# 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
# limitations under the License.
# ============================================================================
"""basic"""
from mindspore import context
from mindspore.ops import operations as P
from mindspore.ops import functional as F
from mindspore.nn.cell import Cell
from mindspore.ops.primitive import constexpr
from mindspore.ops.operations import _inner_ops as inner
from mindspore import _checkparam as validator
from ._utils.utils import raise_none_error, cast_to_tensor, set_param_type, cast_type_for_device,\
raise_not_implemented_util
from ._utils.utils import CheckTuple, CheckTensor
from ._utils.custom_ops import broadcast_to, exp_generic, log_generic
[docs]class Distribution(Cell):
"""
Base class for all mathematical distributions.
Args:
seed (int): The seed is used in sampling. 0 is used if it is None.
dtype (mindspore.dtype): The type of the event samples.
name (str): The name of the distribution.
param (dict): The parameters used to initialize the distribution.
Note:
Derived class must override operations such as `_mean`, `_prob`,
and `_log_prob`. Required arguments, such as `value` for `_prob`,
must be passed in through `args` or `kwargs`. `dist_spec_args` which specifies
a new distribution are optional.
`dist_spec_args` is unique for each type of distribution. For example, `mean` and `sd`
are the `dist_spec_args` for a Normal distribution, while `rate` is the `dist_spec_args`
for an Exponential distribution.
For all functions, passing in `dist_spec_args`, is optional.
Function calls with the additional `dist_spec_args` passed in will evaluate the result with
a new distribution specified by the `dist_spec_args`. However, it will not change the original distribution.
Supported Platforms:
``Ascend`` ``GPU``
"""
def __init__(self,
seed,
dtype,
name,
param):
"""
Constructor of distribution class.
"""
super(Distribution, self).__init__()
if seed is None:
seed = 0
validator.check_value_type('name', name, [str], type(self).__name__)
validator.check_non_negative_int(seed, 'seed', name)
self._name = name
self._seed = seed
self._dtype = cast_type_for_device(dtype)
self._parameters = {}
self.default_parameters = []
self.parameter_names = []
# parsing parameters
for k in param.keys():
if not(k == 'self' or k.startswith('_')):
self._parameters[k] = param[k]
# if not a transformed distribution, set the following attribute
if 'distribution' not in self.parameters.keys():
self.parameter_type = set_param_type(
self.parameters.get('param_dict', {}), dtype)
self._batch_shape = self._calc_batch_shape()
self._is_scalar_batch = self._check_is_scalar_batch()
self._broadcast_shape = self._batch_shape
# set the function to call according to the derived class's attributes
self._set_prob()
self._set_log_prob()
self._set_sd()
self._set_var()
self._set_cdf()
self._set_survival()
self._set_log_cdf()
self._set_log_survival()
self._set_cross_entropy()
self.context_mode = context.get_context('mode')
self.device_target = context.get_context('device_target')
self.checktuple = CheckTuple()
@constexpr(check=False)
def _check_tensor(x, name):
CheckTensor()(x, name)
return x
# we use constexpr to force CheckTensor to run only once in pynative mode
self.checktensor = CheckTensor() if self.context_mode == 0 else _check_tensor
self.broadcast = broadcast_to
# ops needed for the base class
self.cast_base = P.Cast()
self.dtype_base = P.DType()
self.sametypeshape_base = inner.SameTypeShape()
self.sq_base = P.Square()
self.sqrt_base = P.Sqrt()
self.shape_base = P.Shape()
if self.device_target != "Ascend":
self.log_base = P.Log()
self.exp_base = P.Exp()
else:
self.exp_base = exp_generic
self.log_base = log_generic
@property
def name(self):
return self._name
@property
def dtype(self):
return self._dtype
@property
def seed(self):
return self._seed
@property
def parameters(self):
return self._parameters
@property
def is_scalar_batch(self):
return self._is_scalar_batch
@property
def batch_shape(self):
return self._batch_shape
@property
def broadcast_shape(self):
return self._broadcast_shape
def _reset_parameters(self):
self.default_parameters = []
self.parameter_names = []
def _add_parameter(self, value, name):
"""
Cast `value` to a tensor and add it to `self.default_parameters`.
