tf.contrib.distributions.bijectors.RealNVP

RealNVP "affine coupling layer" for vector-valued events.

Inherits From: Bijector

tf.contrib.distributions.bijectors.RealNVP(
    num_masked, shift_and_log_scale_fn, 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] = 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

Args
num_masked	Python int indicating that the first d units of the event should be masked. Must be in the closed interval [1, D-1], where D is the event size of the base distribution.
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.compat.v1.make_template. Returning None for either (both) shift, log_scale is equivalent to (but more efficient than) returning zero.
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 num_masked < 1.

Attributes
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. Note: Jacobian matrix is either constant for both forward and inverse or neither.
name	Returns the string name of this Bijector.
validate_args	Returns True if Tensor arguments will be validated.

Methods

forward

View source

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.

forward_event_shape

View source

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.

forward_event_shape_tensor

View source

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.

forward_log_det_jacobian

View source

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.

inverse

View source

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.

inverse_event_shape

View source

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.

inverse_event_shape_tensor

View source

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.

inverse_log_det_jacobian

View source

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.