infomeasure.estimators.transfer_entropy package

infomeasure.estimators.transfer_entropy package#

Submodules#

infomeasure.estimators.transfer_entropy.discrete module#

Module for the discrete transfer entropy estimator.

class infomeasure.estimators.transfer_entropy.discrete.BaseDiscreteTEEstimator(source, dest, *, cond=None, 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: int | float | str = 'e')[source]#

Bases: ABC

Base class for discrete transfer entropy estimators.

Attributes:

source, destarray_like: The source (X) and destination (Y) data used to estimate the transfer entropy.
condarray_like, optional: The conditional data used to estimate the conditional transfer entropy.
prop_timeint, 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_sizeint, optional: Step size between elements for the state space reconstruction.
src_hist_len, dest_hist_lenint, optional: Number of past observations to consider for the source and destination data.
cond_hist_lenint, optional: Number of past observations to consider for the conditional data. Only used for conditional transfer entropy.

class infomeasure.estimators.transfer_entropy.discrete.DiscreteCTEEstimator(source, dest, *, cond=None, 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: int | float | str = 'e')[source]#

Bases: BaseDiscreteTEEstimator, ConditionalTransferEntropyEstimator

Estimator for discrete conditional transfer entropy.

Attributes:

source, dest, condarray_like: The source (X), destination (Y), and conditional (Z) data used to estimate the conditional transfer entropy.
step_sizeint: Step size between elements for the state space reconstruction.
src_hist_len, dest_hist_len, cond_hist_lenint, optional: Number of past observations to consider for the source, destination, and conditional data.
prop_timeint, optional: Not compatible with the cond parameter / conditional TE.

class infomeasure.estimators.transfer_entropy.discrete.DiscreteTEEstimator(source, dest, *, cond=None, 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: int | float | str = 'e')[source]#

Bases: BaseDiscreteTEEstimator, PValueMixin, EffectiveValueMixin, TransferEntropyEstimator

Estimator for discrete transfer entropy.

Attributes:

source, destarray_like: The source (X) and destination (Y) data used to estimate the transfer entropy.
prop_timeint, 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_sizeint: Step size between elements for the state space reconstruction.
src_hist_len, dest_hist_lenint: Number of past observations to consider for the source and destination data.

infomeasure.estimators.transfer_entropy.kernel module#

Module for the kernel-based transfer entropy estimator.

class infomeasure.estimators.transfer_entropy.kernel.BaseKernelTEEstimator(source, dest, *, cond=None, bandwidth: float | int = None, kernel: str = None, prop_time: int = 0, step_size: int = 1, src_hist_len: int = 1, dest_hist_len: int = 1, cond_hist_len: int = 1, workers: int = 1, offset: int = None, base: int | float | str = 'e')[source]#

Bases: WorkersMixin, ABC

Base class for transfer entropy using Kernel Density Estimation (KDE).

Attributes:

source, destarray_like: The source (X) and destination (Y) data used to estimate the transfer entropy.
condarray_like, optional: The conditional data used to estimate the conditional transfer entropy.
bandwidthfloat | int: The bandwidth for the kernel.
kernelstr: Type of kernel to use, compatible with the KDE implementation kde_probability_density_function().
prop_timeint, 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_sizeint, optional: Step size between elements for the state space reconstruction.
src_hist_len, dest_hist_lenint, optional: Number of past observations to consider for the source and destination data.
cond_hist_lenint, optional: Number of past observations to consider for the conditional data. Only used for conditional transfer entropy.
workersint, optional: Number of workers to use for parallel processing. Default is 1, meaning no parallel processing. If set to -1, all available CPU cores will be used.

class infomeasure.estimators.transfer_entropy.kernel.KernelCTEEstimator(source, dest, *, cond=None, bandwidth: float | int = None, kernel: str = None, prop_time: int = 0, step_size: int = 1, src_hist_len: int = 1, dest_hist_len: int = 1, cond_hist_len: int = 1, workers: int = 1, offset: int = None, base: int | float | str = 'e')[source]#

Bases: BaseKernelTEEstimator, ConditionalTransferEntropyEstimator

Estimator for conditional transfer entropy using Kernel Density Estimation (KDE).

