<jupyter_start><jupyter_text>Copyright 2019 The TensorFlow Authors.Licensed under the Apache License, Version 2.0 (the "License");<jupyter_code>#@title Licensed under the Apache License, Version 2.0 (the "License"); { display-mode: "form" }
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# https://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.<jupyter_output><empty_output><jupyter_text>Learnable Distributions Zoo      Run in Google Colab        View source on GitHub   In this colab we show various examples of building learnable ("trainable") distributions. (We make no effort to explain the distributions, only to show how to build them.)<jupyter_code>import numpy as np
import tensorflow.compat.v2 as tf
import tensorflow_probability as tfp
from tensorflow_probability.python.internal import prefer_static
tfb = tfp.bijectors
tfd = tfp.distributions
tf.enable_v2_behavior()
event_size = 4
num_components = 3<jupyter_output><empty_output><jupyter_text>Learnable Multivariate Normal with Scaled Identity for `chol(Cov)`<jupyter_code>learnable_mvn_scaled_identity = tfd.Independent(
    tfd.Normal(
        loc=tf.Variable(tf.zeros(event_size), name='loc'),
        scale=tfp.util.TransformedVariable(
            tf.ones([event_size, 1]),
            bijector=tfb.Exp()),
            name='scale'),
    reinterpreted_batch_ndims=1,
    name='learnable_mvn_scaled_identity')

print(learnable_mvn_scaled_identity)
print(learnable_mvn_scaled_identity.trainable_variables)<jupyter_output>tfp.distributions.Independent("learnable_mvn_scaled_identity", batch_shape=[4], event_shape=[4], dtype=float32)
(<tf.Variable 'Variable:0' shape=(4,) dtype=float32, numpy=array([0., 0., 0., 0.], dtype=float32)>, <tf.Variable 'Variable:0' shape=(4, 1) dtype=float32, numpy=
array([[0.],
       [0.],
       [0.],
       [0.]], dtype=float32)>)<jupyter_text>Learnable Multivariate Normal with Diagonal for `chol(Cov)`<jupyter_code>learnable_mvndiag = tfd.Independent(
    tfd.Normal(
        loc=tf.Variable(tf.zeros(event_size), name='loc'),
        scale=tfp.util.TransformedVariable(
            tf.ones(event_size),
            bijector=tfb.Softplus()),  # Use Softplus...cuz why not?
            name='scale'),
    reinterpreted_batch_ndims=1,
    name='learnable_mvn_diag')

print(learnable_mvndiag)
print(learnable_mvndiag.trainable_variables)<jupyter_output>tfp.distributions.Independent("learnable_mvn_diag", batch_shape=[], event_shape=[4], dtype=float32)
(<tf.Variable 'Variable:0' shape=(4,) dtype=float32, numpy=array([0., 0., 0., 0.], dtype=float32)>, <tf.Variable 'Variable:0' shape=(4,) dtype=float32, numpy=array([0., 0., 0., 0.], dtype=float32)>)<jupyter_text>Mixture of Multivarite Normal (spherical)<jupyter_code>learnable_mix_mvn_scaled_identity = tfd.MixtureSameFamily(
    mixture_distribution=tfd.Categorical(
        logits=tf.Variable(
            # Changing the `1.` intializes with a geometric decay.
            -tf.math.log(1.) * tf.range(num_components, dtype=tf.float32),
            name='logits')),
    components_distribution=tfd.Independent(
        tfd.Normal(
            loc=tf.Variable(
              tf.random.normal([num_components, event_size]),
              name='loc'),
            scale=tfp.util.TransformedVariable(
              10. * tf.ones([num_components, 1]),
              bijector=tfb.Softplus()),  # Use Softplus...cuz why not?
              name='scale'),
        reinterpreted_batch_ndims=1),
    name='learnable_mix_mvn_scaled_identity')

