Source code for mindspore.nn.probability.distribution.gumbel

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"""Gumbel Distribution"""
import numpy as np
from mindspore.ops import operations as P
from mindspore._checkparam import Validator
from mindspore.common import dtype as mstype
import mindspore.nn as nn
import mindspore.nn.probability.bijector as msb
import mindspore.nn.probability.distribution as msd
from .transformed_distribution import TransformedDistribution
from ._utils.utils import check_distribution_name
from ._utils.custom_ops import exp_generic, log_generic


[docs]class Gumbel(TransformedDistribution): r""" Gumbel distribution. A Gumbel distributio is a continuous distribution with the range :math:`[0, 1]` and the probability density function: .. math:: f(x, a, b) = 1 / b \exp(\exp(-(x - a) / b) - x), where a and b are loc and scale parameter respectively. Args: loc (int, float, list, numpy.ndarray, Tensor): The location of Gumbel distribution. scale (int, float, list, numpy.ndarray, Tensor): The scale of Gumbel distribution. seed (int): the seed used in sampling. The global seed is used if it is None. Default: 0. dtype (mindspore.dtype): type of the distribution. Default: mstype.float32. name (str): the name of the distribution. Default: 'Gumbel'. Note: `scale` must be greater than zero. `dist_spec_args` are `loc` and `scale`. `dtype` must be a float type because Gumbel distributions are continuous. Raises: ValueError: When scale <= 0. TypeError: When the input `dtype` is not a subclass of float. Supported Platforms: ``Ascend`` ``GPU`` Examples: >>> import mindspore >>> import numpy as np >>> import mindspore.nn.probability.distribution as msd >>> import mindspore.nn as nn >>> from mindspore import Tensor >>> class Prob(nn.Cell): ... def __init__(self): ... super(Prob, self).__init__() ... self.gum = msd.Gumbel(np.array([0.0]), np.array([[1.0], [2.0]]), dtype=mindspore.float32) ... ... def construct(self, x_): ... return self.gum.prob(x_) >>> value = np.array([1.0, 2.0]).astype(np.float32) >>> pdf = Prob() >>> output = pdf(Tensor(value, dtype=mindspore.float32)) """ def __init__(self, loc, scale, seed=0, dtype=mstype.float32, name="Gumbel"): """ Constructor of Gumbel distribution. """ valid_dtype = mstype.float_type Validator.check_type_name( "dtype", dtype, valid_dtype, type(self).__name__) gumbel_cdf = msb.GumbelCDF(loc, scale) super(Gumbel, self).__init__( distribution=msd.Uniform(0.0, 1.0, dtype=dtype), bijector=msb.Invert(gumbel_cdf), seed=seed, name=name) # overwrite default_parameters and parameter_names self._reset_parameters() self._loc = self._add_parameter(loc, 'loc') self._scale = self._add_parameter(scale, 'scale') self._gumbel_bijector = gumbel_cdf # ops needed for the class self.cast = P.Cast() self.const = P.ScalarToTensor() self.exp = exp_generic self.expm1 = P.Expm1() self.fill = P.Fill() self.lgamma = nn.LGamma() self.log = log_generic self.shape = P.Shape() self.squeeze = P.Squeeze(0) self.sqrt = P.Sqrt() @property def loc(self): """ Return the location of the distribution after casting to dtype. Output: Tensor, the loc parameter of the distribution. """ return self._loc @property def scale(self): """ Return the scale of the distribution after casting to dtype. Output: Tensor, the scale parameter of the distribution. """ return self._scale def extend_repr(self): """Display instance object as string.""" if self.is_scalar_batch: str_info = 'loc = {}, scale = {}'.format(self._loc, self._scale) else: str_info = 'batch_shape = {}'.format(self._broadcast_shape) return str_info def _get_dist_type(self): return "Gumbel" def _get_dist_args(self, loc=None, scale=None): if scale is None: scale = self.scale else: self.checktensor(scale, 'scale') if loc is None: loc = self.loc else: self.checktensor(loc, 'loc') return loc, scale def _mean(self): r""" The mean of the distribution. .. math:: MEAN(X) = loc + scale * Euler-Mascheroni_constant """ return self.loc + self.scale * np.euler_gamma def _mode(self): """ The mode of the distribution. """ return self.loc * self.fill(self.parameter_type, self.shape(self.scale), 1.0) def _sd(self): r""" The standard deviation of the distribution. .. math:: STD(X) = \frac{\pi}{\sqrt(6)} * scale """ scale = self.scale * \ self.fill(self.parameter_type, self.broadcast_shape, 1.0) return scale * np.pi / self.sqrt(self.const(6., mstype.float32)) def _entropy(self): r""" Evaluate entropy. .. math:: H(X) = 1. + \log(scale) + Euler-Mascheroni_constant """ scale = self.scale * \ self.fill(self.parameter_type, self.broadcast_shape, 1.0) return 1. + self.log(scale) + np.euler_gamma def _log_prob(self, value): r""" .. math:: log_pdf(X) = -(z + \exp(-z)) - \log(scale) where z = \frac{x - loc}{scale} """ value = self._check_value(value, 'value') value = self.cast(value, self.dtype) z = (value - self.loc) / self.scale return -(z + self.exp(-z)) - self.log(self.scale) def _cdf(self, value): r""" .. math:: cdf_pdf(X) = \exp(-\exp(-\frac{x - loc}{scale}) """ value = self._check_value(value, 'value') value = self.cast(value, self.dtype) return self._gumbel_bijector("forward", value) def _cross_entropy(self, dist, loc_b, scale_b): r""" Evaluate cross entropy between Gumbel distributions. Args: dist (str): The type of the distributions. Should be "Gumbel" in this case. loc_b (Tensor): The loc of distribution b. scale_b (Tensor): The scale of distribution b. """ check_distribution_name(dist, 'Gumbel') return self._entropy() + self._kl_loss(dist, loc_b, scale_b) def _kl_loss(self, dist, loc_b, scale_b): r""" Evaluate Gumbel-Gumbel kl divergence, i.e. KL(a||b). Args: dist (str): The type of the distributions. Should be "Gumbel" in this case. loc_b (Tensor): The loc of distribution b. scale_b (Tensor): The scale of distribution b. .. math:: KL(a||b) = \log(scale_b / scale_a) + Euler-Mascheroni_constant * (scale_a / scale_b - 1.) + \exp(\frac{(loc_b - loc_a)}{scale_b}) * \Gamma(scale_a / scale_b + 1.) - 1. """ check_distribution_name(dist, 'Gumbel') loc_b = self._check_value(loc_b, 'loc_b') scale_b = self._check_value(scale_b, 'scale_b') loc_b = self.cast(loc_b, self.parameter_type) scale_b = self.cast(scale_b, self.parameter_type) return self.log(scale_b / self.scale) +\ np.euler_gamma * (self.scale / scale_b - 1.) + (self.loc - loc_b) / scale_b +\ self.expm1((loc_b - self.loc) / scale_b + self.lgamma(self.scale / scale_b + 1.)) def _sample(self, shape=()): shape = self.checktuple(shape, 'shape') origin_shape = shape + self._broadcast_shape if origin_shape == (): sample_shape = (1,) else: sample_shape = origin_shape org_sample = self.distribution("sample", sample_shape) org_sample = self.cast(org_sample, self.dtype) value = self.bijector("forward", org_sample) if origin_shape == (): value = self.squeeze(value) return value