Add `name` into and `self.parameter_names`.
"""
# initialize the attributes if they do not exist yet
if not hasattr(self, 'default_parameters'):
self.default_parameters = []
self.parameter_names = []
# cast value to a tensor if it is not None
value_t = None if value is None else cast_to_tensor(value, self.parameter_type)
self.default_parameters.append(value_t)
self.parameter_names.append(name)
return value_t
def _check_param_type(self, *args):
"""
Check the availability and validity of default parameters and `dist_spec_args`.
`dist_spec_args` passed in must be tensors. If default parameters of the distribution
are None, the parameters must be passed in through `args`.
"""
broadcast_shape = None
broadcast_shape_tensor = None
common_dtype = None
out = []
for arg, name, default in zip(args, self.parameter_names, self.default_parameters):
# check if the argument is a Tensor
if arg is not None:
self.checktensor(arg, name)
else:
arg = default if default is not None else raise_none_error(name)
# broadcast if the number of args > 1
if broadcast_shape is None:
broadcast_shape = self.shape_base(arg)
common_dtype = self.dtype_base(arg)
broadcast_shape_tensor = F.fill(
common_dtype, broadcast_shape, 1.0)
else:
broadcast_shape = self.shape_base(arg + broadcast_shape_tensor)
broadcast_shape_tensor = F.fill(
common_dtype, broadcast_shape, 1.0)
arg = self.broadcast(arg, broadcast_shape_tensor)
# check if the arguments have the same dtype
self.sametypeshape_base(arg, broadcast_shape_tensor)
arg = self.cast_base(arg, self.parameter_type)
out.append(arg)
if len(out) == 1:
return out[0]
# broadcast all args to broadcast_shape
result = ()
for arg in out:
arg = self.broadcast(arg, broadcast_shape_tensor)
result = result + (arg,)
return result
def _check_value(self, value, name):
"""
Check availability of `value` as a Tensor.
"""
self.checktensor(value, name)
return value
def _check_is_scalar_batch(self):
"""
Check if the parameters used during initialization are scalars.
"""
param_dict = self.parameters.get('param_dict')
for value in param_dict.values():
if value is None:
continue
if not isinstance(value, (int, float)):
return False
return True
def _calc_batch_shape(self):
"""
Calculate the broadcast shape of the parameters used during initialization.
"""
broadcast_shape_tensor = None
param_dict = self.parameters.get('param_dict')
for value in param_dict.values():
if value is None:
return None
if broadcast_shape_tensor is None:
broadcast_shape_tensor = cast_to_tensor(value)
else:
value = cast_to_tensor(value)
broadcast_shape_tensor = (value + broadcast_shape_tensor)
return broadcast_shape_tensor.shape
def _set_prob(self):
"""
Set probability function based on the availability of `_prob` and `_log_likehood`.
"""
if hasattr(self, '_prob'):
self._call_prob = self._prob
elif hasattr(self, '_log_prob'):
self._call_prob = self._calc_prob_from_log_prob
else:
self._call_prob = self._raise_not_implemented_error('prob')
def _set_sd(self):
"""
Set standard deviation based on the availability of `_sd` and `_var`.
"""
if hasattr(self, '_sd'):
self._call_sd = self._sd
elif hasattr(self, '_var'):
self._call_sd = self._calc_sd_from_var
else:
self._call_sd = self._raise_not_implemented_error('sd')
def _set_var(self):
"""
Set variance based on the availability of `_sd` and `_var`.
"""
if hasattr(self, '_var'):
self._call_var = self._var
elif hasattr(self, '_sd'):
self._call_var = self._calc_var_from_sd
else:
self._call_var = self._raise_not_implemented_error('var')
def _set_log_prob(self):
"""
Set log probability based on the availability of `_prob` and `_log_prob`.
"""
if hasattr(self, '_log_prob'):
self._call_log_prob = self._log_prob
elif hasattr(self, '_prob'):
self._call_log_prob = self._calc_log_prob_from_prob
else:
self._call_log_prob = self._raise_not_implemented_error('log_prob')
def _set_cdf(self):
"""
Set cumulative distribution function (cdf) based on the availability of `_cdf` and `_log_cdf` and
`survival_functions`.