print(learnable_mix_mvn_scaled_identity)
print(learnable_mix_mvn_scaled_identity.trainable_variables)<jupyter_output>tfp.distributions.MixtureSameFamily("learnable_mix_mvn_scaled_identity", batch_shape=[], event_shape=[4], dtype=float32)
(<tf.Variable 'Variable:0' shape=(3, 4) dtype=float32, numpy=
array([[-0.11800266, -1.3127382 , -0.1813932 ,  0.24975719],
       [ 0.97209346, -0.91694   ,  0.84734786, -1.3201759 ],
       [ 0.15194772,  0.33787215, -0.4269769 , -0.26286215]],
      dtype=float32)>, <tf.Variable 'Variable:0' shape=(3, 1) dtype=float32, numpy=
array([[-4.600166],
       [-4.600166],
       [-4.600166]], dtype=float32)>, <tf.Variable 'logits:0' shape=(3,) dtype=float32, numpy=array([-0., -0., -0.], dtype=float32)>)<jupyter_text>Mixture of Multivariate Normal (spherical) with first mix weight unlearnable<jupyter_code>learnable_mix_mvndiag_first_fixed = tfd.MixtureSameFamily(
    mixture_distribution=tfd.Categorical(
        logits=tfp.util.TransformedVariable(
            # Initialize logits as geometric decay.
            -tf.math.log(1.5) * tf.range(num_components, dtype=tf.float32),
            tfb.Pad(paddings=[[1, 0]], constant_values=0)),
            name='logits'),
    components_distribution=tfd.Independent(
        tfd.Normal(
            loc=tf.Variable(
                # Use Rademacher...cuz why not?
                tfp.math.random_rademacher([num_components, event_size]),
                name='loc'),
            scale=tfp.util.TransformedVariable(
                10. * tf.ones([num_components, 1]),
                bijector=tfb.Softplus()),  # Use Softplus...cuz why not?
                name='scale'),
        reinterpreted_batch_ndims=1),
    name='learnable_mix_mvndiag_first_fixed')

print(learnable_mix_mvndiag_first_fixed)
print(learnable_mix_mvndiag_first_fixed.trainable_variables)<jupyter_output>tfp.distributions.MixtureSameFamily("learnable_mix_mvndiag_first_fixed", batch_shape=[], event_shape=[4], dtype=float32)
(<tf.Variable 'Variable:0' shape=(3, 4) dtype=float32, numpy=
array([[-1., -1.,  1., -1.],
       [-1., -1., -1., -1.],
       [ 1.,  1.,  1., -1.]], dtype=float32)>, <tf.Variable 'Variable:0' shape=(3, 4) dtype=float32, numpy=
array([[-4.600166, -4.600166, -4.600166, -4.600166],
       [-4.600166, -4.600166, -4.600166, -4.600166],
       [-4.600166, -4.600166, -4.600166, -4.600166]], dtype=float32)>, <tf.Variable 'Variable:0' shape=(2,) dtype=float32, numpy=array([-0.4054651, -0.8109302], dtype=float32)>)<jupyter_text>Mixture of Multivariate Normal (full `Cov`)<jupyter_code>learnable_mix_mvntril = tfd.MixtureSameFamily(
    mixture_distribution=tfd.Categorical(
        logits=tf.Variable(
            # Changing the `1.` intializes with a geometric decay.
            -tf.math.log(1.) * tf.range(num_components, dtype=tf.float32),
            name='logits')),
    components_distribution=tfd.MultivariateNormalTriL(
        loc=tf.Variable(tf.zeros([num_components, event_size]), name='loc'),
        scale_tril=tfp.util.TransformedVariable(
            10. * tf.eye(event_size, batch_shape=[num_components]),
            bijector=tfb.FillScaleTriL()),
            name='scale_tril'),
    name='learnable_mix_mvntril')

print(learnable_mix_mvntril)
print(learnable_mix_mvntril.trainable_variables)<jupyter_output>tfp.distributions.MixtureSameFamily("learnable_mix_mvntril", batch_shape=[], event_shape=[4], dtype=float32)
(<tf.Variable 'Variable:0' shape=(3, 4) dtype=float32, numpy=
array([[ 1.4036556 , -0.22486973,  0.8365339 ,  1.1744921 ],
       [-0.14385273,  1.5095806 ,  0.78327304, -0.64133334],
       [-0.22640549,  1.908316  ,  1.1216396 , -1.2109828 ]],
      dtype=float32)>, <tf.Variable 'Variable:0' shape=(3, 10) dtype=float32, numpy=
array([[-4.6011715,  0.       ,  0.       ,  0.       , -4.6011715,
        -4.6011715,  0.       ,  0.       ,  0.       , -4.6011715],
       [-4.6011715,  0.       ,  0.       ,  0.       , -4.6011715,
        -4.6011715,  0.       ,  0.       ,  0.       , -4.6011715],
       [-4.6011715,  0.       ,  0.       ,  0.       , -4.6011715,
        -4.6011715,  0.       ,  0.       ,  0.       , -4.6011715]],
      dtype=float32)>, <tf.Variable 'logits:0' shape=(3,) dtype=float32, numpy=array([-0., -0., -0.], dtype=float32)>)<jupyter_text>Mixture of Multivariate Normal (full `Cov`) with unlearnable first mix & first component<jupyter_code># Make a bijector which pads an eye to what otherwise fills a tril.
num_tril_nonzero = lambda num_rows: num_rows * (num_rows + 1) // 2

