Source code for pyro.distributions.conjugate

from __future__ import absolute_import, division, print_function

import numbers

import torch
from torch.distributions import constraints
from torch.distributions.utils import broadcast_all

from pyro.distributions.torch import Beta, Binomial, Dirichlet, Gamma, Multinomial, Poisson
from pyro.distributions.torch_distribution import TorchDistribution


def _log_beta(x, y):
    return torch.lgamma(x) + torch.lgamma(y) - torch.lgamma(x + y)


def _log_beta_1(alpha, value, is_sparse):
    if is_sparse:
        mask = (value != 0)
        value, alpha, mask = torch.broadcast_tensors(value, alpha, mask)
        result = torch.zeros_like(value)
        value = value[mask]
        alpha = alpha[mask]
        result[mask] = torch.lgamma(1 + value) + torch.lgamma(alpha) - torch.lgamma(value + alpha)
        return result
    else:
        return torch.lgamma(1 + value) + torch.lgamma(alpha) - torch.lgamma(value + alpha)


[docs]class BetaBinomial(TorchDistribution): r""" Compound distribution comprising of a beta-binomial pair. The probability of success (``probs`` for the :class:`~pyro.distributions.Binomial` distribution) is unknown and randomly drawn from a :class:`~pyro.distributions.Beta` distribution prior to a certain number of Bernoulli trials given by ``total_count``. :param float or torch.Tensor concentration1: 1st concentration parameter (alpha) for the Beta distribution. :param float or torch.Tensor concentration0: 2nd concentration parameter (beta) for the Beta distribution. :param int or torch.Tensor total_count: number of Bernoulli trials. """ arg_constraints = {'concentration1': constraints.positive, 'concentration0': constraints.positive, 'total_count': constraints.nonnegative_integer} has_enumerate_support = True support = Binomial.support def __init__(self, concentration1, concentration0, total_count=1, validate_args=None): concentration1, concentration0, total_count = broadcast_all( concentration1, concentration0, total_count) self._beta = Beta(concentration1, concentration0) self.total_count = total_count super(BetaBinomial, self).__init__(self._beta._batch_shape, validate_args=validate_args) @property def concentration1(self): return self._beta.concentration1 @property def concentration0(self): return self._beta.concentration0
[docs] def expand(self, batch_shape, _instance=None): new = self._get_checked_instance(BetaBinomial, _instance) batch_shape = torch.Size(batch_shape) new._beta = self._beta.expand(batch_shape) new.total_count = self.total_count.expand_as(new._beta.concentration0) super(BetaBinomial, new).__init__(batch_shape, validate_args=False) new._validate_args = self._validate_args return new
[docs] def sample(self, sample_shape=()): probs = self._beta.sample(sample_shape) return Binomial(self.total_count, probs).sample()
[docs] def log_prob(self, value): if self._validate_args: self._validate_sample(value) log_factorial_n = torch.lgamma(self.total_count + 1) log_factorial_k = torch.lgamma(value + 1) log_factorial_nmk = torch.lgamma(self.total_count - value + 1) return (log_factorial_n - log_factorial_k - log_factorial_nmk + _log_beta(value + self.concentration1, self.total_count - value + self.concentration0) - _log_beta(self.concentration0, self.concentration1))
@property def mean(self): return self._beta.mean * self.total_count @property def variance(self): return self._beta.variance * self.total_count * (self.concentration0 + self.concentration1 + self.total_count)
[docs] def enumerate_support(self, expand=True): total_count = int(self.total_count.max()) if not self.total_count.min() == total_count: raise NotImplementedError("Inhomogeneous total count not supported by `enumerate_support`.") values = torch.arange(1 + total_count, dtype=self.concentration1.dtype, device=self.concentration1.device) values = values.view((-1,) + (1,) * len(self._batch_shape)) if expand: values = values.expand((-1,) + self._batch_shape) return values
