"""Module for the Renyi transfer entropy estimator."""
from abc import ABC
from numpy import issubdtype, integer
from ..base import (
TransferEntropyEstimator,
ConditionalTransferEntropyEstimator,
)
from ..entropy.renyi import RenyiEntropyEstimator
from ... import Config
from ...utils.types import LogBaseType
[docs]
class BaseRenyiTEEstimator(ABC):
r"""Base class for the Renyi transfer entropy.
Attributes
----------
source, dest : array-like
The source (X) and dest (Y) data used to estimate the transfer entropy.
cond : array-like, optional
The conditional data used to estimate the conditional transfer entropy.
k : int
The number of nearest neighbors used in the estimation.
alpha : float | int
The Rényi parameter, order or exponent.
Sometimes denoted as :math:`\alpha` or :math:`q`.
noise_level : float
The standard deviation of the Gaussian noise to add to the data to avoid
issues with zero distances.
prop_time : int, optional
Number of positions to shift the data arrays relative to each other (multiple of
``step_size``).
Delay/lag/shift between the variables, representing propagation time.
Assumed time taken by info to transfer from source to destination.
Not compatible with the ``cond`` parameter / conditional TE.
Alternatively called `offset`.
step_size : int, optional
Step size between elements for the state space reconstruction.
src_hist_len, dest_hist_len : int, optional
Number of past observations to consider for the source and destination data.
cond_hist_len : int, optional
Number of past observations to consider for the conditional data.
Only used for conditional transfer entropy.
Raises
------
ValueError
If the Renyi parameter is not a positive number.
ValueError
If the number of nearest neighbors is not a positive integer.
ValueError
If the step_size is not a non-negative integer.
"""
def __init__(
self,
source,
dest,
*, # Enforce keyword-only arguments
cond=None,
k: int = 4,
alpha: float | int = None,
noise_level=1e-8,
prop_time: int = 0,
step_size: int = 1,
src_hist_len: int = 1,
dest_hist_len: int = 1,
cond_hist_len: int = 1,
offset: int = None,
base: LogBaseType = Config.get("base"),
**kwargs,
):
"""Initialize the BaseRenyiTEEstimator.
Parameters
----------
source, dest : array-like
The source (X) and destination (Y) data used to estimate the transfer entropy.
cond : array-like, optional
The conditional data used to estimate the conditional transfer entropy.
k : int
The number of nearest neighbors to consider.
alpha : float | int
The Renyi parameter, order or exponent.
Sometimes denoted as :math:`\alpha` or :math:`q`.
prop_time : int, optional
Number of positions to shift the data arrays relative to each other (multiple of
``step_size``).
Delay/lag/shift between the variables, representing propagation time.
Assumed time taken by info to transfer from source to destination
Not compatible with the ``cond`` parameter / conditional TE.
Alternatively called `offset`.
step_size : int, optional
Step size between elements for the state space reconstruction.
src_hist_len, dest_hist_len : int, optional
Number of past observations to consider for the source and destination data.
cond_hist_len : int, optional
Number of past observations to consider for the conditional data.
Only used for conditional transfer entropy.
"""
if cond is None:
super().__init__(
source,
dest,
prop_time=prop_time,
src_hist_len=src_hist_len,
dest_hist_len=dest_hist_len,
step_size=step_size,
offset=offset,
base=base,
**kwargs,
)
else:
super().__init__(
source,
dest,
cond=cond,
step_size=step_size,
src_hist_len=src_hist_len,
dest_hist_len=dest_hist_len,
cond_hist_len=cond_hist_len,
prop_time=prop_time,
offset=offset,
base=base,
**kwargs,
)
if not isinstance(alpha, (int, float)) or alpha <= 0:
raise ValueError("The Renyi parameter must be a positive number.")
if not issubdtype(type(k), integer) or k <= 0:
raise ValueError(
"The number of nearest neighbors must be a positive integer."
)
if not issubdtype(type(step_size), integer) or step_size < 0:
raise ValueError("The step_size must be a non-negative integer.")
self.k = k
self.alpha = alpha
self.noise_level = noise_level
[docs]
class RenyiTEEstimator(BaseRenyiTEEstimator, TransferEntropyEstimator):
r"""Estimator for the Renyi transfer entropy.
Attributes
----------
source, dest : array-like
The source (X) and dest (Y) data used to estimate the transfer entropy.
k : int
The number of nearest neighbors used in the estimation.
alpha : float | int
The Rényi parameter, order or exponent.
Sometimes denoted as :math:`\alpha` or :math:`q`.
noise_level : float
The standard deviation of the Gaussian noise to add to the data to avoid
issues with zero distances.
prop_time : int, optional
Number of positions to shift the data arrays relative to each other (multiple of
``step_size``).
Delay/lag/shift between the variables, representing propagation time.
Assumed time taken by info to transfer from source to destination.
Alternatively called `offset`.
step_size : int, optional
Step size between elements for the state space reconstruction.
src_hist_len, dest_hist_len : int, optional
Number of past observations to consider for the source and destination data.
Raises
------
ValueError
If the Renyi parameter is not a positive number.
ValueError
If the number of nearest neighbors is not a positive integer.
ValueError
If the step_size is not a non-negative integer.
Notes
-----
The Rényi entropy is a generalization of Shannon entropy,
where the small values of probabilities are emphasized for :math:`\alpha < 1`,
and higher probabilities are emphasized for :math:`\alpha > 1`.
For :math:`\alpha = 1`, it reduces to Shannon entropy.
The Rényi-Entropy class can be particularly interesting for systems where additivity
(in Shannon sense) is not always preserved, especially in nonlinear complex systems,
such as when dealing with long-range forces.
"""
def _calculate(self):
"""Estimate the Renyi transfer entropy."""
return self._generic_te_from_entropy(
estimator=RenyiEntropyEstimator,
noise_level=self.noise_level,
kwargs=dict(k=self.k, alpha=self.alpha, base=self.base),
)
[docs]
class RenyiCTEEstimator(BaseRenyiTEEstimator, ConditionalTransferEntropyEstimator):
r"""Estimator for the Renyi conditional transfer entropy.
Attributes
----------
source, dest, cond : array-like
The source (X), destination (Y), and conditional (Z) data used to estimate the
conditional transfer entropy.
k : int
The number of nearest neighbors used in the estimation.
alpha : float | int
The Rényi parameter, order or exponent.
Sometimes denoted as :math:`\alpha` or :math:`q`.
noise_level : float
The standard deviation of the Gaussian noise to add to the data to avoid
issues with zero distances.
step_size : int
Step size between elements for the state space reconstruction.
src_hist_len, dest_hist_len, cond_hist_len : int
Number of past observations to consider for the source, destination,
and conditional data.
Raises
------
ValueError
If the Renyi parameter is not a positive number.
ValueError
If the number of nearest neighbors is not a positive integer.
ValueError
If the step_size is not a non-negative integer.
Notes
-----
The Rényi entropy is a generalization of Shannon entropy,
where the small values of probabilities are emphasized for :math:`\alpha < 1`,
and higher probabilities are emphasized for :math:`\alpha > 1`.
For :math:`\alpha = 1`, it reduces to Shannon entropy.
The Rényi-Entropy class can be particularly interesting for systems where additivity
(in Shannon sense) is not always preserved, especially in nonlinear complex systems,
such as when dealing with long-range forces.
"""
def _calculate(self):
"""Estimate the Renyi conditional transfer entropy."""
return self._generic_cte_from_entropy(
estimator=RenyiEntropyEstimator,
noise_level=self.noise_level,
kwargs=dict(k=self.k, alpha=self.alpha, base=self.base),
)
