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RealNVP 'affine coupling layer' for vector-valued events.
Inherits From: Bijector
tfp.substrates.numpy.bijectors.RealNVP(
num_masked=None, fraction_masked=None, shift_and_log_scale_fn=None,
bijector_fn=None, is_constant_jacobian=False, validate_args=False, name=None
)
Real NVP models a normalizing flow on a D
-dimensional distribution via a
single D-d
-dimensional conditional distribution [(Dinh et al., 2017)][1]:
y[d:D] = x[d:D] * tf.exp(log_scale_fn(x[0:d])) + shift_fn(x[0:d])
y[0:d] = x[0:d]
The last D-d
units are scaled and shifted based on the first d
units only,
while the first d
units are 'masked' and left unchanged. Real NVP's
shift_and_log_scale_fn
computes vector-valued quantities. For
scale-and-shift transforms that do not depend on any masked units, i.e.
d=0
, use the tfb.Scale
and tfb.Shift
bijectors with learned parameters
instead.
Masking is currently only supported for base distributions with
event_ndims=1
. For more sophisticated masking schemes like checkerboard or
channel-wise masking [(Papamakarios et al., 2016)[4], use the tfb.Permute
bijector to re-order desired masked units into the first d
units. For base
distributions with event_ndims > 1
, use the tfb.Reshape
bijector to
flatten the event shape.
Recall that the MAF bijector [(Papamakarios et al., 2016)][4] implements a normalizing flow via an autoregressive transformation. MAF and IAF have opposite computational tradeoffs - MAF can train all units in parallel but must sample units sequentially, while IAF must train units sequentially but can sample in parallel. In contrast, Real NVP can compute both forward and inverse computations in parallel. However, the lack of an autoregressive transformations makes it less expressive on a per-bijector basis.
A 'valid' shift_and_log_scale_fn
must compute each shift
(aka loc
or
'mu' in [Papamakarios et al. (2016)][4]) and log(scale)
(aka 'alpha' in
[Papamakarios et al. (2016)][4]) 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,
real_nvp_default_template
is offered as a possible shift_and_log_scale_fn
function.
NICE [(Dinh et al., 2014)][2] is a special case of the Real NVP bijector
which discards the scale transformation, resulting in a constant-time
inverse-log-determinant-Jacobian. To use a NICE bijector instead of Real
NVP, shift_and_log_scale_fn
should return (shift, None)
, and
is_constant_jacobian
should be set to True
in the RealNVP
constructor.
Calling real_nvp_default_template
with shift_only=True
returns one such
NICE-compatible shift_and_log_scale_fn
.
The bijector_fn
argument allows specifying a more general coupling relation,
such as the LSTM-inspired activation from [5], or Neural Spline Flow [6].
Caching: the scalar input depth D
of the base distribution is not known at
construction time. The first call to any of forward(x)
, inverse(x)
,
inverse_log_det_jacobian(x)
, or forward_log_det_jacobian(x)
memoizes
D
, which is re-used in subsequent calls. This shape must be known prior to
graph execution (which is the case if using tf.layers).
Examples
tfd = tfp.distributions
tfb = tfp.bijectors
# A common choice for a normalizing flow is to use a Gaussian for the base
# distribution. (However, any continuous distribution would work.) E.g.,
nvp = tfd.TransformedDistribution(
distribution=tfd.MultivariateNormalDiag(loc=[0., 0., 0.]),
bijector=tfb.RealNVP(
num_masked=2,
shift_and_log_scale_fn=tfb.real_nvp_default_template(
hidden_layers=[512, 512])))
x = nvp.sample()
nvp.log_prob(x)
nvp.log_prob([0.0, 0.0, 0.0])
For more examples, see [Jang (2018)][3].
References
[1]: Laurent Dinh, Jascha Sohl-Dickstein, and Samy Bengio. Density Estimation using Real NVP. In International Conference on Learning Representations, 2017. https://arxiv.org/abs/1605.08803
[2]: Laurent Dinh, David Krueger, and Yoshua Bengio. NICE: Non-linear Independent Components Estimation. arXiv preprint arXiv:1410.8516, 2014. https://arxiv.org/abs/1410.8516
[3]: Eric Jang. Normalizing Flows Tutorial, Part 2: Modern Normalizing Flows. Technical Report, 2018. http://blog.evjang.com/2018/01/nf2.html
[4]: 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
[5]: 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
[6]: Conor Durkan, Artur Bekasov, Iain Murray, George Papamakarios. Neural Spline Flows, 2019. http://arxiv.org/abs/1906.04032
Args | |
---|---|
num_masked
|
Python int , indicating the number of units of the
event that should should be masked. Must be in the closed interval
[0, D-1] , where D is the event size of the base distribution.
