def __init__(self, concentration, rate, validate_args=None):
base_dist = Gamma(concentration, rate)
super().__init__(
base_dist,
PowerTransform(-base_dist.rate.new_ones(())),
validate_args=validate_args,
)
def __init__(self, concentration):
if concentration.data.min() < 1:
raise NotImplementedError('concentration < 1 is not supported')
self.concentration = concentration
self._standard_gamma = Gamma(
concentration,
concentration.new([1.]).squeeze().expand_as(concentration))
# The following are Marsaglia & Tsang's variable names.
self._d = self.concentration - 1.0 / 3.0
self._c = 1.0 / torch.sqrt(9.0 * self._d)
# Compute log scale using Gamma.log_prob().
x = self._d.detach() # just an arbitrary x.
log_scale = self.propose_log_prob(x) + self.log_prob_accept(
x) - self.log_prob(x)
super(RejectionStandardGamma,
self).__init__(self.propose, self.log_prob_accept, log_scale)
def filter(self, value):
"""
Compute posteriors over the multiplier and the final state
given a sequence of observations. The posterior is a pair of
Gamma and MultivariateNormal distributions (i.e. a GammaGaussian
instance).
:param ~torch.Tensor value: A sequence of observations.
:return: A pair of posterior distributions over the mixing and the latent
state at the final time step.
:rtype: a tuple of ~pyro.distributions.Gamma and ~pyro.distributions.MultivariateNormal
"""
# Combine observation and transition factors.
logp = self._trans + self._obs.condition(value).event_pad(
left=self.hidden_dim)
# Eliminate time dimension.
logp = _sequential_gamma_gaussian_tensordot(
logp.expand(logp.batch_shape))
# Combine initial factor.
logp = gamma_gaussian_tensordot(self._init, logp, dims=self.hidden_dim)
# Posterior of the scale
gamma_dist = logp.event_logsumexp()
scale_post = Gamma(gamma_dist.concentration,
gamma_dist.rate,
validate_args=self._validate_args)
# Conditional of last state on unit scale
scale_tril = logp.precision.cholesky()
loc = logp.info_vec.unsqueeze(-1).cholesky_solve(scale_tril).squeeze(
-1)
mvn = MultivariateNormal(loc,
scale_tril=scale_tril,
validate_args=self._validate_args)
return scale_post, mvn
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)
def __init__(self, concentration1, concentration0, validate_args=None):
super(NaiveBeta, self).__init__(concentration1,
concentration0,
validate_args=validate_args)
alpha_beta = torch.stack([concentration1, concentration0], -1)
self._gamma = Gamma(alpha_beta, torch.ones_like(alpha_beta))
def __init__(self, concentration, validate_args=None):
super(NaiveDirichlet, self).__init__(concentration)
self._gamma = Gamma(concentration,
torch.ones_like(concentration),
validate_args=validate_args)
def __init__(self, concentration, rate, validate_args=None):
base_dist = Gamma(concentration, rate)
super(InverseGamma, self).__init__(base_dist, PowerTransform(-1.0), validate_args=validate_args)
def __init__(self, concentration):
super(NaiveDirichlet, self).__init__(concentration)
self._gamma = Gamma(concentration, torch.ones_like(concentration))