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student_t.py
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student_t.py
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# student_t.py
# Contact: Jacob Schreiber <jmschreiber91@gmail.com>
import math
import torch
from .._utils import _cast_as_tensor
from .._utils import _cast_as_parameter
from .._utils import _update_parameter
from .._utils import _check_parameter
from .normal import Normal
class StudentT(Normal):
"""A Student T distribution.
A Student T distribution models the probability of a variable occurring under
a bell-shaped curve with heavy tails. Basically, this is a version of the
normal distribution that is less resistant to outliers. It is described by
a vector of mean values and a vector of variance values. This
distribution can assume that features are independent of the others if
the covariance type is 'diag' or 'sphere', but if the type is 'full' then
the features are not independent.
There are two ways to initialize this object. The first is to pass in
the tensor of probability parameters, at which point they can immediately be
used. The second is to not pass in the rate parameters and then call
either `fit` or `summary` + `from_summaries`, at which point the probability
parameter will be learned from data.
Parameters
----------
means: list, numpy.ndarray, torch.Tensor or None, shape=(d,), optional
The mean values of the distributions. Default is None.
covs: list, numpy.ndarray, torch.Tensor, or None, optional
The variances and covariances of the distribution. If covariance_type
is 'full', the shape should be (self.d, self.d); if 'diag', the shape
should be (self.d,); if 'sphere', it should be (1,). Note that this is
the variances or covariances in all settings, and not the standard
deviation, as may be more common for diagonal covariance matrices.
Default is None.
covariance_type: str, optional
The type of covariance matrix. Must be one of 'full', 'diag', or
'sphere'. Default is 'full'.
min_cov: float or None, optional
The minimum variance or covariance.
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, dofs, means=None, covs=None, covariance_type='diag',
min_cov=None, inertia=0.0, frozen=False, check_data=True):
self.name = "StudentT"
dofs = _check_parameter(_cast_as_tensor(dofs), "dofs", min_value=1,
ndim=0, dtypes=(torch.int32, torch.int64))
self.dofs = dofs
super().__init__(means=means, covs=covs, min_cov=min_cov,
covariance_type=covariance_type, inertia=inertia, frozen=frozen,
check_data=check_data)
del self.dofs
self.register_buffer("dofs", _cast_as_tensor(dofs))
self.register_buffer("_lgamma_dofsp1", torch.lgamma((dofs + 1) / 2.0))
self.register_buffer("_lgamma_dofs", torch.lgamma(dofs / 2.0))
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.
"""
super()._reset_cache()
if self._initialized == False:
return
self.register_buffer("_log_sqrt_dofs_pi_cov", torch.log(torch.sqrt(
self.dofs * math.pi * self.covs)))
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.StudentT(self.means, self.covs).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.
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", ndim=2,
shape=(-1, self.d), check_parameter=self.check_data)
t = (X - self.means) ** 2 / self.covs
return torch.sum(self._lgamma_dofsp1 - self._lgamma_dofs - \
self._log_sqrt_dofs_pi_cov -((self.dofs + 1) / 2.0) *
torch.log(1 + t / self.dofs), dim=-1)