y
and the inverse transformation is
def inverse(y):
shift, log_scale = shift_and_log_scale_fn(y)
return (y - shift) / tf.exp(log_scale)
Notice that the inverse
does not need a for-loop. This is because in the
forward pass each calculation of shift
and log_scale
is based on the y
calculated so far (not x
). In the inverse
, the y
is fully known, thus
is equivalent to the scaling used in forward
after event_size
passes,
i.e., the 'last' y
used to compute shift
, log_scale
. (Roughly speaking,
this also proves the transform is bijective.)
The bijector_fn
argument allows specifying a more general coupling relation,
such as the LSTM-inspired activation from [4], or Neural Spline Flow [5]. It
must logically operate on each element of the input individually, and still
obey the 'autoregressive property' described above. The forward
transformation is
def forward(x):
y = zeros_like(x)
event_size = x.shape[-event_dims:].num_elements()
for _ in range(event_size):
bijector = bijector_fn(y)
y = bijector.forward(x)
return y
and inverse transformation is
def inverse(y):
bijector = bijector_fn(y)
return bijector.inverse(y)
Examples
tfd = tfp.distributions
tfb = tfp.bijectors
dims = 2
# A common choice for a normalizing flow is to use a Gaussian for the base
# distribution. (However, any continuous distribution would work.) Here, we
# use `tfd.Sample` to create a joint Gaussian distribution with diagonal
# covariance for the base distribution (note that in the Gaussian case,
# `tfd.MultivariateNormalDiag` could also be used.)
maf = tfd.TransformedDistribution(
distribution=tfd.Sample(
tfd.Normal(loc=0., scale=1.), sample_shape=[dims]),
bijector=tfb.MaskedAutoregressiveFlow(
shift_and_log_scale_fn=tfb.AutoregressiveNetwork(
params=2, hidden_units=[512, 512])))
x = maf.sample() # Expensive; uses `tf.while_loop`, no Bijector caching.
maf.log_prob(x) # Almost free; uses Bijector caching.
# Cheap; no `tf.while_loop` despite no Bijector caching.
maf.log_prob(tf.zeros(dims))
# [Papamakarios et al. (2016)][3] also describe an Inverse Autoregressive
# Flow [(Kingma et al., 2016)][2]:
iaf = tfd.TransformedDistribution(
distribution=tfd.Sample(
tfd.Normal(loc=0., scale=1.), sample_shape=[dims]),
bijector=tfb.Invert(tfb.MaskedAutoregressiveFlow(
shift_and_log_scale_fn=tfb.AutoregressiveNetwork(
params=2, hidden_units=[512, 512]))))
x = iaf.sample() # Cheap; no `tf.while_loop` despite no Bijector caching.
iaf.log_prob(x) # Almost free; uses Bijector caching.
# Expensive; uses `tf.while_loop`, no Bijector caching.
iaf.log_prob(tf.zeros(dims))
# In many (if not most) cases the default `shift_and_log_scale_fn` will be a
# poor choice. Here's an example of using a 'shift only' version and with a
# different number/depth of hidden layers.
made = tfb.AutoregressiveNetwork(params=1, hidden_units=[32])
maf_no_scale_hidden2 = tfd.TransformedDistribution(
distribution=tfd.Sample(
tfd.Normal(loc=0., scale=1.), sample_shape=[dims]),
bijector=tfb.MaskedAutoregressiveFlow(
lambda y: (made(y)[..., 0], None),
is_constant_jacobian=True))
maf_no_scale_hidden2._made = made # Ensure maf_no_scale_hidden2.trainable
# NOTE: The last line ensures that maf_no_scale_hidden2.trainable_variables
# will include all variables from `made`.
Variable Tracking
A tfb.MaskedAutoregressiveFlow
instance saves a reference to the values
passed as shift_and_log_scale_fn
and bijector_fn
to its constructor.
Thus, for most values passed as shift_and_log_scale_fn
or bijector_fn
,
variables referenced by those values will be found and tracked by the
tfb.MaskedAutoregressiveFlow
instance. Please see the tf.Module
documentation for further details.
