add categorical class (#27695)

* add multinomial cpu kernel

* fix C++ notype error

* fix windows ci array len error

* let array len be const

* change array to vector

* add cuda kernrl with num_distribution is 1, and not support replacement=False

* add multinomial python api

* support num_distribution different multinomial distributions

* add categorical class

* fix test_distribution enable_static error

* add unittest for different setting of Categorical

* optimize format

* little change

* little change

* add raise error if shape not match, optimize format

* fix windows CI dtype error in concat

* little changes

* little changes2

* change values type to int64

* change values type to int64

* change values type to int64

python/paddle/distribution.py

@@ -28,13 +28,14 @@ from .fluid.layers import nn
 from .fluid import core
 from .fluid.framework import in_dygraph_mode
 from .tensor.math import elementwise_mul, elementwise_div, elementwise_add, elementwise_sub
+from .tensor import arange, gather_nd, concat, multinomial
 import math
 import numpy as np
 import warnings
 
 from .fluid.data_feeder import convert_dtype, check_variable_and_dtype, check_type, check_dtype
 
-__all__ = ['Distribution', 'Uniform', 'Normal']
+__all__ = ['Distribution', 'Uniform', 'Normal', 'Categorical']
 
 
 class Distribution(object):
@@ -640,3 +641,318 @@ class Normal(Distribution):
         t1 = (t1 * t1)
         return elementwise_add(
             0.5 * var_ratio, 0.5 * (t1 - 1. - nn.log(var_ratio)), name=name)
+
+
+class Categorical(Distribution):
+    """
+    Categorical distribution is a discrete probability distribution that 
+    describes the possible results of a random variable that can take on 
+    one of K possible categories, with the probability of each category 
+    separately specified.
+
+    The probability mass function (pmf) is:
+
+    .. math::
+
+        pmf(k; p_i) = \prod_{i=1}^{k} p_i^{[x=i]}
+
+    In the above equation:
+
+    * :math:`[x=i]` : it evaluates to 1 if :math:`x==i` , 0 otherwise.
+
+    Args:
+        logits(list|numpy.ndarray|Tensor): The logits input of categorical distribution. The data type is float32 or float64.
+
+    Examples:
+        .. code-block:: python
+
+          import paddle
+          from paddle.distribution import Categorical
+
+          x = paddle.rand([6])
+          print(x.numpy())
+          # [0.32564053, 0.99334985, 0.99034804,
+          #  0.09053693, 0.30820143, 0.19095989]
+          y = paddle.rand([6])
+          print(y.numpy())
+          # [0.6365463 , 0.7278677 , 0.90260243, 
+          # 0.5226815 , 0.35837543, 0.13981032]
+
+          cat = Categorical(x)
+          cat2 = Categorical(y)
+
+          cat.sample([2,3])
+          # [[5, 1, 1],
+          # [0, 1, 2]]
+
+          cat.entropy()
+          # [1.71887]
+
+          cat.kl_divergence(cat2)
+          # [0.0278455]
+
+          value = paddle.to_tensor([2,1,3])
+          cat.probs(value)
+          # [0.341613 0.342648 0.03123]
+
+          cat.log_prob(value)
+          # [-1.07408 -1.07105 -3.46638]
+
+    """
+
+    def __init__(self, logits, name=None):
+        """
+        Args:
+            logits(list|numpy.ndarray|Variable): The logits input of categorical distribution. The data type is float32 or float64.
+        """
+        if not in_dygraph_mode():
+            check_type(logits, 'logits', (np.ndarray, tensor.Variable, list),
+                       'Categorical')
+
+        self.name = name if name is not None else 'Categorical'
+        self.dtype = 'float32'
+
+        if self._validate_args(logits):
+            self.logits = logits
+            self.dtype = convert_dtype(logits.dtype)
+        else:
+            if isinstance(logits, np.ndarray) and str(
+                    logits.dtype) in ['float32', 'float64']:
+                self.dtype = logits.dtype
+            self.logits = self._to_tensor(logits)[0]