num_tril_rows = lambda nnz: prefer_static.cast(
    prefer_static.sqrt(0.25 + 2. * prefer_static.cast(nnz, tf.float32)) - 0.5,
    tf.int32)

# TFP doesn't have a concat bijector, so we roll out our own.
class PadEye(tfb.Bijector):

  def __init__(self, tril_fn=None):
    if tril_fn is None:
      tril_fn = tfb.FillScaleTriL()
    self._tril_fn = getattr(tril_fn, 'inverse', tril_fn)
    super(PadEye, self).__init__(
        forward_min_event_ndims=2,
        inverse_min_event_ndims=2,
        is_constant_jacobian=True,
        name='PadEye')

  def _forward(self, x):
    num_rows = int(num_tril_rows(tf.compat.dimension_value(x.shape[-1])))
    eye = tf.eye(num_rows, batch_shape=prefer_static.shape(x)[:-2])
    return tf.concat([self._tril_fn(eye)[..., tf.newaxis, :], x],
                     axis=prefer_static.rank(x) - 2)

  def _inverse(self, y):
    return y[..., 1:, :]

  def _forward_log_det_jacobian(self, x):
    return tf.zeros([], dtype=x.dtype)

  def _inverse_log_det_jacobian(self, y):
    return tf.zeros([], dtype=y.dtype)

  def _forward_event_shape(self, in_shape):
    n = prefer_static.size(in_shape)
    return in_shape + prefer_static.one_hot(n - 2, depth=n, dtype=tf.int32)

  def _inverse_event_shape(self, out_shape):
    n = prefer_static.size(out_shape)
    return out_shape - prefer_static.one_hot(n - 2, depth=n, dtype=tf.int32)


tril_bijector = tfb.FillScaleTriL(diag_bijector=tfb.Softplus())
learnable_mix_mvntril_fixed_first = tfd.MixtureSameFamily(
  mixture_distribution=tfd.Categorical(
      logits=tfp.util.TransformedVariable(
          # Changing the `1.` intializes with a geometric decay.
          -tf.math.log(1.) * tf.range(num_components, dtype=tf.float32),
          bijector=tfb.Pad(paddings=[(1, 0)]),
          name='logits')),
  components_distribution=tfd.MultivariateNormalTriL(
      loc=tfp.util.TransformedVariable(
          tf.zeros([num_components, event_size]),
          bijector=tfb.Pad(paddings=[(1, 0)], axis=-2),
          name='loc'),
      scale_tril=tfp.util.TransformedVariable(
          10. * tf.eye(event_size, batch_shape=[num_components]),
          bijector=tfb.Chain([tril_bijector, PadEye(tril_bijector)]),
          name='scale_tril')),
  name='learnable_mix_mvntril_fixed_first')


print(learnable_mix_mvntril_fixed_first)
print(learnable_mix_mvntril_fixed_first.trainable_variables)<jupyter_output>tfp.distributions.MixtureSameFamily("learnable_mix_mvntril_fixed_first", batch_shape=[], event_shape=[4], dtype=float32)
(<tf.Variable 'loc:0' shape=(2, 4) dtype=float32, numpy=
array([[ 0.53900903, -0.17989647, -1.196744  , -1.0601326 ],
       [ 0.46199334,  1.2968503 ,  0.20908853, -0.36455044]],
      dtype=float32)>, <tf.Variable 'Variable:0' shape=(2, 10) dtype=float32, numpy=
array([[-4.6011715,  0.       ,  0.       ,  0.       , -4.6011715,
        -4.6011715,  0.       ,  0.       ,  0.       , -4.6011715],
       [-4.6011715,  0.       ,  0.       ,  0.       , -4.6011715,
        -4.6011715,  0.       ,  0.       ,  0.       , -4.6011715]],
      dtype=float32)>, <tf.Variable 'logits:0' shape=(2,) dtype=float32, numpy=array([-0., -0.], dtype=float32)>)
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