Attributes:

source, dest, condarray_like: The source (X), destination (Y), and conditional (Z) data used to estimate the conditional transfer entropy.
bandwidthfloat | int: The bandwidth for the kernel.
kernelstr: Type of kernel to use, compatible with the KDE implementation kde_probability_density_function().
step_sizeint: Step size between elements for the state space reconstruction.
src_hist_len, dest_hist_len, cond_hist_lenint, optional: Number of past observations to consider for the source, destination, and conditional data.
prop_timeint, optional: Not compatible with the cond parameter / conditional TE.

Notes

A small bandwidth can lead to under-sampling, while a large bandwidth may over-smooth the data, obscuring details.

class infomeasure.estimators.transfer_entropy.kernel.KernelTEEstimator(source, dest, *, cond=None, bandwidth: float | int = None, kernel: str = None, prop_time: int = 0, step_size: int = 1, src_hist_len: int = 1, dest_hist_len: int = 1, cond_hist_len: int = 1, workers: int = 1, offset: int = None, base: int | float | str = 'e')[source]#

Bases: BaseKernelTEEstimator, PValueMixin, EffectiveValueMixin, TransferEntropyEstimator

Estimator for transfer entropy using Kernel Density Estimation (KDE).

Attributes:

source, destarray_like: The source (X) and destination (Y) data used to estimate the transfer entropy.
bandwidthfloat | int: The bandwidth for the kernel.
kernelstr: Type of kernel to use, compatible with the KDE implementation kde_probability_density_function().
prop_timeint, 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_sizeint: Step size between elements for the state space reconstruction.
src_hist_len, dest_hist_lenint: Number of past observations to consider for the source and destination data.

Notes

A small bandwidth can lead to under-sampling, while a large bandwidth may over-smooth the data, obscuring details.

infomeasure.estimators.transfer_entropy.kraskov_stoegbauer_grassberger module#

Module for the Kraskov-Stoegbauer-Grassberger (KSG) transfer entropy estimator.

class infomeasure.estimators.transfer_entropy.kraskov_stoegbauer_grassberger.BaseKSGTEEstimator(source, dest, *, cond=None, k: int = 4, noise_level=1e-08, minkowski_p=inf, 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: int | float | str = 'e')[source]#

Bases: ABC

Base class for transfer entropy using the Kraskov-Stoegbauer-Grassberger (KSG) method.

Attributes:

source, destarray_like: The source (X) and destination (Y) data used to estimate the transfer entropy.
cond: The conditional data used to estimate the conditional transfer entropy.
kint: Number of nearest neighbors to consider.
noise_levelfloat, None or False: Standard deviation of Gaussian noise to add to the data. Adds $\mathcal{N}(0, \text{noise}^2)$ to each data point.
minkowski_pfloat, $1 \leq p \leq \infty$: The power parameter for the Minkowski metric. Default is np.inf for maximum norm. Use 2 for Euclidean distance.
prop_timeint, 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_sizeint, optional: Step size between elements for the state space reconstruction.
src_hist_len, dest_hist_lenint, optional: Number of past observations to consider for the source and destination data.
cond_hist_lenint, optional: Number of past observations to consider for the conditional data. Only used for conditional transfer entropy.

class infomeasure.estimators.transfer_entropy.kraskov_stoegbauer_grassberger.KSGCTEEstimator(source, dest, *, cond=None, k: int = 4, noise_level=1e-08, minkowski_p=inf, 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: int | float | str = 'e')[source]#

Bases: BaseKSGTEEstimator, ConditionalTransferEntropyEstimator

Estimator for conditional transfer entropy using the Kraskov-Stoegbauer-Grassberger (KSG) method.

