infomeasure package

Subpackages

• infomeasure.composite_measures package
  • Submodules
  • infomeasure.composite_measures.jsd module
    • jensen_shannon_divergence()
  • infomeasure.composite_measures.kld module
    • kullback_leiber_divergence()
  • Module contents
    • jensen_shannon_divergence()
    • kullback_leiber_divergence()
• infomeasure.estimators package
  • Subpackages
    • infomeasure.estimators.entropy package
      • Submodules
      • infomeasure.estimators.entropy.ansb module
      • infomeasure.estimators.entropy.bayes module
      • infomeasure.estimators.entropy.bonachela module
      • infomeasure.estimators.entropy.chao_shen module
      • infomeasure.estimators.entropy.chao_wang_jost module
      • infomeasure.estimators.entropy.discrete module
      • infomeasure.estimators.entropy.grassberger module
      • infomeasure.estimators.entropy.kernel module
      • infomeasure.estimators.entropy.kozachenko_leonenko module
      • infomeasure.estimators.entropy.miller_madow module
      • infomeasure.estimators.entropy.nsb module
      • infomeasure.estimators.entropy.ordinal module
      • infomeasure.estimators.entropy.renyi module
      • infomeasure.estimators.entropy.shrink module
      • infomeasure.estimators.entropy.tsallis module
      • infomeasure.estimators.entropy.zhang module
      • Module contents
    • infomeasure.estimators.mutual_information package
      • Submodules
      • infomeasure.estimators.mutual_information.ansb module
      • infomeasure.estimators.mutual_information.bayes module
      • infomeasure.estimators.mutual_information.bonachela module
      • infomeasure.estimators.mutual_information.chao_shen module
      • infomeasure.estimators.mutual_information.chao_wang_jost module
      • infomeasure.estimators.mutual_information.discrete module
      • infomeasure.estimators.mutual_information.grassberger module
      • infomeasure.estimators.mutual_information.kernel module
      • infomeasure.estimators.mutual_information.kraskov_stoegbauer_grassberger module
      • infomeasure.estimators.mutual_information.miller_madow module
      • infomeasure.estimators.mutual_information.nsb module
      • infomeasure.estimators.mutual_information.ordinal module
      • infomeasure.estimators.mutual_information.renyi module
      • infomeasure.estimators.mutual_information.shrink module
      • infomeasure.estimators.mutual_information.tsallis module
      • infomeasure.estimators.mutual_information.zhang module
      • Module contents
    • infomeasure.estimators.transfer_entropy package
      • Submodules
      • infomeasure.estimators.transfer_entropy.ansb module
      • infomeasure.estimators.transfer_entropy.bayes module
      • infomeasure.estimators.transfer_entropy.bonachela module
      • infomeasure.estimators.transfer_entropy.chao_shen module
      • infomeasure.estimators.transfer_entropy.chao_wang_jost module
      • infomeasure.estimators.transfer_entropy.discrete module
      • infomeasure.estimators.transfer_entropy.grassberger module
      • infomeasure.estimators.transfer_entropy.kernel module
      • infomeasure.estimators.transfer_entropy.kraskov_stoegbauer_grassberger module
      • infomeasure.estimators.transfer_entropy.miller_madow module
      • infomeasure.estimators.transfer_entropy.nsb module
      • infomeasure.estimators.transfer_entropy.ordinal module
      • infomeasure.estimators.transfer_entropy.renyi module
