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|
Masked Autoencoder for Distribution Estimation [Germain et al. (2015)][1].
tfp.bijectors.AutoregressiveNetwork(
params,
event_shape=None,
conditional=False,
conditional_event_shape=None,
conditional_input_layers='all_layers',
hidden_units=None,
input_order='left-to-right',
hidden_degrees='equal',
activation=None,
use_bias=True,
kernel_initializer='glorot_uniform',
bias_initializer='zeros',
kernel_regularizer=None,
bias_regularizer=None,
kernel_constraint=None,
bias_constraint=None,
validate_args=False,
**kwargs
)
A AutoregressiveNetwork takes as input a Tensor of shape [..., event_size]
and returns a Tensor of shape [..., event_size, params].
The output satisfies the autoregressive property. That is, the layer is
configured with some permutation ord of {0, ..., event_size-1} (i.e., an
ordering of the input dimensions), and the output output[batch_idx, i, ...]
for input dimension i depends only on inputs x[batch_idx, j] where
ord(j) < ord(i). The autoregressive property allows us to use
output[batch_idx, i] to parameterize conditional distributions:
p(x[batch_idx, i] | x[batch_idx, j] for ord(j) < ord(i))
which give us a tractable distribution over input x[batch_idx]:
p(x[batch_idx]) = prod_i p(x[batch_idx, ord(i)] | x[batch_idx, ord(0:i)])
For example, when params is 2, the output of the layer can parameterize
the location and log-scale of an autoregressive Gaussian distribution.
Example
The AutoregressiveNetwork can be used to do density estimation as is shown
in the below example:
# Generate data -- as in Figure 1 in [Papamakarios et al. (2017)][2]).
n = 2000
x2 = np.random.randn(n).astype(dtype=np.float32) * 2.
x1 = np.random.randn(n).astype(dtype=np.float32) + (x2 * x2 / 4.)
data = np.stack([x1, x2], axis=-1)
# Density estimation with MADE.
made = tfb.AutoregressiveNetwork(params=2, hidden_units=[10, 10])
distribution = tfd.TransformedDistribution(
distribution=tfd.Sample(tfd.Normal(loc=0., scale=1.), sample_shape=[2]),
bijector=tfb.MaskedAutoregressiveFlow(made))
# Construct and fit model.
x_ = tfkl.Input(shape=(2,), dtype=tf.float32)
log_prob_ = distribution.log_prob(x_)
model = tfk.Model(x_, log_prob_)
model.compile(optimizer=tf.optimizers.Adam(),
loss=lambda _, log_prob: -log_prob)
batch_size = 25
model.fit(x=data,
y=np.zeros((n, 0), dtype=np.float32),
batch_size=batch_size,
epochs=1,
steps_per_epoch=1, # Usually `n // batch_size`.
shuffle=True,
verbose=True)
# Use the fitted distribution.
distribution.sample((3, 1))
distribution.log_prob(np.ones((3, 2), dtype=np.float32))
The conditional argument can be used to instead build a conditional density
estimator. To do this the conditioning variable must be passed as a kwarg:
# Generate data as the mixture of two distributions.
n = 2000
c = np.r_[
np.zeros(n//2),
np.ones(n//2)
]
mean_0, mean_1 = 0, 5
x = np.r_[
np.random.randn(n//2).astype(dtype=np.float32) + mean_0,
np.random.randn(n//2).astype(dtype=np.float32) + mean_1
]
# Density estimation with MADE.
made = tfb.AutoregressiveNetwork(
params=2,
hidden_units=[2, 2],
event_shape=(1,),
conditional=True,
kernel_initializer=tfk.initializers.VarianceScaling(0.1),
conditional_event_shape=(1,)
)
distribution = tfd.TransformedDistribution(
distribution=tfd.Sample(tfd.Normal(loc=0., scale=1.), sample_shape=[1]),
bijector=tfb.MaskedAutoregressiveFlow(made))