However, if the value passed to shift_and_log_scale_fn
or bijector_fn
is a
Python function, then tfb.MaskedAutoregressiveFlow
cannot automatically
track variables used inside shift_and_log_scale_fn
or bijector_fn
. To get
tfb.MaskedAutoregressiveFlow
to track such variables, either:
Replace the Python function with a
tf.Module
,tf.keras.Layer
, or other callable object through whichtf.Module
can find variables.Or, add a reference to the variables to the
tfb.MaskedAutoregressiveFlow
instance by setting an attribute -- for example:```` made1 = tfb.AutoregressiveNetwork(params=1, hidden_units=[10, 10]) made2 = tfb.AutoregressiveNetwork(params=1, hidden_units=[10, 10]) maf = tfb.MaskedAutoregressiveFlow(lambda y: (made1(y), made2(y) + 1.)) maf._made_variables = made1.variables + made2.variables ````
References
[1]: Mathieu Germain, Karol Gregor, Iain Murray, and Hugo Larochelle. MADE: Masked Autoencoder for Distribution Estimation. In International Conference on Machine Learning, 2015. https://arxiv.org/abs/1502.03509
[2]: Diederik P. Kingma, Tim Salimans, Rafal Jozefowicz, Xi Chen, Ilya Sutskever, and Max Welling. Improving Variational Inference with Inverse Autoregressive Flow. In Neural Information Processing Systems, 2016. https://arxiv.org/abs/1606.04934
[3]: George Papamakarios, Theo Pavlakou, and Iain Murray. Masked Autoregressive Flow for Density Estimation. In Neural Information Processing Systems, 2017. https://arxiv.org/abs/1705.07057
[4]: Diederik P Kingma, Tim Salimans, Max Welling. Improving Variational Inference with Inverse Autoregressive Flow. In Neural Information Processing Systems, 2016. https://arxiv.org/abs/1606.04934
[5]: Conor Durkan, Artur Bekasov, Iain Murray, George Papamakarios. Neural Spline Flows, 2019. http://arxiv.org/abs/1906.04032
Args
shift_and_log_scale_fn
Python callable
which computesshift
andlog_scale
from the inverse domain (y
). Calculation must respect the 'autoregressive property' (see class docstring). Suggested defaulttfb.AutoregressiveNetwork(params=2, hidden_layers=...)
. Typically the function containstf.Variables
. ReturningNone
for either (both)shift
,log_scale
is equivalent to (but more efficient than) returning zero. Ifshift_and_log_scale_fn
returns a singleTensor
, the returned value will be unstacked to get theshift
andlog_scale
:tf.unstack(shift_and_log_scale_fn(y), num=2, axis=-1)
.bijector_fn
Python callable
which returns atfb.Bijector
which transforms event tensor with the signature(input, **condition_kwargs) -> bijector
. The bijector must operate on scalar events and must not alter the rank of its input. Thebijector_fn
will be called withTensors
from the inverse domain (y
). Calculation must respect the 'autoregressive property' (see class docstring).is_constant_jacobian
Python bool
. Default:False
. WhenTrue
the implementation assumeslog_scale
does not depend on the forward domain (x
) or inverse domain (y
) values. (No validation is made;is_constant_jacobian=False
is always safe but possibly computationally inefficient.)validate_args
Python bool
indicating whether arguments should be checked for correctness.unroll_loop
Python bool
indicating whether thetf.while_loop
in_forward
should be replaced with a static for loop. Requires that the final dimension ofx
be known at graph construction time. Defaults toFalse
.event_ndims
Python integer
, the intrinsic dimensionality of this bijector. 1 corresponds to a simple vector autoregressive bijector as implemented by thetfp.bijectors.AutoregressiveNetwork
, 2 might be useful for a 2D convolutionalshift_and_log_scale_fn
and so on.name
Python str
, name given to ops managed by this object.Raises
ValueError
If both or none of shift_and_log_scale_fn
andbijector_fn
are specified.Methods
copy
copy( **override_parameters_kwargs )
Creates a copy of the bijector.
Args **override_parameters_kwargs
String/value dictionary of initialization arguments to override with new values. Returns bijector
A new instance of type(self)
initialized from the union of self.parameters and override_parameters_kwargs, i.e.,dict(self.parameters, **override_parameters_kwargs)
.experimental_batch_shape
experimental_batch_shape( x_event_ndims=None, y_event_ndims=None )
Returns the batch shape of this bijector for inputs of the given rank.