      • infomeasure.estimators.transfer_entropy.shrink module
      • infomeasure.estimators.transfer_entropy.tsallis module
      • infomeasure.estimators.transfer_entropy.zhang module
      • Module contents
    • infomeasure.estimators.utils package
      • Submodules
      • infomeasure.estimators.utils.array module
      • infomeasure.estimators.utils.discrete_interaction_information module
      • infomeasure.estimators.utils.discrete_transfer_entropy module
      • infomeasure.estimators.utils.exponential_family module
      • infomeasure.estimators.utils.kde module
      • infomeasure.estimators.utils.normalize module
      • infomeasure.estimators.utils.ordinal module
      • infomeasure.estimators.utils.te_slicing module
      • infomeasure.estimators.utils.test_unit_ball_volume module
      • infomeasure.estimators.utils.unit_ball_volume module
      • Module contents
  • Submodules
  • infomeasure.estimators.base module
    • ConditionalMutualInformationEstimator
    • ConditionalTransferEntropyEstimator
    • DiscreteHEstimator
      • DiscreteHEstimator.from_counts()
      • DiscreteHEstimator.from_probabilities()
    • EntropyEstimator
      • EntropyEstimator.local_vals()
    • Estimator
      • Estimator.calculate()
      • Estimator.global_val()
      • Estimator.local_vals()
      • Estimator.result()
    • MutualInformationEstimator
    • TransferEntropyEstimator
  • infomeasure.estimators.functional module
    • conditional_mutual_information()
    • conditional_transfer_entropy()
    • cross_entropy()
    • entropy()
    • estimator()
    • get_estimator_class()
    • mutual_information()
    • transfer_entropy()
  • infomeasure.estimators.mixins module
    • DiscreteMIMixin
    • DiscreteTEMixin
    • EffectiveValueMixin
      • EffectiveValueMixin.effective_val()
    • RandomGeneratorMixin
    • StatisticalTestingMixin
      • StatisticalTestingMixin.statistical_test()
    • WorkersMixin
  • Module contents
• infomeasure.utils package
  • Submodules
  • infomeasure.utils.config module
    • Config
      • Config.get()
      • Config.get_logarithmic_unit()
      • Config.get_logarithmic_unit_description()
      • Config.reset()
      • Config.set()
      • Config.set_log_level()
      • Config.set_logarithmic_unit()
  • infomeasure.utils.data module
    • DiscreteData
      • DiscreteData.K
      • DiscreteData.N
      • DiscreteData.counts
      • DiscreteData.data
      • DiscreteData.distribution_dict
      • DiscreteData.from_counts()
      • DiscreteData.from_data()
      • DiscreteData.probabilities
      • DiscreteData.uniq
    • StatisticalTestResult
      • StatisticalTestResult.confidence_interval()
      • StatisticalTestResult.method
      • StatisticalTestResult.n_tests
      • StatisticalTestResult.null_mean
      • StatisticalTestResult.null_std
      • StatisticalTestResult.observed_value
      • StatisticalTestResult.p_value
      • StatisticalTestResult.percentile()
      • StatisticalTestResult.t_score
      • StatisticalTestResult.test_values
  • infomeasure.utils.exceptions module
    • TheoreticalInconsistencyError
  • infomeasure.utils.types module
  • Module contents
    • Config
      • Config.get()
      • Config.get_logarithmic_unit()
      • Config.get_logarithmic_unit_description()
      • Config.reset()
      • Config.set()
      • Config.set_log_level()
      • Config.set_logarithmic_unit()

