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+# Copyright 2016 The TensorFlow Authors. All Rights Reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://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.
+# ==============================================================================
+"""The Beta distribution class."""
+
+from __future__ import absolute_import
+from __future__ import division
+from __future__ import print_function
+
+import numpy as np
+
+from tensorflow.python.framework import constant_op
+from tensorflow.python.framework import dtypes
+from tensorflow.python.framework import ops
+from tensorflow.python.framework import tensor_shape
+from tensorflow.python.ops import array_ops
+from tensorflow.python.ops import check_ops
+from tensorflow.python.ops import control_flow_ops
+from tensorflow.python.ops import math_ops
+from tensorflow.python.ops import nn
+from tensorflow.python.ops import random_ops
+from tensorflow.python.ops.distributions import distribution
+from tensorflow.python.ops.distributions import kullback_leibler
+from tensorflow.python.ops.distributions import util as distribution_util
+
+
+__all__ = [
+    "Beta",
+    "BetaWithSoftplusConcentration",
+]
+
+
+_beta_sample_note = """Note: `x` must have dtype `self.dtype` and be in
+`[0, 1].` It must have a shape compatible with `self.batch_shape()`."""
+
+
+class Beta(distribution.Distribution):
+  """Beta distribution.
+
+  The Beta distribution is defined over the `(0, 1)` interval using parameters
+  `concentration1` (aka "alpha") and `concentration0` (aka "beta").
+
+  #### Mathematical Details
+
+  The probability density function (pdf) is,
+
+  ```none
+  pdf(x; alpha, beta) = x**(alpha - 1) (1 - x)**(beta - 1) / Z
+  Z = Gamma(alpha) Gamma(beta) / Gamma(alpha + beta)
+  ```
+
+  where:
+
+  * `concentration1 = alpha`,
+  * `concentration0 = beta`,
+  * `Z` is the normalization constant, and,
+  * `Gamma` is the [gamma function](
+    https://en.wikipedia.org/wiki/Gamma_function).
+
+  The concentration parameters represent mean total counts of a `1` or a `0`,
+  i.e.,
+
+  ```none
+  concentration1 = alpha = mean * total_concentration
+  concentration0 = beta  = (1. - mean) * total_concentration
+  ```
+
+  where `mean` in `(0, 1)` and `total_concentration` is a positive real number
+  representing a mean `total_count = concentration1 + concentration0`.
+
+  Distribution parameters are automatically broadcast in all functions; see
+  examples for details.
+
+  #### Examples
+
+  ```python
+  # Create a batch of three Beta distributions.
+  alpha = [1, 2, 3]
+  beta = [1, 2, 3]
+  dist = Beta(alpha, beta)
+
+  dist.sample([4, 5])  # Shape [4, 5, 3]
+
+  # `x` has three batch entries, each with two samples.
+  x = [[.1, .4, .5],
+       [.2, .3, .5]]
+  # Calculate the probability of each pair of samples under the corresponding
+  # distribution in `dist`.
+  dist.prob(x)         # Shape [2, 3]
+  ```
+
+  ```python
+  # Create batch_shape=[2, 3] via parameter broadcast:
+  alpha = [[1.], [2]]      # Shape [2, 1]
+  beta = [3., 4, 5]        # Shape [3]
+  dist = Beta(alpha, beta)
+
+  # alpha broadcast as: [[1., 1, 1,],
+  #                      [2, 2, 2]]
+  # beta broadcast as:  [[3., 4, 5],
+  #                      [3, 4, 5]]
+  # batch_Shape [2, 3]
+  dist.sample([4, 5])  # Shape [4, 5, 2, 3]
+
+  x = [.2, .3, .5]
+  # x will be broadcast as [[.2, .3, .5],
+  #                         [.2, .3, .5]],
+  # thus matching batch_shape [2, 3].
+  dist.prob(x)         # Shape [2, 3]
+  ```
+
+  """
+
+  def __init__(self,
+               concentration1=None,
+               concentration0=None,
+               validate_args=False,
+               allow_nan_stats=True,
+               name="Beta"):
+    """Initialize a batch of Beta distributions.
+
+    Args:
+      concentration1: Positive floating-point `Tensor` indicating mean
+        number of successes; aka "alpha". Implies `self.dtype` and
+        `self.batch_shape`, i.e.,
+        `concentration1.shape = [N1, N2, ..., Nm] = self.batch_shape`.
+      concentration0: Positive floating-point `Tensor` indicating mean
+        number of failures; aka "beta". Otherwise has same semantics as
+        `concentration1`.