The batch shape of a bijector decribes the set of distinct transformations it represents on events of a given size. For example: the bijector
tfb.Scale([1., 2.])
has batch shape[2]
for scalar events (event_ndims = 0
), because applying it to a scalar event produces two scalar outputs, the result of two different scaling transformations. The same bijector has batch shape[]
for vector events, because applying it to a vector produces (via elementwise multiplication) a single vector output.Bijectors that operate independently on multiple state parts, such as
tfb.JointMap
, must broadcast to a coherent batch shape. Some events may not be valid: for example, the bijectortfd.JointMap([tfb.Scale([1., 2.]), tfb.Scale([1., 2., 3.])])
does not produce a valid batch shape whenevent_ndims = [0, 0]
, since the batch shapes of the two parts are inconsistent. The same bijector does define valid batch shapes of[]
,[2]
, and[3]
ifevent_ndims
is[1, 1]
,[0, 1]
, or[1, 0]
, respectively.Since transforming a single event produces a scalar log-det-Jacobian, the batch shape of a bijector with non-constant Jacobian is expected to equal the shape of
forward_log_det_jacobian(x, event_ndims=x_event_ndims)
orinverse_log_det_jacobian(y, event_ndims=y_event_ndims)
, forx
ory
of the specifiedndims
.Args x_event_ndims
Optional Python int
(structure) number of dimensions in a probabilistic event passed toforward
; this must be greater than or equal toself.forward_min_event_ndims
. IfNone
, defaults toself.forward_min_event_ndims
. Mutually exclusive withy_event_ndims
. Default value:None
.y_event_ndims
Optional Python int
(structure) number of dimensions in a probabilistic event passed toinverse
; this must be greater than or equal toself.inverse_min_event_ndims
. Mutually exclusive withx_event_ndims
. Default value:None
.Returns batch_shape
TensorShape
batch shape of this bijector for a value with the given event rank. May be unknown or partially defined.experimental_batch_shape_tensor
experimental_batch_shape_tensor( x_event_ndims=None, y_event_ndims=None )
Returns the batch shape of this bijector for inputs of the given rank.
The batch shape of a bijector decribes the set of distinct transformations it represents on events of a given size. For example: the bijector
tfb.Scale([1., 2.])
has batch shape[2]
for scalar events (event_ndims = 0
), because applying it to a scalar event produces two scalar outputs, the result of two different scaling transformations. The same bijector has batch shape[]
for vector events, because applying it to a vector produces (via elementwise multiplication) a single vector output.Bijectors that operate independently on multiple state parts, such as
tfb.JointMap
, must broadcast to a coherent batch shape. Some events may not be valid: for example, the bijectortfd.JointMap([tfb.Scale([1., 2.]), tfb.Scale([1., 2., 3.])])
does not produce a valid batch shape whenevent_ndims = [0, 0]
, since the batch shapes of the two parts are inconsistent. The same bijector does define valid batch shapes of[]
,[2]
, and[3]
ifevent_ndims
is[1, 1]
,[0, 1]
, or[1, 0]
, respectively.Since transforming a single event produces a scalar log-det-Jacobian, the batch shape of a bijector with non-constant Jacobian is expected to equal the shape of
forward_log_det_jacobian(x, event_ndims=x_event_ndims)
orinverse_log_det_jacobian(y, event_ndims=y_event_ndims)
, forx
ory
of the specifiedndims
.Args x_event_ndims
Optional Python int
(structure) number of dimensions in a probabilistic event passed toforward
; this must be greater than or equal toself.forward_min_event_ndims
. IfNone
, defaults toself.forward_min_event_ndims
. Mutually exclusive withy_event_ndims
. Default value:None
.y_event_ndims
Optional Python int
(structure) number of dimensions in a probabilistic event passed toinverse
; this must be greater than or equal toself.inverse_min_event_ndims
. Mutually exclusive withx_event_ndims
. Default value:None
.Returns batch_shape_tensor
integer Tensor
batch shape of this bijector for a value with the given event rank.experimental_compute_density_correction
experimental_compute_density_correction( x, tangent_space, backward_compat=False, **kwargs )
Density correction for this transformation wrt the tangent space, at x.
