tfp.bijectors.AutoregressiveNetwork

View source on GitHub

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:

1. 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))
   

2. We can parameterize a distribution with neither cross-channel nor within-pixel autoregressivity:

       r0    g0   b0
       ^     ^    ^
       |     |    |
       |     |    |
       r1    g1   b1
   

   as:

   # 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, :]), where channel is 0, 1, or 2.

   To use separate weights for each channel, we could construct an AutoregressiveNetwork and TransformedDistribution for each channel, and combine them with a tfd.Blockwise distribution.

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

self.input_spec = tf.keras.layers.InputSpec(ndim=4)

ValueError: Input 0 of layer conv2d is incompatible with the layer:
expected ndim=4, found ndim=1. Full shape received: [2]

class MyLayer(tf.keras.layers.Layer):
  def call(self, inputs):
    self.add_loss(tf.abs(tf.reduce_mean(inputs)))
    return inputs
l = MyLayer()
l(np.ones((10, 1)))
l.losses
[1.0]

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.
len(model.losses)
0
model.add_loss(tf.abs(tf.reduce_mean(x)))
len(model.losses)
1

inputs = tf.keras.Input(shape=(10,))
d = tf.keras.layers.Dense(10, kernel_initializer='ones')
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))
model.losses
[<tf.Tensor: shape=(), dtype=float32, numpy=1.0>]

a = tf.Module()
b = tf.Module()
c = tf.Module()
a.b = b
b.c = c
list(a.submodules) == [b, c]
True
list(b.submodules) == [c]
True
list(c.submodules) == []
True

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))

build

View source

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.

compute_mask

compute_mask(
    inputs, mask=None
)

Computes an output mask tensor.

compute_output_shape

View source

compute_output_shape(
    input_shape
)

See tfkl.Layer.compute_output_shape.

count_params

count_params()

Count the total number of scalars composing the weights.

from_config

@classmethod
from_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).

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.

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.

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)]

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().

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().

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)]

with_name_scope

@classmethod
with_name_scope(
    method
)

Decorator to automatically enter the module name scope.

class MyModule(tf.Module):
  @tf.Module.with_name_scope
  def __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)>

__call__

__call__(
    *args, **kwargs
)

Wraps call, applying pre- and post-processing steps.