# Copyright 2020 Huawei Technologies Co., Ltd
#
# 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
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# ============================================================================
"""Categorical Distribution"""
import numpy as np
from mindspore import context
from mindspore.common import Tensor
from mindspore.ops import operations as P
from mindspore.ops import functional as F
from mindspore.ops import composite as C
from mindspore.ops.functional import stop_gradient
from mindspore.ops.operations import _inner_ops as inner
from mindspore import _checkparam as Validator
import mindspore.ops as ops
import mindspore.nn as nn
from mindspore.common import dtype as mstype
from .distribution import Distribution
from ._utils.utils import check_prob, check_sum_equal_one, check_rank,\
check_distribution_name
from ._utils.custom_ops import exp_generic, log_generic, broadcast_to, log_generic_with_check
[docs]class Categorical(Distribution):
r"""
Categorical distribution.
A Categorical Distribution is a discrete distribution with the range :math:`\{1, 2, ..., k\}`
and the probability mass function as :math:`P(X = i) = p_i, i = 1, ..., k`.
Args:
probs (Tensor, list, numpy.ndarray): Event probabilities. Default: ``None`` .
seed (int): The global seed is used in sampling. Global seed is used if it is None. Default: ``None`` .
dtype (mindspore.dtype): The type of the event samples. Default: ``mstype.int32`` .
name (str): The name of the distribution. Default: ``Categorical`` .
Note:
`probs` must have rank at least 1, values are proper probabilities and sum to 1.
Raises:
ValueError: When the sum of all elements in `probs` is not 1.
Supported Platforms:
``Ascend`` ``GPU``
Examples:
>>> import mindspore
>>> import mindspore.nn as nn
>>> import mindspore.nn.probability.distribution as msd
>>> from mindspore import Tensor
>>> # To initialize a Categorical distribution of probs [0.5, 0.5]
>>> ca1 = msd.Categorical(probs=[0.2, 0.8], dtype=mindspore.int32)
>>> # A Categorical distribution can be initialized without arguments.
>>> # In this case, `probs` must be passed in through arguments during function calls.
>>> ca2 = msd.Categorical(dtype=mindspore.int32)
>>> # Here are some tensors used below for testing
>>> value = Tensor([1, 0], dtype=mindspore.int32)
>>> probs_a = Tensor([0.5, 0.5], dtype=mindspore.float32)
>>> probs_b = Tensor([0.35, 0.65], dtype=mindspore.float32)
>>> # Private interfaces of probability functions corresponding to public interfaces, including
>>> # `prob`, `log_prob`, `cdf`, `log_cdf`, `survival_function`, and `log_survival`, are the same as follows.
>>> # Args:
>>> # value (Tensor): the value to be evaluated.
>>> # probs (Tensor): event probabilities. Default: self.probs.
>>> # Examples of `prob`.
>>> # Similar calls can be made to other probability functions
>>> # by replacing `prob` by the name of the function.
>>> ans = ca1.prob(value)
>>> print(ans.shape)
(2,)
>>> # Evaluate `prob` with respect to distribution b.
>>> ans = ca1.prob(value, probs_b)
>>> print(ans.shape)
(2,)
>>> # `probs` must be passed in during function calls.
>>> ans = ca2.prob(value, probs_a)
>>> print(ans.shape)
(2,)
>>> # Functions `mean`, `sd`, `var`, and `entropy` have the same arguments.
>>> # Args:
>>> # probs (Tensor): event probabilities. Default: self.probs.
>>> # Examples of `mean`. `sd`, `var`, and `entropy` are similar.
>>> ans = ca1.mean() # return 0.8
>>> print(ans.shape)
(1,)
>>> ans = ca1.mean(probs_b)
>>> print(ans.shape)
(1,)
>>> # `probs` must be passed in during function calls.
>>> ans = ca2.mean(probs_a)
>>> print(ans.shape)
(1,)
>>> # Interfaces of `kl_loss` and `cross_entropy` are the same as follows:
>>> # Args:
>>> # dist (str): the name of the distribution. Only 'Categorical' is supported.