Subclasses of Bijector may call the most specific applicable method of
TangentSpace
, based on whether the transformation is dimension-preserving, coordinate-wise, a projection, or something more general. The backward-compatible assumption is that the transformation is dimension-preserving (goes from R^n to R^n).Args x
Tensor
(structure). The point at which to calculate the density.tangent_space
TangentSpace
or one of its subclasses. The tangent to the support manifold atx
.backward_compat
bool
specifying whether to assume that the Bijector is dimension-preserving.**kwargs
Optional keyword arguments forwarded to tangent space methods. Returns density_correction
Tensor
representing the density correction---in log space---under the transformation that this Bijector denotes.Raises TypeError if backward_compat
is False but no method ofTangentSpace
has been called explicitly.forward
forward( x, name='forward', **kwargs )
Returns the forward
Bijector
evaluation, i.e., X = g(Y).Args x
Tensor
(structure). The input to the 'forward' evaluation.name
The name to give this op. **kwargs
Named arguments forwarded to subclass implementation. Returns Tensor
(structure).Raises TypeError
if self.dtype
is specified andx.dtype
is notself.dtype
.NotImplementedError
if _forward
is not implemented.forward_dtype
forward_dtype( dtype=UNSPECIFIED, name='forward_dtype', **kwargs )
Returns the dtype returned by
forward
for the provided input.forward_event_ndims
forward_event_ndims( event_ndims, **kwargs )
Returns the number of event dimensions produced by
forward
.Args event_ndims
Structure of Python and/or Tensor int
s, and/orNone
values. The structure should match that ofself.forward_min_event_ndims
, and all non-None
values must be greater than or equal to the corresponding value inself.forward_min_event_ndims
.**kwargs
Optional keyword arguments forwarded to nested bijectors. Returns forward_event_ndims
Structure of integers and/or None
values matchingself.inverse_min_event_ndims
. These are computed using 'prefer static' semantics: if any inputs areNone
, some or all of the outputs may beNone
, indicating that the output dimension could not be inferred (conversely, if all inputs are non-None
, all outputs will be non-None
). If all inputevent_ndims
are Pythonint
s, all of the (non-None
) outputs will be Pythonint
s; otherwise, some or all of the outputs may beTensor
int
s.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
(structure) indicating event-portion shape passed intoforward
function.Returns forward_event_shape_tensor
TensorShape
(structure) indicating event-portion shape after applyingforward
. 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
1DTensor
.Args input_shape
Tensor
,int32
vector (structure) indicating event-portion shape passed intoforward
function.name
name to give to the op Returns forward_event_shape_tensor
Tensor
,int32
vector (structure) indicating event-portion shape after applyingforward
.forward_log_det_jacobian
forward_log_det_jacobian( x, event_ndims=None, name='forward_log_det_jacobian', **kwargs )
Returns both the forward_log_det_jacobian.
Args x
Tensor
(structure). The input to the 'forward' Jacobian determinant evaluation.event_ndims
Optional number of dimensions in the probabilistic events being transformed; this must be greater than or equal to self.forward_min_event_ndims
. Ifevent_ndims
is specified, the log Jacobian determinant is summed to produce a scalar log-determinant for each event. Otherwise (ifevent_ndims
isNone
), no reduction is performed. Multipart bijectors require structured event_ndims, such that the batch rankrank(y[i]) - event_ndims[i]
is the same for all elementsi
of the structured input. In most cases (with the exception oftfb.JointMap
) they further require thatevent_ndims[i] - self.inverse_min_event_ndims[i]
is the same for all elementsi
of the structured input. Default value:None
(equivalent toself.forward_min_event_ndims
).name
The name to give this op. **kwargs
Named arguments forwarded to subclass implementation. Returns Tensor
(structure), if this bijector is injective. If not injective this is not implemented.Raises TypeError
if y
's dtype is incompatible with the expected output dtype.NotImplementedError
if neither _forward_log_det_jacobian
nor {_inverse
,_inverse_log_det_jacobian
} are implemented, or this is a non-injective bijector.ValueError
if the value of event_ndims
is not valid for this bijector.inverse
inverse( y, name='inverse', **kwargs )
Returns the inverse
Bijector
evaluation, i.e., X = g^{-1}(Y).Args y
Tensor
(structure). The input to the 'inverse' evaluation.name
The name to give this op. **kwargs
Named arguments forwarded to subclass implementation. Returns Tensor
(structure), if this bijector is injective. If not injective, returns the k-tuple containing the uniquek
points(x1, ..., xk)
such thatg(xi) = y
.Raises TypeError
if y
's structured dtype is incompatible with the expected output dtype.NotImplementedError
if _inverse
is not implemented.inverse_dtype
inverse_dtype( dtype=UNSPECIFIED, name='inverse_dtype', **kwargs )
Returns the dtype returned by
inverse