Attributes:

source, dest, condarray_like: The source (X), destination (Y), and conditional (Z) data used to estimate the conditional transfer entropy.
kint: Number of nearest neighbors to consider.
noise_levelfloat, None or False: Standard deviation of Gaussian noise to add to the data. Adds $\mathcal{N}(0, ext{noise}^2)$ to each data point.
minkowski_pfloat, $1 \leq p \leq \infty$: The power parameter for the Minkowski metric. Default is np.inf for maximum norm. Use 2 for Euclidean distance.
step_sizeint: Step size between elements for the state space reconstruction.
src_hist_len, dest_hist_len, cond_hist_lenint, optional: Number of past observations to consider for the source, destination, and conditional data.
prop_timeint, optional: Not compatible with the cond parameter / conditional TE.

Notes

Changing the number of nearest neighbors k can change the outcome, but the default value of $k=4$ is recommended by [KStogbauerG11].

class infomeasure.estimators.transfer_entropy.kraskov_stoegbauer_grassberger.KSGTEEstimator(source, dest, *, cond=None, k: int = 4, noise_level=1e-08, minkowski_p=inf, 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: int | float | str = 'e')[source]#

Bases: BaseKSGTEEstimator, PValueMixin, EffectiveValueMixin, TransferEntropyEstimator

Estimator for transfer entropy using the Kraskov-Stoegbauer-Grassberger (KSG) method.

Attributes:

source, destarray_like: The source (X) and destination (Y) data used to estimate the transfer entropy.
kint: Number of nearest neighbors to consider.
noise_levelfloat, None or False: Standard deviation of Gaussian noise to add to the data. Adds $\mathcal{N}(0, \text{noise}^2)$ to each data point.
minkowski_pfloat, $1 \leq p \leq \infty$: The power parameter for the Minkowski metric. Default is np.inf for maximum norm. Use 2 for Euclidean distance.
prop_timeint, 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_sizeint, optional: Step size between elements for the state space reconstruction.
src_hist_len, dest_hist_lenint: Number of past observations to consider for the source and destination data.

Notes

Changing the number of nearest neighbors k can change the outcome, but the default value of $k=4$ is recommended by [KStogbauerG11].

infomeasure.estimators.transfer_entropy.ordinal module#

Module for the Ordinal / Permutation transfer entropy estimator.

class infomeasure.estimators.transfer_entropy.ordinal.BaseOrdinalTEEstimator(source, dest, *, cond=None, embedding_dim: int, stable: bool = False, 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: int | float | str = 'e')[source]#

Bases: ABC

Base class for the Ordinal / Permutation transfer entropy.

Attributes:

source, destarray_like: The source (X) and dest (Y) data used to estimate the transfer entropy.
condarray_like, optional: The conditional data used to estimate the conditional transfer entropy.
embedding_dimint: The size of the permutation patterns.
stablebool, optional: If True, when sorting the data, the order of equal elements is preserved. This can be useful for reproducibility and testing, but might be slower.
prop_timeint, 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. Not compatible with the cond parameter / conditional TE. Alternatively called offset.
step_sizeint, optional: Step size between elements for the state space reconstruction.
src_hist_len, dest_hist_lenint, optional: Number of past observations to consider for the source and destination data.
cond_hist_lenint, optional: Number of past observations to consider for the conditional data. Only used for conditional transfer entropy.

Raises:

ValueError: If the embedding_dim is negative or not an integer.
ValueError: If the embedding_dim is too large for the given data.
ValueError: If step_size, prop_time, and embedding_dim are such that the data is too small.
TypeError: If the data are not 1d array-like(s).

Notes

If embedding_dim is set to 1, the transfer entropy is always 0.

class infomeasure.estimators.transfer_entropy.ordinal.OrdinalCTEEstimator(source, dest, *, cond=None, embedding_dim: int, stable: bool = False, 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: int | float | str = 'e')[source]#

Bases: BaseOrdinalTEEstimator, ConditionalTransferEntropyEstimator

Estimator for the Ordinal / Permutation conditional transfer entropy.

Attributes:

source, dest, condarray_like: The source (X), destination (Y), and conditional (Z) data used to estimate the conditional transfer entropy.
embedding_dimint: The size of the permutation patterns.
prop_timeint, 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.
step_sizeint: Step size between elements for the state space reconstruction.
src_hist_len, dest_hist_len, cond_hist_lenint: Number of past observations to consider for the source, destination, and conditional data.