+            if self.dtype != convert_dtype(self.logits.dtype):
+                self.logits = tensor.cast(self.logits, dtype=self.dtype)
+
+    def sample(self, shape):
+        """Generate samples of the specified shape.
+
+        Args:
+          shape (list): Shape of the generated samples.
+
+        Returns:
+          Tensor: A tensor with prepended dimensions shape.
+        
+        Examples:
+        .. code-block:: python
+
+          import paddle
+          from paddle.distribution import Categorical
+
+          x = paddle.rand([6])
+          print(x.numpy())
+          # [0.32564053, 0.99334985, 0.99034804,
+          #  0.09053693, 0.30820143, 0.19095989]
+
+          cat = Categorical(x)
+
+          cat.sample([2,3])
+          # [[5, 1, 1],
+          # [0, 1, 2]]
+
+        """
+        name = self.name + '_sample'
+        if not in_dygraph_mode():
+            check_type(shape, 'shape', (list), 'sample')
+
+        num_samples = np.prod(np.array(shape))
+
+        logits_shape = list(self.logits.shape)
+        if len(logits_shape) > 1:
+            sample_shape = shape + logits_shape[:-1]
+            logits = nn.reshape(self.logits,
+                                [np.prod(logits_shape[:-1]), logits_shape[-1]])
+        else:
+            sample_shape = shape
+            logits = self.logits
+
+        sample_index = multinomial(logits, num_samples, True)
+        return nn.reshape(sample_index, sample_shape, name=name)
+
+    def kl_divergence(self, other):
+        """The KL-divergence between two Categorical distributions.
+
+        Args:
+            other (Categorical): instance of Categorical. The data type is float32.
+
+        Returns:
+            Variable: kl-divergence between two Categorical distributions.
+        
+        Examples:
+        .. code-block:: python
+
+          import paddle
+          from paddle.distribution import Categorical
+
+          x = paddle.rand([6])
+          print(x.numpy())
+          # [0.32564053, 0.99334985, 0.99034804,
+          #  0.09053693, 0.30820143, 0.19095989]
+          y = paddle.rand([6])
+          print(y.numpy())
+          # [0.6365463 , 0.7278677 , 0.90260243, 
+          # 0.5226815 , 0.35837543, 0.13981032]
+
+          cat = Categorical(x)
+          cat2 = Categorical(y)
+
+          cat.kl_divergence(cat2)
+          # [0.0278455]
+
+        """
+        name = self.name + '_kl_divergence'
+        if not in_dygraph_mode():
+            check_type(other, 'other', Categorical, 'kl_divergence')
+
+        logits = self.logits - nn.reduce_max(self.logits, dim=-1, keep_dim=True)
+        other_logits = other.logits - nn.reduce_max(
+            other.logits, dim=-1, keep_dim=True)
+        e_logits = ops.exp(logits)
+        other_e_logits = ops.exp(other_logits)
+        z = nn.reduce_sum(e_logits, dim=-1, keep_dim=True)
+        other_z = nn.reduce_sum(other_e_logits, dim=-1, keep_dim=True)
+        prob = e_logits / z
+        kl = nn.reduce_sum(
+            prob * (logits - nn.log(z) - other_logits + nn.log(other_z)),
+            dim=-1,
+            keep_dim=True,
+            name=name)
+
+        return kl
+
+    def entropy(self):
+        """Shannon entropy in nats.
+
+        Returns:
+          Variable: Shannon entropy of Categorical distribution. The data type is float32.
+        
+        Examples:
+        .. code-block:: python
+
+          import paddle
+          from paddle.distribution import Categorical
+
+          x = paddle.rand([6])
+          print(x.numpy())
+          # [0.32564053, 0.99334985, 0.99034804,
+          #  0.09053693, 0.30820143, 0.19095989]
+
+          cat = Categorical(x)
+
+          cat.entropy()
+          # [1.71887]
+
+        """
+        name = self.name + '_entropy'
+        logits = self.logits - nn.reduce_max(self.logits, dim=-1, keep_dim=True)
+        e_logits = ops.exp(logits)
+        z = nn.reduce_sum(e_logits, dim=-1, keep_dim=True)
+        prob = e_logits / z