# Construct and fit model.
x_ = tfkl.Input(shape=(1,), dtype=tf.float32)
c_ = tfkl.Input(shape=(1,), dtype=tf.float32)
log_prob_ = distribution.log_prob(
x_, bijector_kwargs={'conditional_input': c_})
model = tfk.Model([x_, c_], log_prob_)
model.compile(optimizer=tf.optimizers.Adam(learning_rate=0.1),
loss=lambda _, log_prob: -log_prob)
batch_size = 25
model.fit(x=[x, c],
y=np.zeros((n, 0), dtype=np.float32),
batch_size=batch_size,
epochs=3,
steps_per_epoch=n // batch_size,
shuffle=True,
verbose=True)
# Use the fitted distribution to sample condition on c = 1
n_samples = 1000
cond = 1
samples = distribution.sample(
(n_samples,),
bijector_kwargs={'conditional_input': cond * np.ones((n_samples, 1))})
Examples: Handling Rank-2+ Tensors
AutoregressiveNetwork can be used as a building block to achieve different
autoregressive structures over rank-2+ tensors. For example, suppose we want
to build an autoregressive distribution over images with dimension [weight,
height, channels] with channels = 3:
We can parameterize a 'fully autoregressive' distribution, with cross-channel and within-pixel autoregressivity:
r0 g0 b0 r0 g0 b0 r0 g0 b0 ^ ^ ^ ^ ^ ^ ^ ^ ^ | / ____/ \ | / \____ \ | | /__/ \ | / \__\ | r1 g1 b1 r1 <- g1 b1 r1 g1 <- b1 ^ | \_________/as:
# Generate random images for training data. images = np.random.uniform(size=(100, 8, 8, 3)).astype(np.float32) n, width, height, channels = images.shape # Reshape images to achieve desired autoregressivity. event_shape = [height * width * channels] reshaped_images = tf.reshape(images, [n, event_shape]) # Density estimation with MADE. made = tfb.AutoregressiveNetwork(params=2, event_shape=event_shape, hidden_units=[20, 20], activation='relu') distribution = tfd.TransformedDistribution( distribution=tfd.Sample( tfd.Normal(loc=0., scale=1.), sample_shape=[dims]), bijector=tfb.MaskedAutoregressiveFlow(made)) # Construct and fit model. x_ = tfkl.Input(shape=event_shape, dtype=tf.float32) log_prob_ = distribution.log_prob(x_) model = tfk.Model(x_, log_prob_) model.compile(optimizer=tf.optimizers.Adam(), loss=lambda _, log_prob: -log_prob) batch_size = 10 model.fit(x=data, y=np.zeros((n, 0), dtype=np.float32), batch_size=batch_size, epochs=10, steps_per_epoch=n // batch_size, shuffle=True, verbose=True) # Use the fitted distribution. distribution.sample((3, 1)) distribution.log_prob(np.ones((5, 8, 8, 3), dtype=np.float32))We can parameterize a distribution with neither cross-channel nor within-pixel autoregressivity:
r0 g0 b0 ^ ^ ^ | | | | | | r1 g1 b1as:
# Generate fake images. images = np.random.choice([0, 1], size=(100, 8, 8, 3)) n, width, height, channels = images.shape # Reshape images to achieve desired autoregressivity. reshaped_images = np.transpose( np.reshape(images, [n, width * height, channels]), axes=[0, 2, 1]) made = tfb.AutoregressiveNetwork(params=1, event_shape=[width * height], hidden_units=[20, 20], activation='relu') # Density estimation with MADE. # # NOTE: Parameterize an autoregressive distribution over an event_shape of # [channels, width * height], with univariate Bernoulli conditional # distributions. distribution = tfd.Autoregressive( lambda x: tfd.Independent( tfd.Bernoulli(logits=tf.unstack(made(x), axis=-1)[0], dtype=tf.float32), reinterpreted_batch_ndims=2), sample0=tf.zeros([channels, width * height], dtype=tf.float32)) # Construct and fit model. x_ = tfkl.Input(shape=(channels, width * height), dtype=tf.float32) log_prob_ = distribution.log_prob(x_) model = tfk.Model(x_, log_prob_) model.compile(optimizer=tf.optimizers.Adam(), loss=lambda _, log_prob: -log_prob) batch_size = 10 model.fit(x=reshaped_images, y=np.zeros((n, 0), dtype=np.float32), batch_size=batch_size, epochs=10, steps_per_epoch=n // batch_size, shuffle=True, verbose=True) distribution.sample(7) distribution.log_prob(np.ones((4, 8, 8, 3), dtype=np.float32))Note that one set of weights is shared for the mapping for each channel from image to distribution parameters -- i.e., the mapping
layer(reshaped_images[..., channel, :]), wherechannelis 0, 1, or 2.To use separate weights for each channel, we could construct an
AutoregressiveNetworkandTransformedDistributionfor each channel, and combine them with atfd.Blockwisedistribution.