"""
if hasattr(self, '_cdf'):
self._call_cdf = self._cdf
elif hasattr(self, '_log_cdf'):
self._call_cdf = self._calc_cdf_from_log_cdf
elif hasattr(self, '_survival_function'):
self._call_cdf = self._calc_cdf_from_survival
elif hasattr(self, '_log_survival'):
self._call_cdf = self._calc_cdf_from_log_survival
else:
self._call_cdf = self._raise_not_implemented_error('cdf')
def _set_survival(self):
"""
Set survival function based on the availability of _survival function and `_log_survival`
and `_call_cdf`.
"""
if not (hasattr(self, '_survival_function') or hasattr(self, '_log_survival') or
hasattr(self, '_cdf') or hasattr(self, '_log_cdf')):
self._call_survival = self._raise_not_implemented_error(
'survival_function')
elif hasattr(self, '_survival_function'):
self._call_survival = self._survival_function
elif hasattr(self, '_log_survival'):
self._call_survival = self._calc_survival_from_log_survival
elif hasattr(self, '_call_cdf'):
self._call_survival = self._calc_survival_from_call_cdf
def _set_log_cdf(self):
"""
Set log cdf based on the availability of `_log_cdf` and `_call_cdf`.
"""
if not (hasattr(self, '_log_cdf') or hasattr(self, '_cdf') or
hasattr(self, '_survival_function') or hasattr(self, '_log_survival')):
self._call_log_cdf = self._raise_not_implemented_error('log_cdf')
elif hasattr(self, '_log_cdf'):
self._call_log_cdf = self._log_cdf
elif hasattr(self, '_call_cdf'):
self._call_log_cdf = self._calc_log_cdf_from_call_cdf
def _set_log_survival(self):
"""
Set log survival based on the availability of `_log_survival` and `_call_survival`.
"""
if not (hasattr(self, '_log_survival') or hasattr(self, '_survival_function') or
hasattr(self, '_log_cdf') or hasattr(self, '_cdf')):
self._call_log_survival = self._raise_not_implemented_error(
'log_cdf')
elif hasattr(self, '_log_survival'):
self._call_log_survival = self._log_survival
elif hasattr(self, '_call_survival'):
self._call_log_survival = self._calc_log_survival_from_call_survival
def _set_cross_entropy(self):
"""
Set log survival based on the availability of `_cross_entropy`.
"""
if hasattr(self, '_cross_entropy'):
self._call_cross_entropy = self._cross_entropy
else:
self._call_cross_entropy = self._raise_not_implemented_error(
'cross_entropy')
def _get_dist_args(self, *args, **kwargs):
return raise_not_implemented_util('get_dist_args', self.name, *args, **kwargs)
[docs] def get_dist_args(self, *args, **kwargs):
"""
Check the availability and validity of default parameters and `dist_spec_args`.
Args:
*args (list): the list of positional arguments forwarded to subclasses.
**kwargs (dict): the dictionary of keyword arguments forwarded to subclasses.
Note:
`dist_spec_args` must be passed in through list or dictionary. The order of `dist_spec_args`
should follow the initialization order of default parameters through `_add_parameter`.
If some `dist_spec_args` is None, the corresponding default parameter is returned.
Return:
list[Tensor], the list of parameters.
"""
return self._get_dist_args(*args, **kwargs)
def _get_dist_type(self):
return raise_not_implemented_util('get_dist_type', self.name)
[docs] def get_dist_type(self):
"""
Return the type of the distribution.
Return:
string, the name of distribution.
"""
return self._get_dist_type()
def _raise_not_implemented_error(self, func_name):
name = self.name
def raise_error(*args, **kwargs):
return raise_not_implemented_util(func_name, name, *args, **kwargs)
return raise_error
[docs] def log_prob(self, value, *args, **kwargs):
"""
Evaluate the log probability(pdf or pmf) at the given value.
Args:
value (Tensor): value to be evaluated.
*args (list): the list of positional arguments forwarded to subclasses.