If the value is negative, then the last d units of the event are
masked instead. Must be None if fraction_masked is defined.
|
fraction_masked
|
Python float , indicating the number of units of the
event that should should be masked. Must be in the closed interval
[-1, 1] , and the value represents the fraction of the values to be
masked. The final number of values to be masked will be the input size
times the fraction, rounded to the the nearest integer towards zero.
If negative, then the last fraction of units are masked instead. Must
be None if num_masked is defined.
|
shift_and_log_scale_fn
|
Python callable which computes shift and
log_scale from both the forward domain (x ) and the inverse domain
(y ). Calculation must respect the 'autoregressive property' (see class
docstring). Suggested default
masked_autoregressive_default_template(hidden_layers=...) .
Typically the function contains tf.Variables and is wrapped using
tf.make_template . Returning None for either (both) shift ,
log_scale is equivalent to (but more efficient than) returning zero.
|
bijector_fn
|
Python callable which returns a tfb.Bijector which
transforms the last D-d unit with the signature (masked_units_tensor,
output_units, **condition_kwargs) -> bijector . The bijector must
operate on scalar or vector events and must not alter the rank of its
input.
|
is_constant_jacobian
|
Python bool . Default: False . When True the
implementation assumes log_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.
|
name
|
Python str , name given to ops managed by this object.
|
Raises | |
---|---|
ValueError
|
If both or none of shift_and_log_scale_fn and bijector_fn
are specified.
|
Attributes | |
---|---|
dtype
|
|
forward_min_event_ndims
|
Returns the minimal number of dimensions bijector.forward operates on.
Multipart bijectors return structured |
graph_parents
|
Returns this Bijector 's graph_parents as a Python list.
|
has_static_min_event_ndims
|
Returns True if the bijector has statically-known min_event_ndims .
|
inverse_min_event_ndims
|
Returns the minimal number of dimensions bijector.inverse operates on.
Multipart bijectors return structured |
is_constant_jacobian
|
Returns true iff the Jacobian matrix is not a function of x. |
name
|
Returns the string name of this Bijector .
|
parameters
|
Dictionary of parameters used to instantiate this Bijector .
|
trainable_variables
|
|
validate_args
|
Returns True if Tensor arguments will be validated. |
variables
|
Methods
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 and x.dtype is not
self.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
.
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 into forward function.
|
Returns | |
---|---|
forward_event_shape_tensor
|
TensorShape (structure) 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 (structure) indicating event-portion
shape passed into forward function.
|
name
|
name to give to the op |
Returns | |
---|---|
forward_event_shape_tensor
|
Tensor , int32 vector (structure)
indicating event-portion shape after applying forward .
|
forward_log_det_jacobian
forward_log_det_jacobian(
x, event_ndims, 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
|
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 rank(x) - event_ndims dimensions.
Multipart bijectors require structured event_ndims, such that
rank(y[i]) - rank(event_ndims[i]) is the same for all elements i of
the structured input. Furthermore, the first event_ndims[i] of each
x[i].shape must be the same for all i (broadcasting is not allowed).
|
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.
|
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 unique
k points (x1, ..., xk) such that g(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
.
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 into inverse function.
|
Returns | |
---|---|
inverse_event_shape_tensor
|
TensorShape (structure) 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 (structure) indicating
event-portion shape passed into inverse function.
|
name
|
name to give to the op |
Returns | |
---|---|
inverse_event_shape_tensor
|
Tensor , int32 vector (structure)
indicating event-portion shape after applying inverse .
|
inverse_log_det_jacobian
inverse_log_det_jacobian(
y, event_ndims, 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 at g^{-1}(y)
.
Args | |
---|---|
y
|
Tensor (structure). 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 rank(y) - event_ndims dimensions.
Multipart bijectors require structured event_ndims, such that
rank(y[i]) - rank(event_ndims[i]) is the same for all elements i of
the structured input. Furthermore, the first event_ndims[i] of each
x[i].shape must be the same for all i (broadcasting is not allowed).
|
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))) , where g_i is the restriction
of g to the ith partition Di .
|
Raises | |
---|---|
TypeError
|
if x 's dtype is incompatible with the expected inverse-dtype.
|
NotImplementedError
|
if _inverse_log_det_jacobian is not implemented.
|
__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 , or self.forward .
|
Returns | |
---|---|
composition
|
A tfd.TransformedDistribution if the input was a
tfd.Distribution , a tfb.Chain if the input was a tfb.Bijector , or
a (structure of) Tensor computed by self.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.])
__eq__
__eq__(
other
)
Return self==value.