>>> # probs_b (Tensor): event probabilities of distribution b.
>>> # probs (Tensor): event probabilities of distribution a. Default: self.probs.
>>> # Examples of `kl_loss`, `cross_entropy` is similar.
>>> ans = ca1.kl_loss('Categorical', probs_b)
>>> print(ans.shape)
()
>>> ans = ca1.kl_loss('Categorical', probs_b, probs_a)
>>> print(ans.shape)
()
>>> # An additional `probs` must be passed in.
>>> ans = ca2.kl_loss('Categorical', probs_b, probs_a)
>>> print(ans.shape)
()
"""
def __init__(self,
probs=None,
seed=None,
dtype=mstype.int32,
name="Categorical"):
param = dict(locals())
param['param_dict'] = {'probs': probs}
valid_dtype = mstype.uint_type + mstype.int_type + mstype.float_type
Validator.check_type_name(
"dtype", dtype, valid_dtype, type(self).__name__)
super(Categorical, self).__init__(seed, dtype, name, param)
self._probs = self._add_parameter(probs, 'probs')
if self.probs is not None:
check_rank(self.probs)
check_prob(self.probs)
check_sum_equal_one(probs)
# update is_scalar_batch and broadcast_shape
# drop one dimension
if self.probs.shape[:-1] == ():
self._is_scalar_batch = True
self._broadcast_shape = self._broadcast_shape[:-1]
self.argmax = P.ArgMaxWithValue(axis=-1)
self.broadcast = broadcast_to
self.cast = P.Cast()
self.clip_by_value = ops.clip_by_value
self.concat = P.Concat(-1)
self.cumsum = P.CumSum()
self.dtypeop = P.DType()
self.exp = exp_generic
self.expand_dim = P.ExpandDims()
self.gather = P.GatherNd()
self.greater = P.Greater()
self.issubclass = inner.IsSubClass()
self.less = P.Less()
# when the graph kernel mode is enable
# use Log directly as akg will handle the corner cases
self.log = P.Log() if context.get_context("enable_graph_kernel") else log_generic
self.log_with_check = P.Log() if context.get_context("enable_graph_kernel") else log_generic_with_check
self.log_softmax = P.LogSoftmax()
self.logicor = P.LogicalOr()
self.logicand = P.LogicalAnd()
self.multinomial = P.Multinomial(seed=self.seed)
self.reshape = P.Reshape()
self.reduce_sum = P.ReduceSum(keep_dims=True)
self.select = P.Select()
self.shape = P.Shape()
self.softmax = P.Softmax()
self.squeeze = P.Squeeze()
self.squeeze_first_axis = P.Squeeze(0)
self.squeeze_last_axis = P.Squeeze(-1)
self.square = P.Square()
self.transpose = P.Transpose()
self.index_type = mstype.int32
self.nan = np.nan
@property
def probs(self):
"""
Return the probability after casting to dtype.
Output:
Tensor, the probs of the distribution.
"""
return self._probs
def extend_repr(self):
"""Display instance object as string."""
if self.is_scalar_batch:
s = 'probs = {}'.format(self.probs)
else:
s = 'batch_shape = {}'.format(self._broadcast_shape)
return s
def _get_dist_type(self):
return "Categorical"
def _get_dist_args(self, probs=None):
if probs is not None:
self.checktensor(probs, 'probs')
else:
probs = self.probs
return (probs,)
def _mean(self, probs=None):
r"""
.. math::
E[X] = \sum_{i=0}^{num_classes-1} i*p_i
"""
probs = self._check_param_type(probs)
num_classes = self.shape(probs)[-1]
index = nn.Range(0., num_classes, 1.)()
return self.reduce_sum(index * probs, -1)
def _mode(self, probs=None):
probs = self._check_param_type(probs)
index, _ = self.argmax(probs)
mode = self.cast(index, self.dtype)
return mode
def _var(self, probs=None):
r"""
.. math::
VAR(X) = E[X^{2}] - (E[X])^{2}
"""
probs = self._check_param_type(probs)
num_classes = self.shape(probs)[-1]
index = nn.Range(0., num_classes, 1.)()
return self.reduce_sum(self.square(index) * probs, -1) -\
self.square(self.reduce_sum(index * probs, -1))
def _entropy(self, probs=None):
r"""
Evaluate entropy.
