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exponential.py
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exponential.py
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# exponential.py
# Contact: Jacob Schreiber <jmschreiber91@gmail.com>
import torch
from torch.distributions import Exponential as tExponential
from .._utils import _cast_as_tensor
from .._utils import _cast_as_parameter
from .._utils import _update_parameter
from .._utils import _check_parameter
from ._distribution import Distribution
class Exponential(Distribution):
"""An exponential distribution object.
An exponential distribution models scales of discrete events, and has a
rate parameter describing the average time between event occurrences.
This distribution assumes that each feature is independent of the others.
Although the object is meant to operate on discrete counts, it can be used
on any non-negative continuous data.
There are two ways to initialize this object. The first is to pass in
the tensor of rate 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 rate
parameter will be learned from data.
Parameters
----------
scales: list, numpy.ndarray, torch.Tensor or None, shape=(d,), optional
The rate parameters for each feature. 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, scales=None, inertia=0.0, frozen=False, check_data=True):
super().__init__(inertia=inertia, frozen=frozen, check_data=check_data)
self.name = "Exponential"
self.scales = _check_parameter(_cast_as_parameter(scales), "scales",
min_value=0, ndim=1)
self._initialized = scales is not None
self.d = self.scales.shape[-1] if self._initialized else None
self._reset_cache()
def _initialize(self, d):
"""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.
"""
self.scales = _cast_as_parameter(torch.zeros(d, dtype=self.dtype,
device=self.device))
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, device=self.device))
self.register_buffer("_log_scales", torch.log(self.scales))
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 tExponential(1. / self.scales).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 an exponential distribution, the data must be non-negative.
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,
ndim=2, shape=(-1, self.d), check_parameter=self.check_data)
return torch.sum(-self._log_scales - (1. / self.scales) * X, dim=1)
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, sample_weight = super().summarize(X, sample_weight=sample_weight)
_check_parameter(X, "X", min_value=0, check_parameter=self.check_data)
self._w_sum[:] = self._w_sum + torch.sum(sample_weight, dim=0)
self._xw_sum[:] = self._xw_sum + torch.sum(X * 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
scales = self._xw_sum / self._w_sum
_update_parameter(self.scales, scales, self.inertia)
self._reset_cache()