+      validate_args: Python `bool`, default `False`. When `True` distribution
+        parameters are checked for validity despite possibly degrading runtime
+        performance. When `False` invalid inputs may silently render incorrect
+        outputs.
+      allow_nan_stats: Python `bool`, default `True`. When `True`, statistics
+        (e.g., mean, mode, variance) use the value "`NaN`" to indicate the
+        result is undefined. When `False`, an exception is raised if one or
+        more of the statistic's batch members are undefined.
+      name: Python `str` name prefixed to Ops created by this class.
+    """
+    parameters = locals()
+    with ops.name_scope(name, values=[concentration1, concentration0]):
+      self._concentration1 = self._maybe_assert_valid_concentration(
+          ops.convert_to_tensor(concentration1, name="concentration1"),
+          validate_args)
+      self._concentration0 = self._maybe_assert_valid_concentration(
+          ops.convert_to_tensor(concentration0, name="concentration0"),
+          validate_args)
+      check_ops.assert_same_float_dtype([
+          self._concentration1, self._concentration0])
+      self._total_concentration = self._concentration1 + self._concentration0
+    super(Beta, self).__init__(
+        dtype=self._total_concentration.dtype,
+        validate_args=validate_args,
+        allow_nan_stats=allow_nan_stats,
+        reparameterization_type=distribution.NOT_REPARAMETERIZED,
+        parameters=parameters,
+        graph_parents=[self._concentration1,
+                       self._concentration0,
+                       self._total_concentration],
+        name=name)
+
+  @staticmethod
+  def _param_shapes(sample_shape):
+    return dict(zip(
+        ["concentration1", "concentration0"],
+        [ops.convert_to_tensor(sample_shape, dtype=dtypes.int32)] * 2))
+
+  @property
+  def concentration1(self):
+    """Concentration parameter associated with a `1` outcome."""
+    return self._concentration1
+
+  @property
+  def concentration0(self):
+    """Concentration parameter associated with a `0` outcome."""
+    return self._concentration0
+
+  @property
+  def total_concentration(self):
+    """Sum of concentration parameters."""
+    return self._total_concentration
+
+  def _batch_shape_tensor(self):
+    return array_ops.shape(self.total_concentration)
+
+  def _batch_shape(self):
+    return self.total_concentration.get_shape()
+
+  def _event_shape_tensor(self):
+    return constant_op.constant([], dtype=dtypes.int32)
+
+  def _event_shape(self):
+    return tensor_shape.scalar()
+
+  def _sample_n(self, n, seed=None):
+    expanded_concentration1 = array_ops.ones_like(
+        self.total_concentration, dtype=self.dtype) * self.concentration1
+    expanded_concentration0 = array_ops.ones_like(
+        self.total_concentration, dtype=self.dtype) * self.concentration0
+    gamma1_sample = random_ops.random_gamma(
+        shape=[n],
+        alpha=expanded_concentration1,
+        dtype=self.dtype,
+        seed=seed)
+    gamma2_sample = random_ops.random_gamma(
+        shape=[n],
+        alpha=expanded_concentration0,
+        dtype=self.dtype,
+        seed=distribution_util.gen_new_seed(seed, "beta"))
+    beta_sample = gamma1_sample / (gamma1_sample + gamma2_sample)
+    return beta_sample
+
+  @distribution_util.AppendDocstring(_beta_sample_note)
+  def _log_prob(self, x):
+    return self._log_unnormalized_prob(x) - self._log_normalization()
+
+  @distribution_util.AppendDocstring(_beta_sample_note)
+  def _prob(self, x):
+    return math_ops.exp(self._log_prob(x))
+
+  @distribution_util.AppendDocstring(_beta_sample_note)
+  def _log_cdf(self, x):
+    return math_ops.log(self._cdf(x))
+
+  @distribution_util.AppendDocstring(_beta_sample_note)
+  def _cdf(self, x):
+    return math_ops.betainc(self.concentration1, self.concentration0, x)
+
+  def _log_unnormalized_prob(self, x):
+    x = self._maybe_assert_valid_sample(x)
+    return ((self.concentration1 - 1.) * math_ops.log(x)
+            + (self.concentration0 - 1.) * math_ops.log1p(-x))
+
+  def _log_normalization(self):
+    return (math_ops.lgamma(self.concentration1)
+            + math_ops.lgamma(self.concentration0)
+            - math_ops.lgamma(self.total_concentration))
+
+  def _entropy(self):
+    return (
+        self._log_normalization()
+        - (self.concentration1 - 1.) * math_ops.digamma(self.concentration1)
+        - (self.concentration0 - 1.) * math_ops.digamma(self.concentration0)
+        + ((self.total_concentration - 2.) *
+           math_ops.digamma(self.total_concentration)))
+
+  def _mean(self):
+    return self._concentration1 / self._total_concentration
+
+  def _variance(self):
+    return self._mean() * (1. - self._mean()) / (1. + self.total_concentration)
+
+  @distribution_util.AppendDocstring(
+      """Note: The mode is undefined when `concentration1 <= 1` or
+      `concentration0 <= 1`. If `self.allow_nan_stats` is `True`, `NaN`
+      is used for undefined modes. If `self.allow_nan_stats` is `False` an
+      exception is raised when one or more modes are undefined.""")
+  def _mode(self):
+    mode = (self.concentration1 - 1.) / (self.total_concentration - 2.)
+    if self.allow_nan_stats:
+      nan = array_ops.fill(
+          self.batch_shape_tensor(),
+          np.array(np.nan, dtype=self.dtype.as_numpy_dtype()),
+          name="nan")
+      is_defined = math_ops.logical_and(self.concentration1 > 1.,
+                                        self.concentration0 > 1.)
+      return array_ops.where(is_defined, mode, nan)
+    return control_flow_ops.with_dependencies([
+        check_ops.assert_less(
+            array_ops.ones([], dtype=self.dtype),
+            self.concentration1,
+            message="Mode undefined for concentration1 <= 1."),
+        check_ops.assert_less(
+            array_ops.ones([], dtype=self.dtype),
+            self.concentration0,
+            message="Mode undefined for concentration0 <= 1.")
+    ], mode)
+
+  def _maybe_assert_valid_concentration(self, concentration, validate_args):
+    """Checks the validity of a concentration parameter."""
+    if not validate_args:
+      return concentration
+    return control_flow_ops.with_dependencies([
+        check_ops.assert_positive(
+            concentration,
+            message="Concentration parameter must be positive."),
+    ], concentration)
+
+  def _maybe_assert_valid_sample(self, x):
+    """Checks the validity of a sample."""
+    if not self.validate_args:
+      return x
+    return control_flow_ops.with_dependencies([
+        check_ops.assert_positive(
+            x,
+            message="sample must be positive"),
+        check_ops.assert_less(
+            x, array_ops.ones([], self.dtype),
+            message="sample must be no larger than `1`."),
+    ], x)
+
+
+class BetaWithSoftplusConcentration(Beta):
+  """Beta with softplus transform of `concentration1` and `concentration0`."""
+
+  def __init__(self,
+               concentration1,
+               concentration0,
+               validate_args=False,
+               allow_nan_stats=True,
+               name="BetaWithSoftplusConcentration"):
+    parameters = locals()
+    with ops.name_scope(name, values=[concentration1,
+                                      concentration0]) as ns:
+      super(BetaWithSoftplusConcentration, self).__init__(
+          concentration1=nn.softplus(concentration1,
+                                     name="softplus_concentration1"),
+          concentration0=nn.softplus(concentration0,
+                                     name="softplus_concentration0"),
+          validate_args=validate_args,
+          allow_nan_stats=allow_nan_stats,
+          name=ns)
+    self._parameters = parameters
+
+
+@kullback_leibler.RegisterKL(Beta, Beta)
+def _kl_beta_beta(d1, d2, name=None):
+  """Calculate the batchwise KL divergence KL(d1 || d2) with d1 and d2 Beta.
+
+  Args:
+    d1: instance of a Beta distribution object.
+    d2: instance of a Beta distribution object.
+    name: (optional) Name to use for created operations.
+      default is "kl_beta_beta".
+
+  Returns:
+    Batchwise KL(d1 || d2)
+  """
+  def delta(fn, is_property=True):
+    fn1 = getattr(d1, fn)
+    fn2 = getattr(d2, fn)
+    return (fn2 - fn1) if is_property else (fn2() - fn1())
+  with ops.name_scope(name, "kl_beta_beta", values=[
+      d1.concentration1,
+      d1.concentration0,
+      d1.total_concentration,
+      d2.concentration1,
+      d2.concentration0,
+      d2.total_concentration,
+  ]):
+    return (delta("_log_normalization", is_property=False)
+            - math_ops.digamma(d1.concentration1) * delta("concentration1")
+            - math_ops.digamma(d1.concentration0) * delta("concentration0")
+            + (math_ops.digamma(d1.total_concentration)
+               * delta("total_concentration")))