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import torch |
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from torch import nan, Tensor |
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from torch.distributions import constraints |
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from torch.distributions.distribution import Distribution |
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from torch.distributions.utils import lazy_property, logits_to_probs, probs_to_logits |
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__all__ = ["Categorical"] |
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class Categorical(Distribution): |
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r""" |
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Creates a categorical distribution parameterized by either :attr:`probs` or |
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:attr:`logits` (but not both). |
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.. note:: |
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It is equivalent to the distribution that :func:`torch.multinomial` |
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samples from. |
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Samples are integers from :math:`\{0, \ldots, K-1\}` where `K` is ``probs.size(-1)``. |
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If `probs` is 1-dimensional with length-`K`, each element is the relative probability |
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of sampling the class at that index. |
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If `probs` is N-dimensional, the first N-1 dimensions are treated as a batch of |
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relative probability vectors. |
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.. note:: The `probs` argument must be non-negative, finite and have a non-zero sum, |
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and it will be normalized to sum to 1 along the last dimension. :attr:`probs` |
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will return this normalized value. |
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The `logits` argument will be interpreted as unnormalized log probabilities |
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and can therefore be any real number. It will likewise be normalized so that |
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the resulting probabilities sum to 1 along the last dimension. :attr:`logits` |
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will return this normalized value. |
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See also: :func:`torch.multinomial` |
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Example:: |
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>>> # xdoctest: +IGNORE_WANT("non-deterministic") |
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>>> m = Categorical(torch.tensor([ 0.25, 0.25, 0.25, 0.25 ])) |
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>>> m.sample() # equal probability of 0, 1, 2, 3 |
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tensor(3) |
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Args: |
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probs (Tensor): event probabilities |
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logits (Tensor): event log probabilities (unnormalized) |
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""" |
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arg_constraints = {"probs": constraints.simplex, "logits": constraints.real_vector} |
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has_enumerate_support = True |
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def __init__(self, probs=None, logits=None, validate_args=None): |
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if (probs is None) == (logits is None): |
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raise ValueError( |
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"Either `probs` or `logits` must be specified, but not both." |
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) |
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if probs is not None: |
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if probs.dim() < 1: |
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raise ValueError("`probs` parameter must be at least one-dimensional.") |
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self.probs = probs / probs.sum(-1, keepdim=True) |
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else: |
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if logits.dim() < 1: |
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raise ValueError("`logits` parameter must be at least one-dimensional.") |
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self.logits = logits - logits.logsumexp(dim=-1, keepdim=True) |
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self._param = self.probs if probs is not None else self.logits |
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self._num_events = self._param.size()[-1] |
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batch_shape = ( |
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self._param.size()[:-1] if self._param.ndimension() > 1 else torch.Size() |
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) |
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super().__init__(batch_shape, validate_args=validate_args) |
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def expand(self, batch_shape, _instance=None): |
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new = self._get_checked_instance(Categorical, _instance) |
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batch_shape = torch.Size(batch_shape) |
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param_shape = batch_shape + torch.Size((self._num_events,)) |
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if "probs" in self.__dict__: |
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new.probs = self.probs.expand(param_shape) |
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new._param = new.probs |
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if "logits" in self.__dict__: |
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new.logits = self.logits.expand(param_shape) |
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new._param = new.logits |
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new._num_events = self._num_events |
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super(Categorical, new).__init__(batch_shape, validate_args=False) |
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new._validate_args = self._validate_args |
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return new |
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def _new(self, *args, **kwargs): |
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return self._param.new(*args, **kwargs) |
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@constraints.dependent_property(is_discrete=True, event_dim=0) |
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def support(self): |
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return constraints.integer_interval(0, self._num_events - 1) |
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@lazy_property |
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def logits(self) -> Tensor: |
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return probs_to_logits(self.probs) |
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@lazy_property |
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def probs(self) -> Tensor: |
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return logits_to_probs(self.logits) |
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@property |
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def param_shape(self) -> torch.Size: |
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return self._param.size() |
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@property |
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def mean(self) -> Tensor: |
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return torch.full( |
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self._extended_shape(), |
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nan, |
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dtype=self.probs.dtype, |
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device=self.probs.device, |
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) |
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@property |
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def mode(self) -> Tensor: |
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return self.probs.argmax(dim=-1) |
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@property |
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def variance(self) -> Tensor: |
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return torch.full( |
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self._extended_shape(), |
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nan, |
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dtype=self.probs.dtype, |
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device=self.probs.device, |
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) |
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def sample(self, sample_shape=torch.Size()): |
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if not isinstance(sample_shape, torch.Size): |
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sample_shape = torch.Size(sample_shape) |
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probs_2d = self.probs.reshape(-1, self._num_events) |
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samples_2d = torch.multinomial(probs_2d, sample_shape.numel(), True).T |
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return samples_2d.reshape(self._extended_shape(sample_shape)) |
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def log_prob(self, value): |
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if self._validate_args: |
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self._validate_sample(value) |
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value = value.long().unsqueeze(-1) |
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value, log_pmf = torch.broadcast_tensors(value, self.logits) |
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value = value[..., :1] |
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return log_pmf.gather(-1, value).squeeze(-1) |
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def entropy(self): |
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min_real = torch.finfo(self.logits.dtype).min |
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logits = torch.clamp(self.logits, min=min_real) |
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p_log_p = logits * self.probs |
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return -p_log_p.sum(-1) |
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def enumerate_support(self, expand=True): |
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num_events = self._num_events |
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values = torch.arange(num_events, dtype=torch.long, device=self._param.device) |
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values = values.view((-1,) + (1,) * len(self._batch_shape)) |
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if expand: |
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values = values.expand((-1,) + self._batch_shape) |
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return values |
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