+
+        neg_entropy = nn.reduce_sum(
+            prob * (logits - nn.log(z)), dim=-1, keep_dim=True)
+        entropy = nn.scale(neg_entropy, scale=-1.0, name=name)
+        return entropy
+
+    def probs(self, value):
+        """Probabilities of the given category (``value``).
+
+        If ``logits`` is 2-D or higher dimension, the last dimension will be regarded as 
+        category, and the others represents the different distributions.
+        At the same time, if ``vlaue`` is 1-D Tensor, ``value`` will be broadcast to the 
+        same number of distributions as ``logits``.
+        If ``value`` is not 1-D Tensor, ``value`` should have the same number distributions
+        with ``logits. That is, ``value[:-1] = logits[:-1]``.
+
+        Args:
+          value (Tensor): The input tensor represents the selected category index.
+
+        Returns:
+          Tensor: probability according to the category index.
+        
+        Examples:
+        .. code-block:: python
+
+          import paddle
+          from paddle.distribution import Categorical
+
+          x = paddle.rand([6])
+          print(x.numpy())
+          # [0.32564053, 0.99334985, 0.99034804,
+          #  0.09053693, 0.30820143, 0.19095989]
+
+          cat = Categorical(x)
+
+          value = paddle.to_tensor([2,1,3])
+          cat.probs(value)
+          # [0.341613 0.342648 0.03123]
+
+        """
+        name = self.name + '_probs'
+
+        dist_sum = nn.reduce_sum(self.logits, dim=-1, keep_dim=True)
+        prob = self.logits / dist_sum
+
+        shape = list(prob.shape)
+        value_shape = list(value.shape)
+        if len(shape) == 1:
+            num_value_in_one_dist = np.prod(value_shape)
+            index_value = nn.reshape(value, [num_value_in_one_dist, 1])
+            index = index_value
+        else:
+            num_dist = np.prod(shape[:-1])
+            num_value_in_one_dist = value_shape[-1]
+            prob = nn.reshape(prob, [num_dist, shape[-1]])
+            if len(value_shape) == 1:
+                value = nn.expand(value, [num_dist])
+                value_shape = shape[:-1] + value_shape
+            index_value = nn.reshape(value, [num_dist, -1, 1])
+            if shape[:-1] != value_shape[:-1]:
+                raise ValueError(
+                    "shape of value {} must match shape of logits {}".format(
+                        str(value_shape[:-1]), str(shape[:-1])))
+
+            index_prefix = nn.unsqueeze(
+                arange(
+                    num_dist, dtype=index_value.dtype), axes=-1)
+            index_prefix = nn.expand(index_prefix, [1, num_value_in_one_dist])
+            index_prefix = nn.unsqueeze(index_prefix, axes=-1)
+
+            if index_value.dtype != index_prefix.dtype:
+                tensor.cast(index_prefix, dtype=index_value.dtype)
+            index = concat([index_prefix, index_value], axis=-1)
+
+        # value is the category index to search for the corresponding probability.
+        select_prob = gather_nd(prob, index)
+        return nn.reshape(select_prob, value_shape, name=name)
+
+    def log_prob(self, value):
+        """Log probabilities of the given category. Refer to ``probs`` method.
+
+        Args:
+          value (Tensor): The input tensor represents the selected category index.
+
+        Returns:
+          Tensor: Log probability.
+        
+        Examples:
+        .. code-block:: python
+
+          import paddle
+          from paddle.distribution import Categorical
+
+          x = paddle.rand([6])
+          print(x.numpy())
+          # [0.32564053, 0.99334985, 0.99034804,
+          #  0.09053693, 0.30820143, 0.19095989]
+
+          cat = Categorical(x)
+
+          value = paddle.to_tensor([2,1,3])
+
+          cat.log_prob(value)
+          # [-1.07408 -1.07105 -3.46638]
+
+        """
+        name = self.name + '_log_prob'
+
+        return nn.log(self.probs(value), name=name)