.. math::
H(X) = -\sum(logits * probs)
"""
probs = self._check_param_type(probs)
logits = self.log(probs)
return self.squeeze(P.Neg()(self.reduce_sum(logits * probs, -1)))
def _kl_loss(self, dist, probs_b, probs=None):
"""
Evaluate KL divergence between Categorical distributions.
Args:
dist (str): The type of the distributions. Should be "Categorical" in this case.
probs_b (Tensor): Event probabilities of distribution b.
probs (Tensor): Event probabilities of distribution a. Default: self.probs.
"""
check_distribution_name(dist, 'Categorical')
probs_b = self._check_value(probs_b, 'probs_b')
probs_b = self.cast(probs_b, self.parameter_type)
probs_a = self._check_param_type(probs)
if probs is None:
logits_a = self.log(probs_a)
else:
logits_a = self.log_with_check(probs_a)
logits_b = self.log_with_check(probs_b)
return self.squeeze(self.reduce_sum(
self.softmax(logits_a) * (self.log_softmax(logits_a) - (self.log_softmax(logits_b))), -1))
def _cross_entropy(self, dist, probs_b, probs=None):
"""
Evaluate cross entropy between Categorical distributions.
Args:
dist (str): The type of the distributions. Should be "Categorical" in this case.
probs_b (Tensor): Event probabilities of distribution b.
probs (Tensor): Event probabilities of distribution a. Default: self.probs.
"""
check_distribution_name(dist, 'Categorical')
return self._entropy(probs) + self._kl_loss(dist, probs_b, probs)
def _log_prob(self, value, probs=None):
r"""
Evaluate log probability.
Args:
value (Tensor): The value to be evaluated.
probs (Tensor): Event probabilities. Default: self.probs.
"""
value = self._check_value(value, 'value')
probs = self._check_param_type(probs)
logits = self.log(probs)
# find the right integer to compute index
# here we simulate casting to int but still keeping float dtype
value = self.cast(value, self.dtypeop(probs))
zeros = F.fill(self.dtypeop(value), self.shape(value), 0.0)
between_zero_neone = self.logicand(self.less(value, 0,),
self.greater(value, -1.))
value = self.select(between_zero_neone,
zeros,
P.Floor()(value))
# handle the case when value is of shape () and probs is a scalar batch
drop_dim = False
if self.shape(value) == () and self.shape(probs)[:-1] == ():
drop_dim = True
# manually add one more dimension: () -> (1,)
# drop this dimension before return
value = self.expand_dim(value, -1)
value = self.expand_dim(value, -1)
broadcast_shape_tensor = logits * value
broadcast_shape = self.shape(broadcast_shape_tensor)
num_classes = broadcast_shape[-1]
label_shape = broadcast_shape[:-1]
# broadcasting logits and value
# logit_pmf shape (num of labels, C)
logits = self.broadcast(logits, broadcast_shape_tensor)
value = self.broadcast(value, broadcast_shape_tensor)[..., :1]
# flatten value to shape (number of labels, 1)
# clip value to be in range from 0 to num_classes -1 and cast into int32
value = self.reshape(value, (-1, 1))
out_of_bound = self.squeeze_last_axis(self.logicor(
self.less(value, 0.0), self.less(num_classes-1, value)))