[docs]class DirichletMultinomial(TorchDistribution): r""" Compound distribution comprising of a dirichlet-multinomial pair. The probability of classes (``probs`` for the :class:`~pyro.distributions.Multinomial` distribution) is unknown and randomly drawn from a :class:`~pyro.distributions.Dirichlet` distribution prior to a certain number of Categorical trials given by ``total_count``. :param float or torch.Tensor concentration: concentration parameter (alpha) for the Dirichlet distribution. :param int or torch.Tensor total_count: number of Categorical trials. :param bool is_sparse: Whether to assume value is mostly zero when computing :meth:`log_prob`, which can speed up computation when data is sparse. """ arg_constraints = {'concentration': constraints.positive, 'total_count': constraints.nonnegative_integer} support = Multinomial.support def __init__(self, concentration, total_count=1, is_sparse=False, validate_args=None): if isinstance(total_count, numbers.Number): total_count = concentration.new_tensor(total_count) total_count_1 = total_count.unsqueeze(-1) concentration, total_count = torch.broadcast_tensors(concentration, total_count_1) total_count = total_count_1.squeeze(-1) self._dirichlet = Dirichlet(concentration) self.total_count = total_count self.is_sparse = is_sparse super(DirichletMultinomial, self).__init__( self._dirichlet._batch_shape, self._dirichlet.event_shape, validate_args=validate_args) @property def concentration(self): return self._dirichlet.concentration
[docs] def expand(self, batch_shape, _instance=None): new = self._get_checked_instance(DirichletMultinomial, _instance) batch_shape = torch.Size(batch_shape) new._dirichlet = self._dirichlet.expand(batch_shape) new.total_count = self.total_count.expand(batch_shape) new.is_sparse = self.is_sparse super(DirichletMultinomial, new).__init__( new._dirichlet.batch_shape, new._dirichlet.event_shape, validate_args=False) new._validate_args = self._validate_args return new
[docs] def sample(self, sample_shape=()): probs = self._dirichlet.sample(sample_shape) total_count = int(self.total_count.max()) if not self.total_count.min() == total_count: raise NotImplementedError("Inhomogeneous total count not supported by `sample`.") return Multinomial(total_count, probs).sample()
[docs] def log_prob(self, value): if self._validate_args: self._validate_sample(value) alpha = self.concentration return (_log_beta_1(alpha.sum(-1), value.sum(-1), self.is_sparse) - _log_beta_1(alpha, value, self.is_sparse).sum(-1))
@property def mean(self): return self._dirichlet.mean * self.total_count.unsqueeze(-1) @property def variance(self): n = self.total_count.unsqueeze(-1) alpha = self.concentration alpha_sum = self.concentration.sum(-1, keepdim=True) alpha_ratio = alpha / alpha_sum return n * alpha_ratio * (1 - alpha_ratio) * (n + alpha_sum) / (1 + alpha_sum)
[docs]class GammaPoisson(TorchDistribution): r""" Compound distribution comprising of a gamma-poisson pair, also referred to as a gamma-poisson mixture. The ``rate`` parameter for the :class:`~pyro.distributions.Poisson` distribution is unknown and randomly drawn from a :class:`~pyro.distributions.Gamma` distribution. .. note:: This can be treated as an alternate parametrization of the :class:`~pyro.distributions.NegativeBinomial` (``total_count``, ``probs``) distribution, with `concentration = total_count` and `rate = (1 - probs) / probs`. :param float or torch.Tensor concentration: shape parameter (alpha) of the Gamma distribution. :param float or torch.Tensor rate: rate parameter (beta) for the Gamma distribution. """ arg_constraints = {'concentration': constraints.positive, 'rate': constraints.positive} support = Poisson.support def __init__(self, concentration, rate, validate_args=None): concentration, rate = broadcast_all(concentration, rate) self._gamma = Gamma(concentration, rate) super(GammaPoisson, self).__init__(self._gamma._batch_shape, validate_args=validate_args) @property def concentration(self): return self._gamma.concentration @property def rate(self): return self._gamma.rate
[docs] def expand(self, batch_shape, _instance=None): new = self._get_checked_instance(GammaPoisson, _instance) batch_shape = torch.Size(batch_shape) new._gamma = self._gamma.expand(batch_shape) super(GammaPoisson, new).__init__(batch_shape, validate_args=False) new._validate_args = self._validate_args return new
[docs] def sample(self, sample_shape=()): rate = self._gamma.sample(sample_shape) return Poisson(rate).sample()
[docs] def log_prob(self, value): if self._validate_args: self._validate_sample(value) post_value = self.concentration + value return -_log_beta(self.concentration, value + 1) - post_value.log() + \ self.concentration * self.rate.log() - post_value * (1 + self.rate).log()
@property def mean(self): return self.concentration / self.rate @property def variance(self): return self.concentration / self.rate.pow(2) * (1 + self.rate)