categorical.py

# Copyright (c) 2021 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 math
import warnings

import numpy as np
import paddle
from paddle import _C_ops

from ..fluid import core
from ..fluid.data_feeder import (check_dtype, check_type,
                                 check_variable_and_dtype, convert_dtype)
from ..fluid.framework import in_dygraph_mode
from ..fluid.layers import (control_flow, elementwise_add, elementwise_div,
                            elementwise_mul, elementwise_sub, nn, ops, tensor)
from ..tensor import arange, concat, gather_nd, multinomial
from .distribution import Distribution


class Categorical(Distribution):
    r"""
    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|tuple|numpy.ndarray|Tensor): The logits input of categorical distribution. The data type is float32 or float64.
        name(str, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`.

    Examples:
        .. code-block:: python

            import paddle
            from paddle.distribution import Categorical

            paddle.seed(100) # on CPU device
            x = paddle.rand([6])
            print(x)
            # [0.5535528  0.20714243 0.01162981
            #  0.51577556 0.36369765 0.2609165 ]

            paddle.seed(200) # on CPU device
            y = paddle.rand([6])
            print(y)
            # [0.77663314 0.90824795 0.15685187
            #  0.04279523 0.34468332 0.7955718 ]

            cat = Categorical(x)
            cat2 = Categorical(y)

            paddle.seed(1000) # on CPU device
            cat.sample([2,3])
            # [[0, 0, 5],
            #  [3, 4, 5]]

            cat.entropy()
            # [1.77528]

            cat.kl_divergence(cat2)
            # [0.071952]

            value = paddle.to_tensor([2,1,3])
            cat.probs(value)
            # [0.00608027 0.108298 0.269656]

            cat.log_prob(value)
            # [-5.10271 -2.22287 -1.31061]

    """

    def __init__(self, logits, name=None):
        """
        Args:
            logits(list|tuple|numpy.ndarray|Tensor): The logits input of categorical distribution. The data type is float32 or float64.
            name(str, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`.
        """
        if not in_dygraph_mode():
            check_type(logits, 'logits',
                       (np.ndarray, tensor.Variable, list, tuple),
                       '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

                paddle.seed(100) # on CPU device
                x = paddle.rand([6])
                print(x)
                # [0.5535528  0.20714243 0.01162981
                #  0.51577556 0.36369765 0.2609165 ]

                cat = Categorical(x)

                paddle.seed(1000) # on CPU device
                cat.sample([2,3])
                # [[0, 0, 5],
                #  [3, 4, 5]]

        """
        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 = paddle.reshape(
                self.logits, [np.prod(logits_shape[:-1]), logits_shape[-1]])
        else:
            sample_shape = shape
            logits = self.logits

        sample_index = multinomial(
            self._logits_to_probs(logits), num_samples, True)

        # multinomial sample shape is (logits.shape[:-1], num_samples), need to
        # tanspose to (num_samples, logits.shape[:-1])
        permute = list(range(sample_index.dim()))
        permute.insert(0, permute.pop(-1))
        sample_index = sample_index.transpose(permute)

        return paddle.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:
            Tensor: kl-divergence between two Categorical distributions.

        Examples:
            .. code-block:: python

                import paddle
                from paddle.distribution import Categorical

                paddle.seed(100) # on CPU device
                x = paddle.rand([6])
                print(x)
                # [0.5535528  0.20714243 0.01162981
                #  0.51577556 0.36369765 0.2609165 ]

                paddle.seed(200) # on CPU device
                y = paddle.rand([6])
                print(y)
                # [0.77663314 0.90824795 0.15685187
                #  0.04279523 0.34468332 0.7955718 ]

                cat = Categorical(x)
                cat2 = Categorical(y)

                cat.kl_divergence(cat2)
                # [0.071952]

        """
        name = self.name + '_kl_divergence'
        if not in_dygraph_mode():
            check_type(other, 'other', Categorical, 'kl_divergence')

        logits = self.logits - \
            paddle.max(self.logits, axis=-1, keepdim=True)
        other_logits = other.logits - paddle.max(
            other.logits, axis=-1, keepdim=True)
        e_logits = ops.exp(logits)
        other_e_logits = ops.exp(other_logits)
        z = paddle.sum(e_logits, axis=-1, keepdim=True)
        other_z = paddle.sum(other_e_logits, axis=-1, keepdim=True)
        prob = e_logits / z
        kl = paddle.sum(prob * (
            logits - paddle.log(z) - other_logits + paddle.log(other_z)),
                        axis=-1,
                        keepdim=True,
                        name=name)

        return kl

    def entropy(self):
        """Shannon entropy in nats.

        Returns:
            Tensor: Shannon entropy of Categorical distribution. The data type is float32.

        Examples:
            .. code-block:: python

                import paddle
                from paddle.distribution import Categorical

                paddle.seed(100) # on CPU device
                x = paddle.rand([6])
                print(x)
                # [0.5535528  0.20714243 0.01162981
                #  0.51577556 0.36369765 0.2609165 ]

                cat = Categorical(x)

                cat.entropy()
                # [1.77528]

        """
        name = self.name + '_entropy'
        logits = self.logits - \
            paddle.max(self.logits, axis=-1, keepdim=True)
        e_logits = ops.exp(logits)
        z = paddle.sum(e_logits, axis=-1, keepdim=True)
        prob = e_logits / z

        neg_entropy = paddle.sum(prob * (logits - paddle.log(z)), axis=-1)
        entropy = paddle.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

                paddle.seed(100) # on CPU device
                x = paddle.rand([6])
                print(x)
                # [0.5535528  0.20714243 0.01162981
                #  0.51577556 0.36369765 0.2609165 ]

                cat = Categorical(x)

                value = paddle.to_tensor([2,1,3])
                cat.probs(value)
                # [0.00608027 0.108298 0.269656]

        """
        name = self.name + '_probs'

        dist_sum = paddle.sum(self.logits, axis=-1, keepdim=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 = paddle.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 = paddle.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 = paddle.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 = paddle.unsqueeze(
                arange(
                    num_dist, dtype=index_value.dtype), axis=-1)
            index_prefix = nn.expand(index_prefix, [1, num_value_in_one_dist])
            index_prefix = paddle.unsqueeze(index_prefix, axis=-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 paddle.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

                paddle.seed(100) # on CPU device
                x = paddle.rand([6])
                print(x)
                # [0.5535528  0.20714243 0.01162981
                #  0.51577556 0.36369765 0.2609165 ]

                cat = Categorical(x)

                value = paddle.to_tensor([2,1,3])
                cat.log_prob(value)
                # [-5.10271 -2.22287 -1.31061]

        """
        name = self.name + '_log_prob'

        return paddle.log(self.probs(value), name=name)