Raises:

ValueError: If the embedding_dim is negative or not an integer.
ValueError: If the embedding_dim is too large for the given data.
ValueError: If step_size, prop_time, and embedding_dim are such that the data is too small.

Notes

If embedding_dim is set to 1, the transfer entropy is always 0.

class infomeasure.estimators.transfer_entropy.ordinal.OrdinalTEEstimator(source, dest, *, cond=None, embedding_dim: int, stable: bool = False, 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: int | float | str = 'e')[source]#

Bases: BaseOrdinalTEEstimator, PValueMixin, EffectiveValueMixin, TransferEntropyEstimator

Estimator for the Ordinal / Permutation transfer entropy.

Attributes:

source, destarray_like: The source (X) and dest (Y) data used to estimate the transfer entropy.
embedding_dimint: The size of the permutation patterns.
prop_timeint, 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_sizeint: Step size between elements for the state space reconstruction.
src_hist_len, dest_hist_lenint: Number of past observations to consider for the source and destination data.

Raises:

ValueError: If the embedding_dim is negative or not an integer.
ValueError: If the embedding_dim is too large for the given data.
ValueError: If step_size, prop_time, and embedding_dim are such that the data is too small.

Notes

If embedding_dim is set to 1, the transfer entropy is always 0.

infomeasure.estimators.transfer_entropy.renyi module#

Module for the Renyi transfer entropy estimator.

class infomeasure.estimators.transfer_entropy.renyi.BaseRenyiTEEstimator(source, dest, *, cond=None, k: int = 4, alpha: float | int = None, noise_level=1e-08, 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: int | float | str = 'e')[source]#

Bases: ABC

Base class for the Renyi transfer entropy.

Attributes:

source, destarray_like: The source (X) and dest (Y) data used to estimate the transfer entropy.
condarray_like, optional: The conditional data used to estimate the conditional transfer entropy.
kint: The number of nearest neighbors used in the estimation.
alphafloat | int: The Rényi parameter, order or exponent. Sometimes denoted as $\alpha$ or $q$.
noise_levelfloat: The standard deviation of the Gaussian noise to add to the data to avoid issues with zero distances.
prop_timeint, 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_sizeint, optional: Step size between elements for the state space reconstruction.
src_hist_len, dest_hist_lenint, optional: Number of past observations to consider for the source and destination data.
cond_hist_lenint, 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.

class infomeasure.estimators.transfer_entropy.renyi.RenyiCTEEstimator(source, dest, *, cond=None, k: int = 4, alpha: float | int = None, noise_level=1e-08, 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: int | float | str = 'e')[source]#

Bases: BaseRenyiTEEstimator, ConditionalTransferEntropyEstimator

Estimator for the Renyi conditional transfer entropy.

Attributes:

source, dest, condarray_like: The source (X), destination (Y), and conditional (Z) data used to estimate the conditional transfer entropy.
kint: The number of nearest neighbors used in the estimation.
alphafloat | int: The Rényi parameter, order or exponent. Sometimes denoted as $\alpha$ or $q$.
noise_levelfloat: The standard deviation of the Gaussian noise to add to the data to avoid issues with zero distances.
step_sizeint: Step size between elements for the state space reconstruction.
src_hist_len, dest_hist_len, cond_hist_lenint: 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 $\alpha < 1$, and higher probabilities are emphasized for $\alpha > 1$. For $\alpha = 1$, 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.

class infomeasure.estimators.transfer_entropy.renyi.RenyiTEEstimator(source, dest, *, cond=None, k: int = 4, alpha: float | int = None, noise_level=1e-08, 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: int | float | str = 'e')[source]#

Bases: BaseRenyiTEEstimator, PValueMixin, EffectiveValueMixin, TransferEntropyEstimator

Estimator for the Renyi transfer entropy.

