tf.contrib.distributions.bijectors.BatchNormalization

Compute `Y = g(X) s.t.

Inherits From: Bijector

tf.contrib.distributions.bijectors.BatchNormalization(
    batchnorm_layer=None, training=True, validate_args=False,
    name='batch_normalization'
)

X = g^-1(Y) = (Y - mean(Y)) / std(Y)`.

Applies Batch Normalization [(Ioffe and Szegedy, 2015)][1] to samples from a data distribution. This can be used to stabilize training of normalizing flows ([Papamakarios et al., 2016][3]; [Dinh et al., 2017][2])

When training Deep Neural Networks (DNNs), it is common practice to normalize or whiten features by shifting them to have zero mean and scaling them to have unit variance.

The inverse() method of the BatchNormalization bijector, which is used in the log-likelihood computation of data samples, implements the normalization procedure (shift-and-scale) using the mean and standard deviation of the current minibatch.

Conversely, the forward() method of the bijector de-normalizes samples (e.g. X*std(Y) + mean(Y) with the running-average mean and standard deviation computed at training-time. De-normalization is useful for sampling.


dist = tfd.TransformedDistribution(
    distribution=tfd.Normal()),
    bijector=tfb.BatchNorm())

y = tfd.MultivariateNormalDiag(loc=1., scale=2.).sample(100)  # ~ N(1, 2)
x = dist.bijector.inverse(y)  # ~ N(0, 1)
y = dist.sample()  # ~ N(1, 2)

During training time, BatchNorm.inverse and BatchNorm.forward are not guaranteed to be inverses of each other because inverse(y) uses statistics of the current minibatch, while forward(x) uses running-average statistics accumulated from training. In other words, BatchNorm.inverse(BatchNorm.forward(...)) and BatchNorm.forward(BatchNorm.inverse(...)) will be identical when training=False but may be different when training=True.

References

[1]: Sergey Ioffe and Christian Szegedy. Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift. In International Conference on Machine Learning, 2015. https://arxiv.org/abs/1502.03167

[2]: 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

[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

Args
`batchnorm_layer`	`tf.compat.v1.layers.BatchNormalization` layer object. If `None`, defaults to `tf.compat.v1.layers.BatchNormalization(gamma_constraint=nn_ops.relu(x) 1e-6)`. This ensures positivity of the scale variable. </td> </tr><tr> <td>`training`</td> <td> If True, updates running-average statistics during call to`inverse()`. </td> </tr><tr> <td>`validate_args`</td> <td> Python`bool`indicating whether arguments should be checked for correctness. </td> </tr><tr> <td>`name`</td> <td> Python`str` name given to ops managed by this object.

Args

batchnorm_layer

tf.compat.v1.layers.BatchNormalization layer object. If None, defaults to `tf.compat.v1.layers.BatchNormalization(gamma_constraint=nn_ops.relu(x)

1e-6). This ensures positivity of the scale variable. </td> </tr><tr> <td>training</td> <td> If True, updates running-average statistics during call toinverse(). </td> </tr><tr> <td>validate_args</td> <td> Pythonboolindicating whether arguments should be checked for correctness. </td> </tr><tr> <td>name</td> <td> Pythonstr` name given to ops managed by this object.

Raises
`ValueError`	If bn_layer is not an instance of `tf.compat.v1.layers.BatchNormalization`, or if it is specified with `renorm=True` or a virtual batch size.

Attributes
`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. 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.

tf.contrib.distributions.bijectors.BatchNormalization

References

Args

Raises

Attributes

Methods

forward

forward_event_shape

forward_event_shape_tensor

forward_log_det_jacobian

inverse

inverse_event_shape

inverse_event_shape_tensor

inverse_log_det_jacobian

`forward`

`forward_event_shape`

`forward_event_shape_tensor`

`forward_log_det_jacobian`

`inverse`

`inverse_event_shape`

`inverse_event_shape_tensor`

`inverse_log_det_jacobian`