References
[1]: Mathieu Germain, Karol Gregor, Iain Murray, and Hugo Larochelle. MADE: Masked Autoencoder for Distribution Estimation. In International Conference on Machine Learning, 2015. https://arxiv.org/abs/1502.03509
[2]: George Papamakarios, Theo Pavlakou, Iain Murray, Masked Autoregressive Flow for Density Estimation. In Neural Information Processing Systems, 2017. https://arxiv.org/abs/1705.07057
Args | |
|---|---|
params
|
Python integer specifying the number of parameters to output per input. |
event_shape
|
Python list-like of positive integers (or a single int),
specifying the shape of the input to this layer, which is also the
event_shape of the distribution parameterized by this layer. Currently
only rank-1 shapes are supported. That is, event_shape must be a single
integer. If not specified, the event shape is inferred when this layer
is first called or built.
|
conditional
|
Python boolean describing whether to add conditional inputs. |
conditional_event_shape
|
Python list-like of positive integers (or a
single int), specifying the shape of the conditional input to this layer
(without the batch dimensions). This must be specified if conditional
is True.
|
conditional_input_layers
|
Python str describing how to add conditional
parameters to the autoregressive network. When "all_layers" the
conditional input will be combined with the network at every layer,
whilst "first_layer" combines the conditional input only at the first
layer which is then passed through the network
autoregressively. Default: 'all_layers'.
|
hidden_units
|
Python list-like of non-negative integers, specifying
the number of units in each hidden layer.
|
input_order
|
Order of degrees to the input units: 'random',
'left-to-right', 'right-to-left', or an array of an explicit order. For
example, 'left-to-right' builds an autoregressive model:
p(x) = p(x1) p(x2 | x1) ... p(xD | x<D). Default: 'left-to-right'.
|
hidden_degrees
|
Method for assigning degrees to the hidden units: 'equal', 'random'. If 'equal', hidden units in each layer are allocated equally (up to a remainder term) to each degree. Default: 'equal'. |
activation
|
An activation function. See tf.keras.layers.Dense. Default:
None.
|
use_bias
|
Whether or not the dense layers constructed in this layer
should have a bias term. See tf.keras.layers.Dense. Default: True.
|
kernel_initializer
|
Initializer for the Dense kernel weight
matrices. Default: 'glorot_uniform'.
|
bias_initializer
|
Initializer for the Dense bias vectors. Default:
'zeros'.
|
kernel_regularizer
|
Regularizer function applied to the Dense kernel
weight matrices. Default: None.
|
bias_regularizer
|
Regularizer function applied to the Dense bias
weight vectors. Default: None.
|
kernel_constraint
|
Constraint function applied to the Dense kernel
weight matrices. Default: None.
|
bias_constraint
|
Constraint function applied to the Dense bias
weight vectors. Default: None.
|
validate_args
|
Python bool, default False. When True, layer
parameters are checked for validity despite possibly degrading runtime
performance. When False invalid inputs may silently render incorrect
outputs.
|
**kwargs
|
Additional keyword arguments passed to this layer (but not to
the tf.keras.layer.Dense layers constructed by this layer).
|
Attributes | |
|---|---|
activity_regularizer
|
Optional regularizer function for the output of this layer. |
compute_dtype
|
The dtype of the layer's computations.