**kwargs (dict): the dictionary of keyword arguments forwarded to subclasses.
Note:
A distribution can be optionally passed to the function by passing its `dist_spec_args` through
`args` or `kwargs`.
Return:
Tensor, the value of log probability.
"""
return self._call_log_prob(value, *args, **kwargs)
def _calc_prob_from_log_prob(self, value, *args, **kwargs):
r"""
Evaluate prob from log probability.
.. math::
probability(x) = \exp(log_likehood(x))
"""
return self.exp_base(self._log_prob(value, *args, **kwargs))
[docs] def prob(self, value, *args, **kwargs):
"""
Evaluate the probability (pdf or pmf) at given value. For a discrete distribution,
it is a probability mass function, while for a continuous distribution, it is probability density function.
Args:
value (Tensor): value to be evaluated.
*args (list): the list of positional arguments forwarded to subclasses.
**kwargs (dict): the dictionary of keyword arguments forwarded to subclasses.
Note:
A distribution can be optionally passed to the function by passing its `dist_spec_args` through
`args` or `kwargs`.
Return:
Tensor, the value of probability.
"""
return self._call_prob(value, *args, **kwargs)
def _calc_log_prob_from_prob(self, value, *args, **kwargs):
r"""
Evaluate log probability from probability.
.. math::
log_prob(x) = \log(prob(x))
"""
return self.log_base(self._prob(value, *args, **kwargs))
[docs] def cdf(self, value, *args, **kwargs):
"""
Evaluate the cumulative distribution function(cdf) at given value.
Args:
value (Tensor): value to be evaluated.
*args (list): the list of positional arguments forwarded to subclasses.
**kwargs (dict): the dictionary of keyword arguments forwarded to subclasses.
Note:
A distribution can be optionally passed to the function by passing its `dist_spec_args` through
`args` or `kwargs`.
Return:
Tensor, the cdf of the distribution.
"""
return self._call_cdf(value, *args, **kwargs)
def _calc_cdf_from_log_cdf(self, value, *args, **kwargs):
r"""
Evaluate cdf from log_cdf.
.. math::
cdf(x) = \exp(log_cdf(x))
"""
return self.exp_base(self._log_cdf(value, *args, **kwargs))
def _calc_cdf_from_survival(self, value, *args, **kwargs):
r"""
Evaluate cdf from survival function.
.. math::
cdf(x) = 1 - (survival_function(x))
"""
return 1.0 - self._survival_function(value, *args, **kwargs)
def _calc_cdf_from_log_survival(self, value, *args, **kwargs):
r"""
Evaluate cdf from log survival function.
.. math::
cdf(x) = 1 - (\exp(log_survival(x)))
"""
return 1.0 - self.exp_base(self._log_survival(value, *args, **kwargs))
[docs] def log_cdf(self, value, *args, **kwargs):
"""
Evaluate the log the cumulative distribution function(cdf) at given value.
Args:
value (Tensor): value to be evaluated.
*args (list): the list of positional arguments forwarded to subclasses.
**kwargs (dict): the dictionary of keyword arguments forwarded to subclasses.
Note:
A distribution can be optionally passed to the function by passing its `dist_spec_args` through
`args` or `kwargs`.
Return:
Tensor, the log cdf of the distribution.
"""
return self._call_log_cdf(value, *args, **kwargs)
def _calc_log_cdf_from_call_cdf(self, value, *args, **kwargs):
r"""
Evaluate log cdf from cdf.
.. math::
log_cdf(x) = \log(cdf(x))
"""
return self.log_base(self._call_cdf(value, *args, **kwargs))
[docs] def survival_function(self, value, *args, **kwargs):
"""
Evaluate the survival function at given value.
Args:
value (Tensor): value to be evaluated.
*args (list): the list of positional arguments forwarded to subclasses.
**kwargs (dict): the dictionary of keyword arguments forwarded to subclasses.
Note:
A distribution can be optionally passed to the function by passing its `dist_spec_args` through
`args` or `kwargs`.
Return:
Tensor, the survival function of the distribution.
"""
return self._call_survival(value, *args, **kwargs)
def _calc_survival_from_call_cdf(self, value, *args, **kwargs):
r"""
Evaluate survival function from cdf.
