Class RealNVP
Inherits From: Bijector
Defined in tensorflow/contrib/distributions/python/ops/bijectors/real_nvp.py
.
RealNVP "affine coupling layer" for vector-valued events.
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] = y[d:D] * math_ops.exp(log_scale_fn(y[d:D])) + shift_fn(y[d: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.Affine
bijector 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_nvp
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
.
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).
Example Use
import tensorflow_probability as tfp
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.,
num_dims = 3
num_samples = 1
nvp = tfd.TransformedDistribution(
distribution=tfd.MultivariateNormalDiag(loc=np.zeros(num_dims)),
bijector=tfb.RealNVP(
num_masked=2,
shift_and_log_scale_fn=tfb.real_nvp_default_template(
hidden_layers=[512, 512])))
x = nvp.sample(num_samples)
nvp.log_prob(x)
nvp.log_prob(np.zeros([num_samples, num_dims]))
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
__init__
__init__(
num_masked,
shift_and_log_scale_fn,
is_constant_jacobian=False,
validate_args=False,
name=None
)
Creates the Real NVP or NICE bijector. (deprecated)
Args:
num_masked
: Pythonint
indicating that the firstd
units of the event should be masked. Must be in the closed interval[1, D-1]
, whereD
is the event size of the base distribution.shift_and_log_scale_fn
: Pythoncallable
which computesshift
andlog_scale
from both the forward domain (x
) and the inverse domain (y
). Calculation must respect the "autoregressive property" (see class docstring). Suggested defaultmasked_autoregressive_default_template(hidden_layers=...)
. Typically the function containstf.Variables
and is wrapped usingtf.make_template
. ReturningNone
for either (both)shift
,log_scale
is equivalent to (but more efficient than) returning zero.is_constant_jacobian
: Pythonbool
. 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
: Pythonbool
indicating whether arguments should be checked for correctness.name
: Pythonstr
, name given to ops managed by this object.
Raises:
ValueError
: If num_masked < 1.
Properties
dtype
dtype of Tensor
s 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
: Pythonbool
.
name
Returns the string name of this Bijector
.
validate_args
Returns True if Tensor arguments will be validated.
Methods
tf.contrib.distributions.bijectors.RealNVP.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
: ifself.dtype
is specified andx.dtype
is notself.dtype
.NotImplementedError
: if_forward
is not implemented.
tf.contrib.distributions.bijectors.RealNVP.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 intoforward
function.
Returns:
forward_event_shape_tensor
:TensorShape
indicating event-portion shape after applyingforward
. Possibly unknown.
tf.contrib.distributions.bijectors.RealNVP.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 intoforward
function.name
: name to give to the op
Returns:
forward_event_shape_tensor
:Tensor
,int32
vector indicating event-portion shape after applyingforward
.
tf.contrib.distributions.bijectors.RealNVP.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 toself.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 shapex.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
: ifself.dtype
is specified andy.dtype
is notself.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.RealNVP.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
: ifself.dtype
is specified andy.dtype
is notself.dtype
.NotImplementedError
: if_inverse
is not implemented.
tf.contrib.distributions.bijectors.RealNVP.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 intoinverse
function.
Returns:
inverse_event_shape_tensor
:TensorShape
indicating event-portion shape after applyinginverse
. Possibly unknown.
tf.contrib.distributions.bijectors.RealNVP.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 intoinverse
function.name
: name to give to the op
Returns:
inverse_event_shape_tensor
:Tensor
,int32
vector indicating event-portion shape after applyinginverse
.
tf.contrib.distributions.bijectors.RealNVP.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 toself.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 shapey.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
: ifself.dtype
is specified andy.dtype
is notself.dtype
.NotImplementedError
: if_inverse_log_det_jacobian
is not implemented.