class Multinomial(Distribution):
r"""
Creates a Multinomial distribution parameterized by :attr:`total_count` and
either :attr:`probs` or :attr:`logits` (but not both). The innermost dimension of
:attr:`probs` indexes over categories. All other dimensions index over batches.
Note that :attr:`total_count` need not be specified if only :meth:`log_prob` is
called (see example below)
.. note:: The `probs` argument must be non-negative, finite and have a non-zero sum,
and it will be normalized to sum to 1 along the last dimension. :attr:`probs`
will return this normalized value.
The `logits` argument will be interpreted as unnormalized log probabilities
and can therefore be any real number. It will likewise be normalized so that
the resulting probabilities sum to 1 along the last dimension. :attr:`logits`
will return this normalized value.
- :meth:`sample` requires a single shared `total_count` for all
parameters and samples.
- :meth:`log_prob` allows different `total_count` for each parameter and
sample.
Example::
>>> m = Multinomial(100, torch.tensor([ 1., 1., 1., 1.]))
>>> x = m.sample() # equal probability of 0, 1, 2, 3
tensor([ 21., 24., 30., 25.])
>>> Multinomial(probs=torch.tensor([1., 1., 1., 1.])).log_prob(x)
tensor([-4.1338])
Args:
total_count (int): number of trials
probs (Tensor): event probabilities
logits (Tensor): event log probabilities (unnormalized)
"""
arg_constraints = {
'probs': constraints.simplex,
'logits': constraints.real_vector
}
total_count: int
@property
def mean(self):
return self.probs * self.total_count
@property
def variance(self):
return self.total_count * self.probs * (1 - self.probs)
def __init__(self,
total_count=1,
probs=None,
logits=None,
validate_args=None):
if not isinstance(total_count, int):
raise NotImplementedError(
'inhomogeneous total_count is not supported')
self.total_count = total_count
self._categorical = Categorical(probs=probs, logits=logits)
self._binomial = Binomial(total_count=total_count, probs=self.probs)
batch_shape = self._categorical.batch_shape
event_shape = self._categorical.param_shape[-1:]
super(Multinomial, self).__init__(batch_shape,
event_shape,
validate_args=validate_args)
def expand(self, batch_shape, _instance=None):
new = self._get_checked_instance(Multinomial, _instance)
batch_shape = torch.Size(batch_shape)
new.total_count = self.total_count
new._categorical = self._categorical.expand(batch_shape)
super(Multinomial, new).__init__(batch_shape,
self.event_shape,
validate_args=False)
new._validate_args = self._validate_args
return new
def _new(self, *args, **kwargs):
return self._categorical._new(*args, **kwargs)
@constraints.dependent_property(is_discrete=True, event_dim=1)
def support(self):
return constraints.multinomial(self.total_count)
@property
def logits(self):
return self._categorical.logits
@property
def probs(self):
return self._categorical.probs
@property
def param_shape(self):
return self._categorical.param_shape
def sample(self, sample_shape=torch.Size()):
sample_shape = torch.Size(sample_shape)
samples = self._categorical.sample(
torch.Size((self.total_count, )) + sample_shape)
# samples.shape is (total_count, sample_shape, batch_shape), need to change it to
# (sample_shape, batch_shape, total_count)
shifted_idx = list(range(samples.dim()))
shifted_idx.append(shifted_idx.pop(0))
samples = samples.permute(*shifted_idx)
counts = samples.new(self._extended_shape(sample_shape)).zero_()
counts.scatter_add_(-1, samples, torch.ones_like(samples))
return counts.type_as(self.probs)
def entropy(self):
n = torch.tensor(self.total_count)
cat_entropy = self._categorical.entropy()
term1 = n * cat_entropy - torch.lgamma(n + 1)
support = self._binomial.enumerate_support(expand=False)[1:]
binomial_probs = torch.exp(self._binomial.log_prob(support))
weights = torch.lgamma(support + 1)
term2 = (binomial_probs * weights).sum([0, -1])
return term1 + term2
def log_prob(self, value):
if self._validate_args:
self._validate_sample(value)
logits, value = broadcast_all(self.logits, value)
logits = logits.clone(memory_format=torch.contiguous_format)
log_factorial_n = torch.lgamma(value.sum(-1) + 1)
log_factorial_xs = torch.lgamma(value + 1).sum(-1)
logits[(value == 0) & (logits == -inf)] = 0
log_powers = (logits * value).sum(-1)
return log_factorial_n - log_factorial_xs + log_powers
def p_infected(self, n, p):
binom_dist = Binomial(n, p)
# returns 1 - p(0 transmissions to susceptible | 'n' nearby infected, 'p' prob. of transmission)
p0 = binom_dist.log_prob(torch.tensor(0.))
out = torch.log(1 - torch.exp(p0))
return out