Module contents

infomeasure package.

class infomeasure.Config

Bases: object

Configuration settings for the package.

This class provides configuration settings for the package. The settings are stored as class attributes and can be accessed and modified using the class methods.

Default settings:

• base: “e” (nats)

• statistical_test_method: “permutation_test”

• statistical_test_n_tests: 200

Attributes:

_settingsdict

A dictionary containing the configuration settings.

Methods

get(key)	Get the value of a configuration setting.
get_logarithmic_unit()	Get the logarithmic unit for entropy calculations.
get_logarithmic_unit_description()	Get the description of the logarithmic unit for entropy calculations.
reset()	Reset the configuration settings to the default values.
set(key, value)	Set the value of a configuration setting.
set_log_level(level)	Set the logging level for the package.
set_logarithmic_unit(unit)	Set the base for the logarithmic unit.

classmethod get(key: str)

Get the value of a configuration setting.

Parameters:

keystr

The key of the configuration setting.

Returns:

Any

The value of the configuration setting.

classmethod get_logarithmic_unit() → str

Get the logarithmic unit for entropy calculations.

Returns:

str

The logarithmic unit.

classmethod get_logarithmic_unit_description() → str

Get the description of the logarithmic unit for entropy calculations.

Returns:

str

The description of the logarithmic unit.

Raises:

ValueError

If there is no description for the logarithmic unit.

classmethod reset()

Reset the configuration settings to the default values.

classmethod set(key: str, value)

Set the value of a configuration setting.

Parameters:

keystr

The key of the configuration setting.

valueAny

The value to set the configuration setting to.

Raises:

KeyError

If the key is not recognised.

TypeError

If the value is not of the correct type.

static set_log_level(level: int | str) → None

Set the logging level for the package.

Parameters:

levelint | str

The logging level. See the logging module for more information.

Raises:

ValueError

If the level is not a valid logging level.

classmethod set_logarithmic_unit(unit: str)

Set the base for the logarithmic unit.

The base determines the logarithmic unit used for entropy calculations:

• ‘bits’ or ‘shannons’ (base 2)

• ‘nats’ (base e)

• ‘hartleys’, ‘bans’, or ‘dits’ (base 10)

Alternatively, you can set the base directly using the ‘base’ key, via set().

Parameters:

unitstr

The logarithmic unit to set. Use ‘bit(s)’ or ‘shannon(s)’ for base 2, ‘nat(s)’ for base e, and ‘hartley(s)’, ‘ban(s)’, or ‘dit(s)’ for base 10.

Raises:

ValueError

If the unit is not recognised.

infomeasure.cmi(*data, **kwargs: any)

Conditional mutual information between two variables given a third variable.

See mutual_information for more information.

infomeasure.conditional_mutual_information(*data, **kwargs: any)

Conditional mutual information between two variables given a third variable.

See mutual_information for more information.

infomeasure.conditional_transfer_entropy(*data, **kwargs: any)

Conditional transfer entropy between two variables given a third variable.

See transfer_entropy for more information.

infomeasure.cross_entropy(*data, **kwargs: any)

Calculate the cross-entropy using a functional interface of different estimators.

See entropy() for more details on the parameters and returns.

infomeasure.cte(*data, **kwargs: any)

Conditional transfer entropy between two variables given a third variable.

See transfer_entropy for more information.

infomeasure.entropy(*data, approach: str, **kwargs: any)

Calculate the (joint) entropy using a functional interface of different estimators.

Supports the following approaches:

1. ansb: Asymptotic NSB entropy estimator.

2. bayes: Bayesian entropy estimator.

3. bonachela: Bonachela entropy estimator.

4. [chao_shen, cs]: Chao-Shen entropy estimator.

5. [chao_wang_jost, cwj]: Chao Wang Jost entropy estimator.

6. discrete: Discrete entropy estimator.

7. grassberger: Grassberger entropy estimator.

8. kernel: Kernel entropy estimator.

9. [metric, kl]: Kozachenko-Leonenko entropy estimator.

10. [miller_madow, mm]: Miller-Madow entropy estimator.

11. nsb: NSB (Nemenman-Shafee-Bialek) entropy estimator.

12. [ordinal, symbolic, permutation]: Ordinal / Permutation entropy estimator.

13. renyi: Renyi entropy estimator.

14. [shrink, js]: Shrinkage (James-Stein) entropy estimator.

15. tsallis: Tsallis entropy estimator.

16. zhang: Zhang entropy estimator.

For the discrete Shannon entropy this is

\[\texttt{im.entropy(data_X, approach="discrete")} = H(X) = -\sum_{x \in X} p(x) \log p(x).\]

Where for \(H(x)\), the estimated pmf \(p(x)\) belongs to the RV \(X\).

\[\texttt{im.entropy(data_P, data_Q, ...)} = H_Q(P) = H_\times(P, Q) = -\sum_{x \in X} p(x) \log q(x)\]

For the cross-entropy \(H_Q(P)\), the estimated pmf \(p(x)\) belongs to the RV \(P\) and \(q(x)\) to the RV \(Q\). For other approaches, this formula is generalized in different forms.

Parameters:

*dataarray_like

The data used to estimate the entropy. For entropy, this can be an array-like. For joint entropy, pass the joint values inside a tuple. For cross-entropy, pass two separate parameters.

approachstr

The name of the estimator to use.

