tf.contrib.distributions.bijectors.RealNVP

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

tfd = tf.contrib.distributions
tfb = tfd.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.)

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

Properties

dtype

dtype of Tensors transformable by this distribution.

event_ndims

Returns then number of event dimensions this bijector operates on.

graph_parents

Returns this Bijector's graph_parents as a Python list.

is_constant_jacobian

Returns true iff the Jacobian is not a function of x.

Note: Jacobian is either constant for both forward and inverse or neither.

Returns:

• is_constant_jacobian: Python bool.

name

Returns the string name of this Bijector.

validate_args

Returns True if Tensor arguments will be validated.

Methods

__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.

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.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.

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: if self.dtype is specified and x.dtype is not self.dtype.
• NotImplementedError: if _forward is not implemented.

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 into forward function.

Returns:

• forward_event_shape_tensor: TensorShape 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 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

forward_log_det_jacobian(
    x,
    name='forward_log_det_jacobian'
)

Returns both the forward_log_det_jacobian.

Args:

• x: Tensor. The input to the "forward" Jacobian evaluation.
• 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

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

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

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

inverse_log_det_jacobian(
    y,
    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 evaluation.
• 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.