This is equivalent to Layers automatically cast their inputs to the compute dtype, which
causes computations and the output to be in the compute dtype as well.
This is done by the base Layer class in Layers often perform certain internal computations in higher precision
when |
dtype
|
The dtype of the layer weights.
This is equivalent to |
dtype_policy
|
The dtype policy associated with this layer.
This is an instance of a |
dynamic
|
Whether the layer is dynamic (eager-only); set in the constructor. |
event_shape
|
|
input
|
Retrieves the input tensor(s) of a layer.
Only applicable if the layer has exactly one input, i.e. if it is connected to one incoming layer. |
input_spec
|
InputSpec instance(s) describing the input format for this layer.
When you create a layer subclass, you can set Now, if you try to call the layer on an input that isn't rank 4
(for instance, an input of shape Input checks that can be specified via
For more information, see |
losses
|
List of losses added using the add_loss() API.
Variable regularization tensors are created when this property is
accessed, so it is eager safe: accessing
|
metrics
|
List of metrics attached to the layer. |
name
|
Name of the layer (string), set in the constructor. |
name_scope
|
Returns a tf.name_scope instance for this class.
|
non_trainable_weights
|
List of all non-trainable weights tracked by this layer.
Non-trainable weights are not updated during training. They are
expected to be updated manually in |
output
|
Retrieves the output tensor(s) of a layer.
Only applicable if the layer has exactly one output, i.e. if it is connected to one incoming layer. |
params
|
|
submodules
|
Sequence of all sub-modules.
Submodules are modules which are properties of this module, or found as properties of modules which are properties of this module (and so on).
|
supports_masking
|
Whether this layer supports computing a mask using compute_mask.
|
trainable
|
|
trainable_weights
|
List of all trainable weights tracked by this layer.
Trainable weights are updated via gradient descent during training. |
variable_dtype
|
Alias of Layer.dtype, the dtype of the weights.
|
weights
|
Returns the list of all layer variables/weights. |
Methods
add_loss
add_loss(
losses, **kwargs
)
Add loss tensor(s), potentially dependent on layer inputs.
Some losses (for instance, activity regularization losses) may be
dependent on the inputs passed when calling a layer. Hence, when reusing
the same layer on different inputs a and b, some entries in
layer.losses may be dependent on a and some on b. This method
automatically keeps track of dependencies.
This method can be used inside a subclassed layer or model's call
function, in which case losses should be a Tensor or list of Tensors.
Example:
class MyLayer(tf.keras.layers.Layer):
def call(self, inputs):
self.add_loss(tf.abs(tf.reduce_mean(inputs)))
return inputs
The same code works in distributed training: the input to add_loss()
is treated like a regularization loss and averaged across replicas
by the training loop (both built-in Model.fit() and compliant custom
training loops).
The add_loss method can also be called directly on a Functional Model
during construction. In this case, any loss Tensors passed to this Model
must be symbolic and be able to be traced back to the model's Inputs.
These losses become part of the model's topology and are tracked in
get_config.
Example:
inputs = tf.keras.Input(shape=(10,))
x = tf.keras.layers.Dense(10)(inputs)
outputs = tf.keras.layers.Dense(1)(x)
model = tf.keras.Model(inputs, outputs)
# Activity regularization.
model.add_loss(tf.abs(tf.reduce_mean(x)))
If this is not the case for your loss (if, for example, your loss
references a Variable of one of the model's layers), you can wrap your
loss in a zero-argument lambda. These losses are not tracked as part of
the model's topology since they can't be serialized.