Attributes:

source, destarray_like: The source (X) and dest (Y) data used to estimate the transfer entropy.
kint: The number of nearest neighbors used in the estimation.
alphafloat | int: The Rényi parameter, order or exponent. Sometimes denoted as $\alpha$ or $q$.
noise_levelfloat: The standard deviation of the Gaussian noise to add to the data to avoid issues with zero distances.
prop_timeint, 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_sizeint, optional: Step size between elements for the state space reconstruction.
src_hist_len, dest_hist_lenint, 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

infomeasure.estimators.transfer_entropy.tsallis module#

Module for the Tsallis transfer entropy estimator.

class infomeasure.estimators.transfer_entropy.tsallis.BaseTsallisTEEstimator(source, dest, *, cond=None, k: int = 4, q: float | int = None, noise_level=1e-08, 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: int | float | str = 'e')[source]#

Bases: ABC

Base class for the Tsallis transfer entropy.

Attributes:

source, destarray_like: The source (X) and dest (Y) data used to estimate the transfer entropy.
condarray_like, optional: The conditional data used to estimate the conditional transfer entropy.
kint: The number of nearest neighbors used in the estimation.
qfloat | int: The Tsallis parameter, order or exponent. Sometimes denoted as $q$, analogous to the Rényi parameter $\alpha$.
noise_levelfloat: The standard deviation of the Gaussian noise to add to the data to avoid issues with zero distances.
prop_timeint, 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_sizeint, optional: Step size between elements for the state space reconstruction.
src_hist_len, dest_hist_lenint, optional: Number of past observations to consider for the source and destination data.
cond_hist_lenint, optional: Number of past observations to consider for the conditional data. Only used for conditional transfer entropy.

Raises:

ValueError: If the Tsallis 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.

class infomeasure.estimators.transfer_entropy.tsallis.TsallisCTEEstimator(source, dest, *, cond=None, k: int = 4, q: float | int = None, noise_level=1e-08, 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: int | float | str = 'e')[source]#

Bases: BaseTsallisTEEstimator, ConditionalTransferEntropyEstimator

Estimator for the Tsallis conditional transfer entropy.

Attributes:

source, dest, condarray_like: The source (X), destination (Y) and conditional (Z) data used to estimate the conditional transfer entropy.
kint: The number of nearest neighbors used in the estimation.
qfloat | int: The Tsallis parameter, order or exponent. Sometimes denoted as $q$, analogous to the Rényi parameter $\alpha$.
noise_levelfloat: The standard deviation of the Gaussian noise to add to the data to avoid issues with zero distances.
step_sizeint, optional: Step size between elements for the state space reconstruction.
src_hist_len, dest_hist_len, cond_hist_lenint, optional: Number of past observations to consider for the source, destination and conditional data.

Raises:

ValueError: If the Tsallis 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

In the $q to 1$ limit, the Jackson sum (q-additivity) reduces to ordinary summation, and the Tallis entropy reduces to Shannon Entropy. This class of entropy measure is in particularly useful in the study in connection with long-range correlated systems and with non-equilibrium phenomena.

class infomeasure.estimators.transfer_entropy.tsallis.TsallisTEEstimator(source, dest, *, cond=None, k: int = 4, q: float | int = None, noise_level=1e-08, 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: int | float | str = 'e')[source]#

Bases: BaseTsallisTEEstimator, PValueMixin, EffectiveValueMixin, TransferEntropyEstimator

Estimator for the Tsallis transfer entropy.

Attributes:

source, destarray_like: The source (X) and dest (Y) data used to estimate the transfer entropy.
kint: The number of nearest neighbors used in the estimation.
qfloat | int: The Tsallis parameter, order or exponent. Sometimes denoted as $q$, analogous to the Rényi parameter $\alpha$.
noise_levelfloat: The standard deviation of the Gaussian noise to add to the data to avoid issues with zero distances.
prop_timeint, 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_sizeint, optional: Step size between elements for the state space reconstruction.
src_hist_len, dest_hist_lenint, optional: Number of past observations to consider for the source and destination data.

Raises:

ValueError: If the Tsallis 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

Module contents#

Transfer entropy estimators.

class infomeasure.estimators.transfer_entropy.DiscreteCTEEstimator(source, dest, *, cond=None, 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: int | float | str = 'e')[source]#

Bases: BaseDiscreteTEEstimator, ConditionalTransferEntropyEstimator

Estimator for discrete conditional transfer entropy.

