class RejectionStandardGamma(Rejector):
"""
Naive Marsaglia & Tsang rejection sampler for standard Gamma distibution.
This assumes `concentration >= 1` and does not boost `concentration` or augment shape.
"""
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_tensor([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 propose(self, sample_shape=torch.Size()):
# Marsaglia & Tsang's x == Naesseth's epsilon
x = self.concentration.new_empty(sample_shape +
self.concentration.shape).normal_()
y = 1.0 + self._c * x
v = y * y * y
return (self._d * v).clamp_(1e-30, 1e30)
def propose_log_prob(self, value):
v = value / self._d
result = -self._d.log()
y = v.pow(1 / 3)
result -= torch.log(3 * y**2)
x = (y - 1) / self._c
result -= self._c.log()
result += Normal(torch.zeros_like(self.concentration),
torch.ones_like(self.concentration)).log_prob(x)
return result
def log_prob_accept(self, value):
v = value / self._d
y = torch.pow(v, 1.0 / 3.0)
x = (y - 1.0) / self._c
log_prob_accept = 0.5 * x * x + self._d * (1.0 - v + torch.log(v))
log_prob_accept[y <= 0] = -float('inf')
return log_prob_accept
def log_prob(self, x):
return self._standard_gamma.log_prob(x)
class RejectionStandardGamma(Rejector):
"""
Naive Marsaglia & Tsang rejection sampler for standard Gamma distibution.
This assumes `concentration >= 1` and does not boost `concentration` or augment shape.
"""
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_tensor([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 propose(self, sample_shape=torch.Size()):
# Marsaglia & Tsang's x == Naesseth's epsilon
x = self.concentration.new_empty(sample_shape + self.concentration.shape).normal_()
y = 1.0 + self._c * x
v = y * y * y
return (self._d * v).clamp_(1e-30, 1e30)
def propose_log_prob(self, value):
v = value / self._d
result = -self._d.log()
y = v.pow(1 / 3)
result -= torch.log(3 * y ** 2)
x = (y - 1) / self._c
result -= self._c.log()
result += Normal(torch.zeros_like(self.concentration), torch.ones_like(self.concentration)).log_prob(x)
return result
def log_prob_accept(self, value):
v = value / self._d
y = torch.pow(v, 1.0 / 3.0)
x = (y - 1.0) / self._c
log_prob_accept = 0.5 * x * x + self._d * (1.0 - v + torch.log(v))
log_prob_accept[y <= 0] = -float('inf')
return log_prob_accept
def log_prob(self, x):
return self._standard_gamma.log_prob(x)
class RejectionStandardGamma(Rejector):
"""
Naive Marsaglia & Tsang rejection sampler for standard Gamma distibution.
This assumes `concentration >= 1` and does not boost `concentration` or augment shape.
"""
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([1.0]).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().__init__(
self.propose,
self.log_prob_accept,
log_scale,
batch_shape=concentration.shape,
event_shape=(),
)
def expand(self, batch_shape, _instance=None):
new = self._get_checked_instance(RejectionStandardGamma, _instance)
batch_shape = torch.Size(batch_shape)
new.concentration = self.concentration.expand(batch_shape)
new._standard_gamma = self._standard_gamma.expand(batch_shape)
new._d = self._d.expand(batch_shape)
new._c = self._c.expand(batch_shape)
# Compute log scale using Gamma.log_prob().
x = new._d.detach() # just an arbitrary x.
log_scale = new.propose_log_prob(x) + new.log_prob_accept(
x) - new.log_prob(x)
super(RejectionStandardGamma, new).__init__(
new.propose,
new.log_prob_accept,
log_scale,
batch_shape=batch_shape,
event_shape=(),
)
new._validate_args = self._validate_args
return new
@weakmethod
def propose(self, sample_shape=torch.Size()):
# Marsaglia & Tsang's x == Naesseth's epsilon`
x = torch.randn(
sample_shape + self.concentration.shape,
dtype=self.concentration.dtype,
device=self.concentration.device,
)
y = 1.0 + self._c * x
v = y * y * y
return (self._d * v).clamp_(1e-30, 1e30)
def propose_log_prob(self, value):
v = value / self._d
result = -self._d.log()
y = v.pow(1 / 3)
result -= torch.log(3 * y**2)
x = (y - 1) / self._c
result -= self._c.log()
result += Normal(torch.zeros_like(self.concentration),
torch.ones_like(self.concentration)).log_prob(x)
return result
@weakmethod
def log_prob_accept(self, value):
v = value / self._d
y = torch.pow(v, 1.0 / 3.0)
x = (y - 1.0) / self._c
log_prob_accept = 0.5 * x * x + self._d * (1.0 - v + torch.log(v))
log_prob_accept[y <= 0] = -float("inf")
return log_prob_accept
def log_prob(self, x):
return self._standard_gamma.log_prob(x)