# deal with the case the there is only one class.
value_clipped = self.clip_by_value(value, 0.0, num_classes - 1)
value_clipped = self.cast(value_clipped, self.index_type)
# create index from 0 ... NumOfLabels
start = Tensor(0, self.index_type)
end = self.cast(self.shape(value)[0], self.index_type)
delta = Tensor(1, self.index_type)
index = self.reshape(ops.range(start, end, delta), (-1, 1))
index = self.concat((index, value_clipped))
# index into logit_pmf, fill in out_of_bound places with -inf
# reshape into label shape N
logits_pmf = self.gather(self.reshape(
logits, (-1, num_classes)), index)
nan = F.fill(self.dtypeop(logits_pmf), self.shape(logits_pmf),
self.nan)
logits_pmf = self.select(out_of_bound, nan, logits_pmf)
ans = self.reshape(logits_pmf, label_shape)
if drop_dim:
return self.squeeze(ans)
return ans
def _cdf(self, value, probs=None):
r"""
Cumulative distribution function (cdf) of Categorical distributions.
Args:
value (Tensor): The value to be evaluated.
probs (Tensor): Event probabilities. Default: self.probs.
"""
value = self._check_value(value, 'value')
probs = self._check_param_type(probs)
value = self.cast(value, self.dtypeop(probs))
zeros = F.fill(self.dtypeop(value), self.shape(value), 0.0)
between_zero_neone = self.logicand(
self.less(value, 0,), self.greater(value, -1.))
value = self.select(between_zero_neone, zeros, P.Floor()(value))
drop_dim = False
if self.shape(value) == () and self.shape(probs)[:-1] == ():
drop_dim = True
value = self.expand_dim(value, -1)
value = self.expand_dim(value, -1)
broadcast_shape_tensor = probs * value
broadcast_shape = self.shape(broadcast_shape_tensor)
num_classes = broadcast_shape[-1]
label_shape = broadcast_shape[:-1]
probs = self.broadcast(probs, broadcast_shape_tensor)
value = self.broadcast(value, broadcast_shape_tensor)[..., :1]
# flatten value to shape (number of labels, 1)
value = self.reshape(value, (-1, 1))
# drop one dimension to match cdf
# clip value to be in range from 0 to num_classes -1 and cast into int32
less_than_zero = self.squeeze_last_axis(self.less(value, 0.0))
value_clipped = self.clip_by_value(value, 0.0, num_classes - 1)
value_clipped = self.cast(value_clipped, self.index_type)
index = self.reshape(nn.Range(0, self.shape(value)[0], 1)(), (-1, 1))
index = self.concat((index, value_clipped))
# reshape probs and fill less_than_zero places with 0
probs = self.reshape(probs, (-1, num_classes))
cdf = self.gather(self.cumsum(probs, 1), index)
zeros = F.fill(self.dtypeop(cdf), self.shape(cdf), 0.0)
cdf = self.select(less_than_zero, zeros, cdf)
cdf = self.reshape(cdf, label_shape)
if drop_dim:
return self.squeeze(cdf)
return cdf
def _sample(self, shape=(), probs=None):
"""
Sampling.
Args:
shape (tuple): The shape of the sample. Default: ().
probs (Tensor): Event probabilities. Default: self.probs.
Returns:
Tensor, shape is shape(probs)[:-1] + sample_shape
"""
shape = self.checktuple(shape, 'shape')
probs = self._check_param_type(probs)
num_classes = self.shape(probs)[-1]
batch_shape = self.shape(probs)[:-1]
sample_shape = shape + batch_shape
drop_dim = False
if sample_shape == ():
drop_dim = True
sample_shape = (1,)
probs_2d = self.reshape(probs, (-1, num_classes))
sample_tensor = F.fill(self.dtype, shape, 1.0)
sample_tensor = self.reshape(sample_tensor, (-1, 1))
num_sample = self.shape(sample_tensor)[0]
samples = C.multinomial(probs_2d, num_sample, seed=self.seed)
samples = self.squeeze(self.transpose(samples, (1, 0)))
samples = self.cast(self.reshape(samples, sample_shape), self.dtype)
if drop_dim:
return self.squeeze_first_axis(samples)
samples = stop_gradient(samples)
return samples