Attributes:

source, dest, condarray_like: The source (X), destination (Y), and conditional (Z) data used to estimate the conditional transfer entropy.
step_sizeint: Step size between elements for the state space reconstruction.
src_hist_len, dest_hist_len, cond_hist_lenint, optional: Number of past observations to consider for the source, destination, and conditional data.
prop_timeint, optional: Not compatible with the cond parameter / conditional TE.

class infomeasure.estimators.transfer_entropy.DiscreteTEEstimator(source, dest, *, cond=None, 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: int | float | str = 'e')[source]#

Bases: BaseDiscreteTEEstimator, PValueMixin, EffectiveValueMixin, TransferEntropyEstimator

Estimator for discrete transfer entropy.

Attributes:

source, destarray_like: The source (X) and destination (Y) data used to estimate the transfer entropy.
prop_timeint, 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_sizeint: Step size between elements for the state space reconstruction.
src_hist_len, dest_hist_lenint: Number of past observations to consider for the source and destination data.

class infomeasure.estimators.transfer_entropy.KSGCTEEstimator(source, dest, *, cond=None, k: int = 4, noise_level=1e-08, minkowski_p=inf, 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: int | float | str = 'e')[source]#

Bases: BaseKSGTEEstimator, ConditionalTransferEntropyEstimator

Estimator for conditional transfer entropy using the Kraskov-Stoegbauer-Grassberger (KSG) method.

Attributes:

source, dest, condarray_like: The source (X), destination (Y), and conditional (Z) data used to estimate the conditional transfer entropy.
kint: Number of nearest neighbors to consider.
noise_levelfloat, None or False: Standard deviation of Gaussian noise to add to the data. Adds $\mathcal{N}(0, ext{noise}^2)$ to each data point.
minkowski_pfloat, $1 \leq p \leq \infty$: The power parameter for the Minkowski metric. Default is np.inf for maximum norm. Use 2 for Euclidean distance.
step_sizeint: Step size between elements for the state space reconstruction.
src_hist_len, dest_hist_len, cond_hist_lenint, optional: Number of past observations to consider for the source, destination, and conditional data.
prop_timeint, optional: Not compatible with the cond parameter / conditional TE.

Notes

Changing the number of nearest neighbors k can change the outcome, but the default value of $k=4$ is recommended by [KStogbauerG11].

class infomeasure.estimators.transfer_entropy.KSGTEEstimator(source, dest, *, cond=None, k: int = 4, noise_level=1e-08, minkowski_p=inf, 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: int | float | str = 'e')[source]#

Bases: BaseKSGTEEstimator, PValueMixin, EffectiveValueMixin, TransferEntropyEstimator

Estimator for transfer entropy using the Kraskov-Stoegbauer-Grassberger (KSG) method.

Attributes:

source, destarray_like: The source (X) and destination (Y) data used to estimate the transfer entropy.
kint: Number of nearest neighbors to consider.
noise_levelfloat, None or False: Standard deviation of Gaussian noise to add to the data. Adds $\mathcal{N}(0, \text{noise}^2)$ to each data point.
minkowski_pfloat, $1 \leq p \leq \infty$: The power parameter for the Minkowski metric. Default is np.inf for maximum norm. Use 2 for Euclidean distance.
prop_timeint, 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_sizeint, optional: Step size between elements for the state space reconstruction.
src_hist_len, dest_hist_lenint: Number of past observations to consider for the source and destination data.

Notes

Changing the number of nearest neighbors k can change the outcome, but the default value of $k=4$ is recommended by [KStogbauerG11].

class infomeasure.estimators.transfer_entropy.KernelCTEEstimator(source, dest, *, cond=None, bandwidth: float | int = None, kernel: str = None, prop_time: int = 0, step_size: int = 1, src_hist_len: int = 1, dest_hist_len: int = 1, cond_hist_len: int = 1, workers: int = 1, offset: int = None, base: int | float | str = 'e')[source]#

Bases: BaseKernelTEEstimator, ConditionalTransferEntropyEstimator

Estimator for conditional transfer entropy using Kernel Density Estimation (KDE).

