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categorical.py
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categorical.py
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# categorical.py
# Contact: Jacob Schreiber <jmschreiber91@gmail.com>
import torch
from .._utils import _inplace_add
from .._utils import _cast_as_tensor
from .._utils import _cast_as_parameter
from .._utils import _update_parameter
from .._utils import _check_parameter
from .._utils import _reshape_weights
from ._distribution import Distribution
class Categorical(Distribution):
"""A categorical distribution object.
A categorical distribution models the probability of a set of distinct
values happening. It is an extension of the Bernoulli distribution to
multiple values. Sometimes it is referred to as a discrete distribution,
but this distribution does not enforce that the numeric values used for the
keys have any relationship based on their identity. Permuting the keys will
have no effect on the calculation. This distribution assumes that the
features are independent from each other.
The keys must be contiguous non-negative integers that begin at zero.
Because the probabilities are represented as a single tensor, each feature
must have values for all keys up to the maximum key of any one distribution.
Specifically, if one feature has 10 keys and a second feature has only 4,
the tensor must go out to 10 for each feature but encode probabilities of
zero for the second feature.
Parameters
----------
probs: list, numpy.ndarray, torch.tensor or None, shape=(k, d), optional
Probabilities for each key for each feature, where k is the largest
number of keys across all features. Default is None
inertia: float, (0, 1), optional
Indicates the proportion of the update to apply to the parameters
during training. When the inertia is 0.0, the update is applied in
its entirety and the previous parameters are ignored. When the
inertia is 1.0, the update is entirely ignored and the previous
parameters are kept, equivalently to if the parameters were frozen.
frozen: bool, optional
Whether all the parameters associated with this distribution are frozen.
If you want to freeze individual pameters, or individual values in those
parameters, you must modify the `frozen` attribute of the tensor or
parameter directly. Default is False.
check_data: bool, optional
Whether to check properties of the data and potentially recast it to
torch.tensors. This does not prevent checking of parameters but can
slightly speed up computation when you know that your inputs are valid.
Setting this to False is also necessary for compiling.
"""
def __init__(self, probs=None, n_categories=None, pseudocount=0.0,
inertia=0.0, frozen=False, check_data=True):
super().__init__(inertia=inertia, frozen=frozen, check_data=check_data)
self.name = "Categorical"
self.probs = _check_parameter(_cast_as_parameter(probs), "probs",
min_value=0, max_value=1, ndim=2)
self.pseudocount = pseudocount
self._initialized = probs is not None
self.d = self.probs.shape[-2] if self._initialized else None
if n_categories is not None:
self.n_keys = n_categories
else:
self.n_keys = self.probs.shape[-1] if self._initialized else None
self._reset_cache()
def _initialize(self, d, n_keys):
"""Initialize the probability distribution.
This method is meant to only be called internally. It initializes the
parameters of the distribution and stores its dimensionality. For more
complex methods, this function will do more.
Parameters
----------
d: int
The dimensionality the distribution is being initialized to.
n_keys: int
The number of keys the distribution is being initialized with.
"""
self.probs = _cast_as_parameter(torch.zeros(d, n_keys,
dtype=self.dtype, device=self.device))
self.n_keys = n_keys
self._initialized = True
super()._initialize(d)
def _reset_cache(self):
"""Reset the internally stored statistics.
This method is meant to only be called internally. It resets the
stored statistics used to update the model parameters as well as
recalculates the cached values meant to speed up log probability
calculations.
"""
if self._initialized == False:
return
self.register_buffer("_w_sum", torch.zeros(self.d, device=self.device))
self.register_buffer("_xw_sum", torch.zeros(self.d, self.n_keys,
device=self.device))
self.register_buffer("_log_probs", torch.log(self.probs))
def sample(self, n):
"""Sample from the probability distribution.
This method will return `n` samples generated from the underlying
probability distribution.
Parameters
----------
n: int
The number of samples to generate.
Returns
-------
X: torch.tensor, shape=(n, self.d)
Randomly generated samples.
"""
return torch.distributions.Categorical(self.probs).sample([n])
def log_probability(self, X):
"""Calculate the log probability of each example.
This method calculates the log probability of each example given the
parameters of the distribution. The examples must be given in a 2D
format. For a categorical distribution, each entry in the data must
be an integer in the range [0, n_keys).
Note: This differs from some other log probability calculation
functions, like those in torch.distributions, because it is not
returning the log probability of each feature independently, but rather
the total log probability of the entire example.
Parameters
----------
X: list, tuple, numpy.ndarray, torch.Tensor, shape=(-1, self.d)
A set of examples to evaluate.
Returns
-------
logp: torch.Tensor, shape=(-1,)
The log probability of each example.
"""
X = _check_parameter(_cast_as_tensor(X), "X", min_value=0.0,
max_value=self.n_keys-1, ndim=2, shape=(-1, self.d),
check_parameter=self.check_data)
logps = torch.zeros(X.shape[0], dtype=self.probs.dtype)
for i in range(self.d):
if isinstance(X, torch.masked.MaskedTensor):
logp_ = self._log_probs[i][X[:, i]._masked_data]
logp_[~X[:, i]._masked_mask] = 0
logps += logp_
else:
logps += self._log_probs[i][X[:, i]]
return logps
def summarize(self, X, sample_weight=None):
"""Extract the sufficient statistics from a batch of data.
This method calculates the sufficient statistics from optionally
weighted data and adds them to the stored cache. The examples must be
given in a 2D format. Sample weights can either be provided as one
value per example or as a 2D matrix of weights for each feature in
each example.
Parameters
----------
X: list, tuple, numpy.ndarray, torch.Tensor, shape=(-1, self.d)
A set of examples to summarize.
sample_weight: list, tuple, numpy.ndarray, torch.Tensor, optional
A set of weights for the examples. This can be either of shape
(-1, self.d) or a vector of shape (-1,). Default is ones.
"""
if self.frozen == True:
return
X = _cast_as_tensor(X)
if not self._initialized:
if self.n_keys is not None:
n_keys = self.n_keys
elif isinstance(X, torch.masked.MaskedTensor):
n_keys = int(torch.max(X._masked_data)) + 1
else:
n_keys = int(torch.max(X)) + 1
self._initialize(X.shape[1], n_keys)
X = _check_parameter(X, "X", min_value=0, max_value=self.n_keys-1,
ndim=2, shape=(-1, self.d), check_parameter=self.check_data)
sample_weight = _reshape_weights(X, _cast_as_tensor(sample_weight))
_inplace_add(self._w_sum, torch.sum(sample_weight, dim=0))
for i in range(self.n_keys):
_inplace_add(self._xw_sum[:, i], torch.sum((X == i) * sample_weight,
dim=0))
def from_summaries(self):
"""Update the model parameters given the extracted statistics.
This method uses calculated statistics from calls to the `summarize`
method to update the distribution parameters. Hyperparameters for the
update are passed in at initialization time.
Note: Internally, a call to `fit` is just a successive call to the
`summarize` method followed by the `from_summaries` method.
"""
if self.frozen == True:
return
probs = (self._xw_sum + self.pseudocount) / (self._w_sum +
self.pseudocount * self.n_keys).unsqueeze(1)
_update_parameter(self.probs, probs, self.inertia)
self._reset_cache()