**kwargs: dict

Additional keyword arguments to pass to the estimator.

Returns:

float

The calculated entropy.

Raises:

ValueError

If the estimator is not recognised.

infomeasure.estimator(*data, cond=None, measure: str = None, approach: str = None, step_size: int = 1, prop_time: int = 0, src_hist_len: int = 1, dest_hist_len: int = 1, cond_hist_len: int = 1, **kwargs: any) → EstimatorType

Get an estimator for a specific measure.

This function provides a simple interface to get an Estimator for a specific measure.

If you are only interested in the global result, use the functional interfaces:

• entropy

• cross_entropy

• mutual_information

• conditional_mutual_information

• transfer_entropy

• conditional_transfer_entropy

Estimators available:

1. Entropy:

   • ansb: Asymptotic NSB entropy estimator.

   • bayes: Bayesian entropy estimator.

   • bonachela: Bonachela entropy estimator.

   • [chao_shen, cs]: Chao-Shen entropy estimator.

   • [chao_wang_jost, cwj]: Chao Wang Jost entropy estimator.

   • discrete: Discrete entropy estimator.

   • grassberger: Grassberger entropy estimator.

   • kernel: Kernel entropy estimator.

   • [metric, kl]: Kozachenko-Leonenko entropy estimator.

   • [miller_madow, mm]: Miller-Madow entropy estimator.

   • nsb: NSB (Nemenman-Shafee-Bialek) entropy estimator.

   • [ordinal, symbolic, permutation]: Ordinal / Permutation entropy estimator.

   • renyi: Renyi entropy estimator.

   • [shrink, js]: Shrinkage (James-Stein) entropy estimator.

   • tsallis: Tsallis entropy estimator.

   • zhang: Zhang entropy estimator.

2. Mutual Information:

   • ansb: Asymptotic NSB mutual information estimator.

   • bayes: Bayesian mutual information estimator.

   • bonachela: Bonachela mutual information estimator.

   • chao_shen: Chao-Shen mutual information estimator.

   • chao_wang_jost: Chao Wang Jost mutual information estimator.

   • discrete: Discrete mutual information estimator.

   • grassberger: Grassberger mutual information estimator.

   • kernel: Kernel mutual information estimator.

   • [metric, ksg]: Kraskov-Stoegbauer-Grassberger mutual information estimator.

   • [miller_madow, mm]: Miller-Madow mutual information estimator.

   • nsb: NSB (Nemenman-Shafee-Bialek) mutual information estimator.

   • [ordinal, symbolic, permutation]: Ordinal mutual information estimator.

   • renyi: Renyi mutual information estimator.

   • shrink: Shrinkage (James-Stein) mutual information estimator.

   • tsallis: Tsallis mutual information estimator.

   • zhang: Zhang mutual information estimator.

3. Transfer Entropy:

   • ansb: Asymptotic NSB transfer entropy estimator.

   • bayes: Bayesian transfer entropy estimator.

   • bonachela: Bonachela transfer entropy estimator.

   • chao_shen: Chao-Shen transfer entropy estimator.

   • chao_wang_jost: Chao Wang Jost transfer entropy estimator.

   • discrete: Discrete transfer entropy estimator.

   • grassberger: Grassberger transfer entropy estimator.

   • kernel: Kernel transfer entropy estimator.

   • [metric, ksg]: Kraskov-Stoegbauer-Grassberger transfer entropy estimator.

   • [miller_madow, mm]: Miller-Madow transfer entropy estimator.

   • nsb: NSB (Nemenman-Shafee-Bialek) transfer entropy estimator.

   • [ordinal, symbolic, permutation]: Ordinal transfer entropy estimator.

   • renyi: Renyi transfer entropy estimator.

   • shrink: Shrinkage (James-Stein) transfer entropy estimator.

   • tsallis: Tsallis transfer entropy estimator.

   • zhang: Zhang transfer entropy estimator.