Attributes:

source, dest, condarray_like: The source (X), destination (Y), and conditional (Z) data used to estimate the conditional transfer entropy.
bandwidthfloat | int: The bandwidth for the kernel.
kernelstr: Type of kernel to use, compatible with the KDE implementation kde_probability_density_function().
step_sizeint: Step size between elements for the state space reconstruction.
src_hist_len, dest_hist_len, cond_hist_lenint, optional: Number of past observations to consider for the source, destination, and conditional data.
prop_timeint, optional: Not compatible with the cond parameter / conditional TE.

Notes

A small bandwidth can lead to under-sampling, while a large bandwidth may over-smooth the data, obscuring details.

class infomeasure.estimators.transfer_entropy.KernelTEEstimator(source, dest, *, cond=None, bandwidth: float | int = None, kernel: str = None, prop_time: int = 0, step_size: int = 1, src_hist_len: int = 1, dest_hist_len: int = 1, cond_hist_len: int = 1, workers: int = 1, offset: int = None, base: int | float | str = 'e')[source]#

Bases: BaseKernelTEEstimator, PValueMixin, EffectiveValueMixin, TransferEntropyEstimator

Estimator for transfer entropy using Kernel Density Estimation (KDE).

Attributes:

source, destarray_like: The source (X) and destination (Y) data used to estimate the transfer entropy.
bandwidthfloat | int: The bandwidth for the kernel.
kernelstr: Type of kernel to use, compatible with the KDE implementation kde_probability_density_function().
prop_timeint, 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_sizeint: Step size between elements for the state space reconstruction.
src_hist_len, dest_hist_lenint: Number of past observations to consider for the source and destination data.

Notes

A small bandwidth can lead to under-sampling, while a large bandwidth may over-smooth the data, obscuring details.

class infomeasure.estimators.transfer_entropy.OrdinalCTEEstimator(source, dest, *, cond=None, embedding_dim: int, stable: bool = False, 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: int | float | str = 'e')[source]#

Bases: BaseOrdinalTEEstimator, ConditionalTransferEntropyEstimator

Estimator for the Ordinal / Permutation conditional transfer entropy.

Attributes:

source, dest, condarray_like: The source (X), destination (Y), and conditional (Z) data used to estimate the conditional transfer entropy.
embedding_dimint: The size of the permutation patterns.
prop_timeint, 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.
step_sizeint: Step size between elements for the state space reconstruction.
src_hist_len, dest_hist_len, cond_hist_lenint: Number of past observations to consider for the source, destination, and conditional data.

Raises:

ValueError: If the embedding_dim is negative or not an integer.
ValueError: If the embedding_dim is too large for the given data.
ValueError: If step_size, prop_time, and embedding_dim are such that the data is too small.

Notes

If embedding_dim is set to 1, the transfer entropy is always 0.

class infomeasure.estimators.transfer_entropy.OrdinalTEEstimator(source, dest, *, cond=None, embedding_dim: int, stable: bool = False, 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: int | float | str = 'e')[source]#

Bases: BaseOrdinalTEEstimator, PValueMixin, EffectiveValueMixin, TransferEntropyEstimator

Estimator for the Ordinal / Permutation transfer entropy.

Attributes:

source, destarray_like: The source (X) and dest (Y) data used to estimate the transfer entropy.
embedding_dimint: The size of the permutation patterns.
prop_timeint, 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_sizeint: Step size between elements for the state space reconstruction.
src_hist_len, dest_hist_lenint: Number of past observations to consider for the source and destination data.

Raises:

ValueError: If the embedding_dim is negative or not an integer.
ValueError: If the embedding_dim is too large for the given data.
ValueError: If step_size, prop_time, and embedding_dim are such that the data is too small.

Notes

If embedding_dim is set to 1, the transfer entropy is always 0.

class infomeasure.estimators.transfer_entropy.RenyiCTEEstimator(source, dest, *, cond=None, k: int = 4, alpha: float | int = None, noise_level=1e-08, 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: int | float | str = 'e')[source]#

Bases: BaseRenyiTEEstimator, ConditionalTransferEntropyEstimator

Estimator for the Renyi conditional transfer entropy.