for the provided input.inverse_event_ndims
inverse_event_ndims( event_ndims, **kwargs )
Returns the number of event dimensions produced by
inverse
.Args event_ndims
Structure of Python and/or Tensor int
s, and/orNone
values. The structure should match that ofself.inverse_min_event_ndims
, and all non-None
values must be greater than or equal to the corresponding value inself.inverse_min_event_ndims
.**kwargs
Optional keyword arguments forwarded to nested bijectors. Returns inverse_event_ndims
Structure of integers and/or None
values matchingself.forward_min_event_ndims
. These are computed using 'prefer static' semantics: if any inputs areNone
, some or all of the outputs may beNone
, indicating that the output dimension could not be inferred (conversely, if all inputs are non-None
, all outputs will be non-None
). If all inputevent_ndims
are Pythonint
s, all of the (non-None
) outputs will be Pythonint
s; otherwise, some or all of the outputs may beTensor
int
s.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
(structure) indicating event-portion shape passed intoinverse
function.Returns inverse_event_shape_tensor
TensorShape
(structure) indicating event-portion shape after applyinginverse
. 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
1DTensor
.Args output_shape
Tensor
,int32
vector (structure) indicating event-portion shape passed intoinverse
function.name
name to give to the op Returns inverse_event_shape_tensor
Tensor
,int32
vector (structure) indicating event-portion shape after applyinginverse
.inverse_log_det_jacobian
inverse_log_det_jacobian( y, event_ndims=None, name='inverse_log_det_jacobian', **kwargs )
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 atg^{-1}(y)
.Args y
Tensor
(structure). The input to the 'inverse' Jacobian determinant evaluation.event_ndims
Optional number of dimensions in the probabilistic events being transformed; this must be greater than or equal to self.inverse_min_event_ndims
. Ifevent_ndims
is specified, the log Jacobian determinant is summed to produce a scalar log-determinant for each event. Otherwise (ifevent_ndims
isNone
), no reduction is performed. Multipart bijectors require structured event_ndims, such that the batch rankrank(y[i]) - event_ndims[i]
is the same for all elementsi
of the structured input. In most cases (with the exception oftfb.JointMap
) they further require thatevent_ndims[i] - self.inverse_min_event_ndims[i]
is the same for all elementsi
of the structured input. Default value:None
(equivalent toself.inverse_min_event_ndims
).name
The name to give this op. **kwargs
Named arguments forwarded to subclass implementation. Returns ildj
Tensor
, if this bijector is injective. If not injective, returns the tuple of local log det Jacobians,log(det(Dg_i^{-1}(y)))
, whereg_i
is the restriction ofg
to theith
partitionDi
.Raises TypeError
if x
's dtype is incompatible with the expected inverse-dtype.NotImplementedError
if _inverse_log_det_jacobian
is not implemented.ValueError
if the value of event_ndims
is not valid for this bijector.parameter_properties
@classmethod
parameter_properties( dtype=tf.float32 )
Returns a dict mapping constructor arg names to property annotations.
This dict should include an entry for each of the bijector's
Tensor
-valued constructor arguments.Args dtype
Optional float dtype
to assume for continuous-valued parameters. Some constraining bijectors require advance knowledge of the dtype because certain constants (e.g.,tfb.Softplus.low
) must be instantiated with the same dtype as the values to be transformed.Returns parameter_properties
A str ->
tfp.python.internal.parameter_properties.ParameterPropertiesdict mapping constructor argument names to
ParameterProperties` instances.__call__
__call__( value, name=None, **kwargs )
Applies or composes the
Bijector
, depending on input type.This is a convenience function which applies the
Bijector
instance in three different ways, depending on the input:- If the input is a
tfd.Distribution
instance, returntfd.TransformedDistribution(distribution=input, bijector=self)
. - If the input is a
tfb.Bijector
instance, returntfb.Chain([self, input])
. - Otherwise, return
self.forward(input)
Args value
A tfd.Distribution
,tfb.Bijector
, or a (structure of)Tensor
.name
Python str
name given to ops created by this function.**kwargs
Additional keyword arguments passed into the created tfd.TransformedDistribution
,tfb.Bijector
, orself.forward
.Returns composition
A tfd.TransformedDistribution
if the input was atfd.Distribution
, atfb.Chain
if the input was atfb.Bijector
, or a (structure of)Tensor
computed byself.forward
.Examples
sigmoid = tfb.Reciprocal()( tfb.Shift(shift=1.)( tfb.Exp()( tfb.Scale(scale=-1.)))) # ==> `tfb.Chain([ # tfb.Reciprocal(), # tfb.Shift(shift=1.), # tfb.Exp(), # tfb.Scale(scale=-1.), # ])` # ie, `tfb.Sigmoid()` log_normal = tfb.Exp()(tfd.Normal(0, 1)) # ==> `tfd.TransformedDistribution(tfd.Normal(0, 1), tfb.Exp())` tfb.Exp()([-1., 0., 1.]) # ==> tf.exp([-1., 0., 1.])
- If the input is a
__eq__
__eq__(
other
)
Return self==value.
__getitem__
__getitem__(
slices
)
__iter__
__iter__()