Example:
inputs = tf.keras.Input(shape=(10,))
d = tf.keras.layers.Dense(10)
x = d(inputs)
outputs = tf.keras.layers.Dense(1)(x)
model = tf.keras.Model(inputs, outputs)
# Weight regularization.
model.add_loss(lambda: tf.reduce_mean(d.kernel))
| Args | |
|---|---|
losses
|
Loss tensor, or list/tuple of tensors. Rather than tensors, losses may also be zero-argument callables which create a loss tensor. |
**kwargs
|
Used for backwards compatibility only. |
build
build(
input_shape
)
See tfkl.Layer.build.
build_from_config
build_from_config(
config
)
Builds the layer's states with the supplied config dict.
By default, this method calls the build(config["input_shape"]) method,
which creates weights based on the layer's input shape in the supplied
config. If your config contains other information needed to load the
layer's state, you should override this method.
| Args | |
|---|---|
config
|
Dict containing the input shape associated with this layer. |
compute_mask
compute_mask(
inputs, mask=None
)
Computes an output mask tensor.
| Args | |
|---|---|
inputs
|
Tensor or list of tensors. |
mask
|
Tensor or list of tensors. |
| Returns | |
|---|---|
| None or a tensor (or list of tensors, one per output tensor of the layer). |
compute_output_shape
compute_output_shape(
input_shape
)
See tfkl.Layer.compute_output_shape.
count_params
count_params()
Count the total number of scalars composing the weights.
| Returns | |
|---|---|
| An integer count. |
| Raises | |
|---|---|
ValueError
|
if the layer isn't yet built (in which case its weights aren't yet defined). |
from_config
@classmethodfrom_config( config )
Creates a layer from its config.
This method is the reverse of get_config,
capable of instantiating the same layer from the config
dictionary. It does not handle layer connectivity
(handled by Network), nor weights (handled by set_weights).
| Args | |
|---|---|
config
|
A Python dictionary, typically the output of get_config. |
| Returns | |
|---|---|
| A layer instance. |
get_build_config
get_build_config()
Returns a dictionary with the layer's input shape.
This method returns a config dict that can be used by
build_from_config(config) to create all states (e.g. Variables and
Lookup tables) needed by the layer.
By default, the config only contains the input shape that the layer was built with. If you're writing a custom layer that creates state in an unusual way, you should override this method to make sure this state is already created when Keras attempts to load its value upon model loading.
| Returns | |
|---|---|
| A dict containing the input shape associated with the layer. |
get_config
get_config()
Returns the config of the layer.
A layer config is a Python dictionary (serializable) containing the configuration of a layer. The same layer can be reinstantiated later (without its trained weights) from this configuration.
The config of a layer does not include connectivity
information, nor the layer class name. These are handled
by Network (one layer of abstraction above).
Note that get_config() does not guarantee to return a fresh copy of
dict every time it is called. The callers should make a copy of the
returned dict if they want to modify it.
| Returns | |
|---|---|
| Python dictionary. |
get_weights
get_weights()
Returns the current weights of the layer, as NumPy arrays.
The weights of a layer represent the state of the layer. This function returns both trainable and non-trainable weight values associated with this layer as a list of NumPy arrays, which can in turn be used to load state into similarly parameterized layers.
For example, a Dense layer returns a list of two values: the kernel
matrix and the bias vector. These can be used to set the weights of
another Dense layer:
layer_a = tf.keras.layers.Dense(1,kernel_initializer=tf.constant_initializer(1.))a_out = layer_a(tf.convert_to_tensor([[1., 2., 3.]]))layer_a.get_weights()[array([[1.],[1.],[1.]], dtype=float32), array([0.], dtype=float32)]layer_b = tf.keras.layers.Dense(1,kernel_initializer=tf.constant_initializer(2.))b_out = layer_b(tf.convert_to_tensor([[10., 20., 30.]]))layer_b.get_weights()[array([[2.],[2.],[2.]], dtype=float32), array([0.], dtype=float32)]layer_b.set_weights(layer_a.get_weights())layer_b.get_weights()[array([[1.],[1.],[1.]], dtype=float32), array([0.], dtype=float32)]
| Returns | |
|---|---|
| Weights values as a list of NumPy arrays. |
load_own_variables
load_own_variables(
store
)
Loads the state of the layer.
You can override this method to take full control of how the state of
the layer is loaded upon calling keras.models.load_model().
| Args | |
|---|---|
store
|
Dict from which the state of the model will be loaded. |
save_own_variables
save_own_variables(
store
)
Saves the state of the layer.
You can override this method to take full control of how the state of
the layer is saved upon calling model.save().
| Args | |
|---|---|
store
|
Dict where the state of the model will be saved. |
set_weights
set_weights(
weights
)
Sets the weights of the layer, from NumPy arrays.
The weights of a layer represent the state of the layer. This function sets the weight values from numpy arrays. The weight values should be passed in the order they are created by the layer. Note that the layer's weights must be instantiated before calling this function, by calling the layer.
For example, a Dense layer returns a list of two values: the kernel
matrix and the bias vector. These can be used to set the weights of
another Dense layer:
layer_a = tf.keras.layers.Dense(1,kernel_initializer=tf.constant_initializer(1.))a_out = layer_a(tf.convert_to_tensor([[1., 2., 3.]]))layer_a.get_weights()[array([[1.],[1.],[1.]], dtype=float32), array([0.], dtype=float32)]layer_b = tf.keras.layers.Dense(1,kernel_initializer=tf.constant_initializer(2.))b_out = layer_b(tf.convert_to_tensor([[10., 20., 30.]]))layer_b.get_weights()[array([[2.],[2.],[2.]], dtype=float32), array([0.], dtype=float32)]layer_b.set_weights(layer_a.get_weights())layer_b.get_weights()[array([[1.],[1.],[1.]], dtype=float32), array([0.], dtype=float32)]
| Args | |
|---|---|
weights
|
a list of NumPy arrays. The number
of arrays and their shape must match
number of the dimensions of the weights
of the layer (i.e. it should match the
output of get_weights).
|
| Raises | |
|---|---|
ValueError
|
If the provided weights list does not match the layer's specifications. |
with_name_scope
@classmethodwith_name_scope( method )
Decorator to automatically enter the module name scope.
class MyModule(tf.Module):@tf.Module.with_name_scopedef __call__(self, x):if not hasattr(self, 'w'):self.w = tf.Variable(tf.random.normal([x.shape[1], 3]))return tf.matmul(x, self.w)
Using the above module would produce tf.Variables and tf.Tensors whose
names included the module name:
mod = MyModule()mod(tf.ones([1, 2]))<tf.Tensor: shape=(1, 3), dtype=float32, numpy=..., dtype=float32)>mod.w<tf.Variable 'my_module/Variable:0' shape=(2, 3) dtype=float32,numpy=..., dtype=float32)>
| Args | |
|---|---|
method
|
The method to wrap. |
| Returns | |
|---|---|
| The original method wrapped such that it enters the module's name scope. |
__call__
__call__(
*args, **kwargs
)
Wraps call, applying pre- and post-processing steps.
| Args | |
|---|---|
*args
|
Positional arguments to be passed to self.call.
|
**kwargs
|
Keyword arguments to be passed to self.call.
|
| Returns | |
|---|---|
| Output tensor(s). |
| Note | |
|---|---|
|
| Raises | |
|---|---|
ValueError
|
if the layer's call method returns None (an invalid
value).
|
RuntimeError
|
if super().__init__() was not called in the
constructor.
|