Parameters:

*data

The data used to estimate the measure. For entropy: a single array-like data. A tuple of data for joint entropy. For cross-entropy: two array-like data. Second input RV relative to the first. For mutual information: arbitrary number of array-like data. For transfer entropy: two array-like data. Source and destination.

condarray_like, optional

Only if the measure is conditional transfer entropy.

measurestr

The measure to estimate. Options: entropy, cross_entropy, mutual_information, transfer_entropy, conditional_mutual_information, conditional_transfer_entropy; aliases: h, hx, mi, te, cmi, cte.

approachstr

The name of the estimator to use. Find the available estimators in the docstring of this function.

*args: tuple

Additional arguments to pass to the estimator.

**kwargs: dict

Additional keyword arguments to pass to the estimator.

Returns:

Estimator

The estimator instance.

Raises:

ValueError

If the measure is not recognised.

infomeasure.get_estimator_class(measure=None, approach=None) → EstimatorType

Get estimator class based on the estimator name and approach.

This function returns the estimator class based on the measure and approach provided. If you want an instance of an estimator, initialized with data and parameters, use the functional interface estimator().

Parameters:

measurestr

The measure to estimate. Options: entropy, mutual_information, transfer_entropy, conditional_mutual_information, conditional_transfer_entropy. Aliases: h, mi, te, cmi, cte.

approachstr

The name of the estimator to use.

Returns:

class

The estimator class.

Raises:

ValueError

If the measure is not recognized.

ValueError

If the approach is not recognized.

infomeasure.h(*data, approach: str, **kwargs: any)

Calculate the (joint) entropy using a functional interface of different estimators.

Supports the following approaches:

1. ansb: Asymptotic NSB entropy estimator.

2. bayes: Bayesian entropy estimator.

3. bonachela: Bonachela entropy estimator.

4. [chao_shen, cs]: Chao-Shen entropy estimator.

5. [chao_wang_jost, cwj]: Chao Wang Jost entropy estimator.

6. discrete: Discrete entropy estimator.

7. grassberger: Grassberger entropy estimator.

8. kernel: Kernel entropy estimator.

9. [metric, kl]: Kozachenko-Leonenko entropy estimator.

10. [miller_madow, mm]: Miller-Madow entropy estimator.

11. nsb: NSB (Nemenman-Shafee-Bialek) entropy estimator.

12. [ordinal, symbolic, permutation]: Ordinal / Permutation entropy estimator.

13. renyi: Renyi entropy estimator.

14. [shrink, js]: Shrinkage (James-Stein) entropy estimator.

15. tsallis: Tsallis entropy estimator.

16. zhang: Zhang entropy estimator.

For the discrete Shannon entropy this is

\[\texttt{im.entropy(data_X, approach="discrete")} = H(X) = -\sum_{x \in X} p(x) \log p(x).\]

Where for \(H(x)\), the estimated pmf \(p(x)\) belongs to the RV \(X\).

\[\texttt{im.entropy(data_P, data_Q, ...)} = H_Q(P) = H_\times(P, Q) = -\sum_{x \in X} p(x) \log q(x)\]

For the cross-entropy \(H_Q(P)\), the estimated pmf \(p(x)\) belongs to the RV \(P\) and \(q(x)\) to the RV \(Q\). For other approaches, this formula is generalized in different forms.

Parameters:

*dataarray_like

The data used to estimate the entropy. For entropy, this can be an array-like. For joint entropy, pass the joint values inside a tuple. For cross-entropy, pass two separate parameters.

approachstr

The name of the estimator to use.

**kwargs: dict

Additional keyword arguments to pass to the estimator.

Returns:

float

The calculated entropy.

Raises:

ValueError

If the estimator is not recognised.

infomeasure.hx(*data, **kwargs: any)

Calculate the cross-entropy using a functional interface of different estimators.

See entropy() for more details on the parameters and returns.

infomeasure.jensen_shannon_divergence(*data, approach: str | None = None, **kwargs)

Calculate the Jensen-Shannon Divergence between two or more distributions.

The Jensen-Shannon Divergence is a symmetrized and smoothed version of the Kullback-Leibler Divergence. It is calculated as the average of the Kullback-Leibler Divergence between each distribution and the average distribution.

\[JSD(P \| