【Hackathon No.8】 add gumbel distribution api

python/paddle/distribution/__init__.py

@@ -17,6 +17,7 @@
 from paddle.distribution.categorical import Categorical
 from paddle.distribution.dirichlet import Dirichlet
 from paddle.distribution.distribution import Distribution
+from paddle.distribution.gumbel import Gumbel
 from paddle.distribution.exponential_family import ExponentialFamily
 from paddle.distribution.independent import Independent
 from paddle.distribution.kl import kl_divergence, register_kl
@@ -32,7 +33,7 @@
 __all__ = [  # noqa
     'Beta', 'Categorical', 'Dirichlet', 'Distribution', 'ExponentialFamily',
     'Multinomial', 'Normal', 'Uniform', 'kl_divergence', 'register_kl',
-    'Independent', 'TransformedDistribution', 'Laplace', 'LogNormal'
+    'Independent', 'TransformedDistribution', 'Laplace', 'LogNormal', 'Gumbel'
 ]
 
 __all__.extend(transform.__all__)

python/paddle/distribution/gumbel.py

@@ -0,0 +1,242 @@
+# Copyright (c) 2022 PaddlePaddle 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.
+
+import paddle
+import numbers
+import math
+import numpy as np
+
+from paddle.distribution.transformed_distribution import TransformedDistribution
+from paddle.fluid import framework as framework
+
+
+class Gumbel(TransformedDistribution):
+    r"""The Gumbel distribution with location `loc` and `scale` parameters.
+
+    Mathematical details
+
+    The probability density function (pdf) is
+
+    .. math::
+
+        pdf(x; mu, sigma) = exp(-(x - mu) / sigma - exp(-(x - mu) / sigma)) / sigma
+
+
+    In the above equation:
+
+    * :math:`loc = \mu`: is the mean.
+    * :math:`scale = \sigma`: is the std.
+
+    Args:
+        loc(int|float|tensor): The mean of gumbel distribution.The data type is int, float, tensor.
+        scale(int|float|tensor): The std of gumbel distribution.The data type is int, float, tensor.
+
+    Examples:
+        .. code-block:: python
+
+          import paddle
+          from paddle.distribution.gumbel import Gumbel
+
+          # Gumbel distributed with loc=0, scale=1
+          dist = Gumbel(paddle.full([1], 0.0), paddle.full([1], 1.0))
+          dist.sample([2])
+          # Tensor(shape=[2, 1], dtype=float32, place=Place(gpu:0), stop_gradient=True, [[-0.27544352], [-0.64499271]])
+          value = paddle.full([1], 0.5)
+          dist.prob(value)
+          # Tensor(shape=[1], dtype=float32, place=Place(gpu:0), stop_gradient=True, [0.33070430])
+          dist.log_prob(value)
+          # Tensor(shape=[1], dtype=float32, place=Place(gpu:0), stop_gradient=True, [-1.10653067])
+          dist.cdf(value)
+          # Tensor(shape=[1], dtype=float32, place=Place(gpu:0), stop_gradient=True, [0.54523915])
+          dist.entropy()
+          # Tensor(shape=[1], dtype=float32, place=Place(gpu:0), stop_gradient=True, [1.57721567])
+          dist.rsample([2])
+          # Tensor(shape=[2, 1], dtype=float32, place=Place(gpu:0), stop_gradient=True, [[0.80463481], [0.91893655]])
+
+    """
+
+    def __init__(self, loc, scale):
+
+        if not isinstance(loc, (numbers.Real, framework.Variable)):
+            raise TypeError(
+                f"Expected type of loc is Real|Variable, but got {type(loc)}")
+        if not isinstance(scale, (numbers.Real, framework.Variable)):
+            raise TypeError(
+                f"Expected type of scale is Real|Variable, but got {type(scale)}"
+            )
+
+        if isinstance(loc, numbers.Real):
+            loc = paddle.full(shape=(), fill_value=loc)
+
+        if isinstance(scale, numbers.Real):
+            scale = paddle.full(shape=(), fill_value=scale)
+
+        if loc.shape != scale.shape:
+            self.loc, self.scale = paddle.broadcast_tensors([loc, scale])
+        else:
+            self.loc, self.scale = loc, scale
+
+        finfo = np.finfo(dtype='float32')
+        self.base_dist = paddle.distribution.Uniform(
+            paddle.full_like(self.loc, float(finfo.tiny)),
+            paddle.full_like(self.loc, float(1 - finfo.eps)))
+
+        self.transforms = ()
+
+        super(Gumbel, self).__init__(self.base_dist, self.transforms)
+
+    @property
+    def mean(self):
+        """Mean of distribution
+
+        The mean is
+
+        .. math::
+
+            mean = \mu + \sigma * γ
+
+        In the above equation:
+
+        * :math:`loc = \mu`: is the location parameter.
+        * :math:`scale = \sigma`: is the scale parameter.
+        * :math:`γ`: is the euler's constant.
+
+        Returns:
+            Tensor: mean value.
+
+        """
+        return self.loc + self.scale * np.euler_gamma
+
+    @property
+    def variance(self):
+        """Variance of distribution.
+
+        The variance is
+
+        .. math::
+
+            variance = \sigma^2 * \pi^2 / 6
+
+        In the above equation:
+
+        * :math:`scale = \sigma`: is the scale parameter.
+
+        Returns:
+            Tensor: The variance value.
+
+        """
+        temp = paddle.full(shape=self.loc.shape,
+                           fill_value=math.pi * math.pi,
+                           dtype=self.scale.dtype)
+
+        return paddle.pow(self.scale, 2) * temp / 6
+
+    @property
+    def stddev(self):
+        """Standard deviation of distribution
+
+        The standard deviation is
+
+        .. math::
+
+            stddev = \sqrt{\sigma^2 * \pi^2 / 6}
+
+        In the above equation:
+        * :math:`scale = \sigma`: is the scale parameter.
+
+        Returns:
+            Tensor: std value
+        """
+        return paddle.sqrt(self.variance)
+
+    def prob(self, value):
+        """Probability density/mass function
+
+        Args:
+            value (Tensor): The input tensor.
+
+        Returns:
+            Tensor: probability.The data type is same with value.
+
+        """
+        y = (self.loc - value) / self.scale
+
+        return paddle.exp(y - paddle.exp(y)) / self.scale
+
+    def log_prob(self, value):
+        """Log probability density/mass function.
+
+        Args:
+            value (Tensor): The input tensor.
+
+        Returns:
+            Tensor: log probability.The data type is same with value.
+
+        """
+        return paddle.log(self.prob(value))
+
+    def cdf(self, value):
+        """Cumulative distribution function.
+        Args:
+            value (Tensor): value to be evaluated.
+
+        Returns:
+            Tensor: cumulative probability of value.
+
+        """
+        return paddle.exp(-paddle.exp(-(value - self.loc) / self.scale))
+
+    def entropy(self):
+        """Entropy of Gumbel distribution.
+
+        Returns:
+            Entropy of distribution.
+
+        """
+        return paddle.log(self.scale) + 1 + np.euler_gamma
+
+    def sample(self, shape):
+        """Sample from ``Gumbel``.
+
+        Args:
+            shape (Sequence[int], optional): The sample shape. Defaults to ().
+
+        Returns:
+            Tensor: A tensor with prepended dimensions shape.The data type is float32.
+
+        """
+        with paddle.no_grad():
+            return self.rsample(shape)
+
+    def rsample(self, shape):
+        """reparameterized sample
+        Args:
+            shape (Sequence[int]): 1D `int32`. Shape of the generated samples.
+
+        Returns:
+            Tensor: A tensor with prepended dimensions shape.The data type is float32.
+
+        """
+        exp_trans = paddle.distribution.ExpTransform()
+        affine_trans_1 = paddle.distribution.AffineTransform(
+            paddle.full(shape=self.scale.shape,
+                        fill_value=0,
+                        dtype=self.loc.dtype), -paddle.ones_like(self.scale))
+        affine_trans_2 = paddle.distribution.AffineTransform(
+            self.loc, -self.scale)
+
+        return affine_trans_2.forward(
+            exp_trans.inverse(
+                affine_trans_1.forward(
+                    exp_trans.inverse(self._base.sample(shape)))))

python/paddle/distribution/transformed_distribution.py

@@ -62,15 +62,19 @@ def __init__(self, base, transforms):
 
         chain = transform.ChainTransform(transforms)
         base_shape = base.batch_shape + base.event_shape
-        if len(base_shape) < chain._domain.event_rank:
+        self._base = base
+        self._transforms = transforms
+        if not transforms:
+            super(TransformedDistribution,
+                  self).__init__(base.batch_shape, base.event_shape)
+            return
+        if len(base.batch_shape + base.event_shape) < chain._domain.event_rank:
             raise ValueError(
-                f"'base' needs to have shape with size at least {chain._domain.event_rank}, but got {len(base_shape)}."
+                f"'base' needs to have shape with size at least {chain._domain.event_rank}, bug got {len(base_shape)}."
             )
         if chain._domain.event_rank > len(base.event_shape):
             base = independent.Independent(
                 (base, chain._domain.event_rank - len(base.event_shape)))
-        self._base = base
-        self._transforms = transforms
 
         transformed_shape = chain.forward_shape(base.batch_shape +
                                                 base.event_shape)

python/paddle/distribution/uniform.py

@@ -123,6 +123,8 @@ def __init__(self, low, high, name=None):
                 self.low = tensor.cast(self.low, dtype=self.dtype)
                 self.high = tensor.cast(self.high, dtype=self.dtype)
 
+        super(Uniform, self).__init__(self.low.shape)
+
     def sample(self, shape, seed=0):
         """Generate samples of the specified shape.