Attributes:

source, dest, condarray_like: The source (X), destination (Y), and conditional (Z) data used to estimate the conditional transfer entropy.
kint: The number of nearest neighbors used in the estimation.
alphafloat | int: The Rényi parameter, order or exponent. Sometimes denoted as $\alpha$ or $q$.
noise_levelfloat: The standard deviation of the Gaussian noise to add to the data to avoid issues with zero distances.
step_sizeint: Step size between elements for the state space reconstruction.
src_hist_len, dest_hist_len, cond_hist_lenint: 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

class infomeasure.estimators.transfer_entropy.RenyiTEEstimator(source, dest, *, cond=None, k: int = 4, alpha: float | int = None, noise_level=1e-08, 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: int | float | str = 'e')[source]#

Bases: BaseRenyiTEEstimator, PValueMixin, EffectiveValueMixin, TransferEntropyEstimator

Estimator for the Renyi transfer entropy.

Attributes:

source, destarray_like: The source (X) and dest (Y) data used to estimate the transfer entropy.
kint: The number of nearest neighbors used in the estimation.
alphafloat | int: The Rényi parameter, order or exponent. Sometimes denoted as $\alpha$ or $q$.
noise_levelfloat: The standard deviation of the Gaussian noise to add to the data to avoid issues with zero distances.
prop_timeint, 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_sizeint, optional: Step size between elements for the state space reconstruction.
src_hist_len, dest_hist_lenint, 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

class infomeasure.estimators.transfer_entropy.TsallisCTEEstimator(source, dest, *, cond=None, k: int = 4, q: float | int = None, noise_level=1e-08, 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: int | float | str = 'e')[source]#

Bases: BaseTsallisTEEstimator, ConditionalTransferEntropyEstimator

Estimator for the Tsallis conditional transfer entropy.

Attributes:

source, dest, condarray_like: The source (X), destination (Y) and conditional (Z) data used to estimate the conditional transfer entropy.
kint: The number of nearest neighbors used in the estimation.
qfloat | int: The Tsallis parameter, order or exponent. Sometimes denoted as $q$, analogous to the Rényi parameter $\alpha$.
noise_levelfloat: The standard deviation of the Gaussian noise to add to the data to avoid issues with zero distances.
step_sizeint, optional: Step size between elements for the state space reconstruction.
src_hist_len, dest_hist_len, cond_hist_lenint, optional: Number of past observations to consider for the source, destination and conditional data.

Raises:

ValueError: If the Tsallis 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

class infomeasure.estimators.transfer_entropy.TsallisTEEstimator(source, dest, *, cond=None, k: int = 4, q: float | int = None, noise_level=1e-08, 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: int | float | str = 'e')[source]#

Bases: BaseTsallisTEEstimator, PValueMixin, EffectiveValueMixin, TransferEntropyEstimator

Estimator for the Tsallis transfer entropy.

Attributes:

source, destarray_like: The source (X) and dest (Y) data used to estimate the transfer entropy.
kint: The number of nearest neighbors used in the estimation.
qfloat | int: The Tsallis parameter, order or exponent. Sometimes denoted as $q$, analogous to the Rényi parameter $\alpha$.
noise_levelfloat: The standard deviation of the Gaussian noise to add to the data to avoid issues with zero distances.
prop_timeint, 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_sizeint, optional: Step size between elements for the state space reconstruction.
src_hist_len, dest_hist_lenint, optional: Number of past observations to consider for the source and destination data.

Raises:

ValueError: If the Tsallis 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

infomeasure.estimators.transfer_entropy package

Contents

infomeasure.estimators.transfer_entropy package#

Submodules#

infomeasure.estimators.transfer_entropy.discrete module#

infomeasure.estimators.transfer_entropy.kernel module#

infomeasure.estimators.transfer_entropy.kraskov_stoegbauer_grassberger module#

infomeasure.estimators.transfer_entropy.ordinal module#

infomeasure.estimators.transfer_entropy.renyi module#

infomeasure.estimators.transfer_entropy.tsallis module#

Module contents#