.. math::
survival_function(x) = 1 - (cdf(x))
"""
return 1.0 - self._call_cdf(value, *args, **kwargs)
def _calc_survival_from_log_survival(self, value, *args, **kwargs):
r"""
Evaluate survival function from log survival function.
.. math::
survival(x) = \exp(survival_function(x))
"""
return self.exp_base(self._log_survival(value, *args, **kwargs))
[docs] def log_survival(self, value, *args, **kwargs):
"""
Evaluate the log survival function at given value.
Args:
value (Tensor): value to be evaluated.
*args (list): the list of positional arguments forwarded to subclasses.
**kwargs (dict): the dictionary of keyword arguments forwarded to subclasses.
Note:
A distribution can be optionally passed to the function by passing its `dist_spec_args` through
`args` or `kwargs`.
Return:
Tensor, the log survival function of the distribution.
"""
return self._call_log_survival(value, *args, **kwargs)
def _calc_log_survival_from_call_survival(self, value, *args, **kwargs):
r"""
Evaluate log survival function from survival function.
.. math::
log_survival(x) = \log(survival_function(x))
"""
return self.log_base(self._call_survival(value, *args, **kwargs))
def _kl_loss(self, *args, **kwargs):
return raise_not_implemented_util('kl_loss', self.name, *args, **kwargs)
[docs] def kl_loss(self, dist, *args, **kwargs):
"""
Evaluate the KL divergence, i.e. KL(a||b).
Args:
dist (str): type of the distribution.
*args (list): the list of positional arguments forwarded to subclasses.
**kwargs (dict): the dictionary of keyword arguments forwarded to subclasses.
Note:
`dist_spec_args` of distribution b must be passed to the function through `args` or `kwargs`.
Passing in `dist_spec_args` of distribution a is optional.
Return:
Tensor, the kl loss function of the distribution.
"""
return self._kl_loss(dist, *args, **kwargs)
def _mean(self, *args, **kwargs):
return raise_not_implemented_util('mean', self.name, *args, **kwargs)
[docs] def mean(self, *args, **kwargs):
"""
Evaluate the mean.
Args:
*args (list): the list of positional arguments forwarded to subclasses.
**kwargs (dict): the dictionary of keyword arguments forwarded to subclasses.
Note:
A distribution can be optionally passed to the function by passing its *dist_spec_args* through
`args` or `kwargs`.
Return:
Tensor, the mean of the distribution.
"""
return self._mean(*args, **kwargs)
def _mode(self, *args, **kwargs):
return raise_not_implemented_util('mode', self.name, *args, **kwargs)
[docs] def mode(self, *args, **kwargs):
"""
Evaluate the mode.
Args:
*args (list): the list of positional arguments forwarded to subclasses.
**kwargs (dict): the dictionary of keyword arguments forwarded to subclasses.
Note:
A distribution can be optionally passed to the function by passing its *dist_spec_args* through
`args` or `kwargs`.
Return:
Tensor, the mode of the distribution.
"""
return self._mode(*args, **kwargs)
[docs] def sd(self, *args, **kwargs):
"""
Evaluate the standard deviation.
Args:
*args (list): the list of positional arguments forwarded to subclasses.
**kwargs (dict): the dictionary of keyword arguments forwarded to subclasses.
Note:
A distribution can be optionally passed to the function by passing its *dist_spec_args* through
`args` or `kwargs`.
Return:
Tensor, the standard deviation of the distribution.
"""
return self._call_sd(*args, **kwargs)
[docs] def var(self, *args, **kwargs):
"""
Evaluate the variance.
Args:
*args (list): the list of positional arguments forwarded to subclasses.
**kwargs (dict): the dictionary of keyword arguments forwarded to subclasses.
Note:
A distribution can be optionally passed to the function by passing its *dist_spec_args* through
`args` or `kwargs`.
Return:
Tensor, the variance of the distribution.
"""
return self._call_var(*args, **kwargs)
def _calc_sd_from_var(self, *args, **kwargs):
r"""
Evaluate log probability from probability.
.. math::
STD(x) = \sqrt(VAR(x))
"""
return self.sqrt_base(self._var(*args, **kwargs))
def _calc_var_from_sd(self, *args, **kwargs):
r"""
Evaluate log probability from probability.
.. math::
VAR(x) = STD(x) ^ 2
"""
return self.sq_base(self._sd(*args, **kwargs))
def _entropy(self, *args, **kwargs):
return raise_not_implemented_util('entropy', self.name, *args, **kwargs)
[docs] def entropy(self, *args, **kwargs):
"""
Evaluate the entropy.
Args:
*args (list): the list of positional arguments forwarded to subclasses.
**kwargs (dict): the dictionary of keyword arguments forwarded to subclasses.
Note:
A distribution can be optionally passed to the function by passing its *dist_spec_args* through
`args` or `kwargs`.
Return:
Tensor, the entropy of the distribution.
"""
return self._entropy(*args, **kwargs)
[docs] def cross_entropy(self, dist, *args, **kwargs):
"""
Evaluate the cross_entropy between distribution a and b.
Args:
dist (str): type of the distribution.
*args (list): the list of positional arguments forwarded to subclasses.
**kwargs (dict): the dictionary of keyword arguments forwarded to subclasses.
Note:
`dist_spec_args` of distribution b must be passed to the function through `args` or `kwargs`.
Passing in `dist_spec_args` of distribution a is optional.
Return:
Tensor, the cross_entropy of two distributions.
"""
return self._call_cross_entropy(dist, *args, **kwargs)
def _calc_cross_entropy(self, dist, *args, **kwargs):
r"""
Evaluate cross_entropy from entropy and kl divergence.
.. math::
H(X, Y) = H(X) + KL(X||Y)
"""
return self._entropy(*args, **kwargs) + self._kl_loss(dist, *args, **kwargs)
def _sample(self, *args, **kwargs):
return raise_not_implemented_util('sample', self.name, *args, **kwargs)
[docs] def sample(self, *args, **kwargs):
"""
Sampling function.
Args:
*args (list): the list of positional arguments forwarded to subclasses.
**kwargs (dict): the dictionary of keyword arguments forwarded to subclasses.
Note:
A distribution can be optionally passed to the function by passing its *dist_spec_args* through
`args` or `kwargs`.
Return:
Tensor, the sample generated from the distribution.
"""
return self._sample(*args, **kwargs)
[docs] def construct(self, name, *args, **kwargs):
"""
Override `construct` in Cell.
Note:
Names of supported functions include:
'prob', 'log_prob', 'cdf', 'log_cdf', 'survival_function', 'log_survival',
'var', 'sd', 'mode', 'mean', 'entropy', 'kl_loss', 'cross_entropy', 'sample',
'get_dist_args', and 'get_dist_type'.
Args:
name (str): The name of the function.
*args (list): A list of positional arguments that the function needs.
**kwargs (dict): A dictionary of keyword arguments that the function needs.
Return:
Tensor, the value of corresponding computation method.
"""
if name == 'log_prob':
return self._call_log_prob(*args, **kwargs)
if name == 'prob':
return self._call_prob(*args, **kwargs)
if name == 'cdf':
return self._call_cdf(*args, **kwargs)
if name == 'log_cdf':
return self._call_log_cdf(*args, **kwargs)
if name == 'survival_function':
return self._call_survival(*args, **kwargs)
if name == 'log_survival':
return self._call_log_survival(*args, **kwargs)
if name == 'kl_loss':
return self._kl_loss(*args, **kwargs)
if name == 'mean':
return self._mean(*args, **kwargs)
if name == 'mode':
return self._mode(*args, **kwargs)
if name == 'sd':
return self._call_sd(*args, **kwargs)
if name == 'var':
return self._call_var(*args, **kwargs)
if name == 'entropy':
return self._entropy(*args, **kwargs)
if name == 'cross_entropy':
return self._call_cross_entropy(*args, **kwargs)
if name == 'sample':
return self._sample(*args, **kwargs)
if name == 'get_dist_args':
return self._get_dist_args(*args, **kwargs)
if name == 'get_dist_type':
return self._get_dist_type()
return raise_not_implemented_util(name, self.name, *args, **kwargs)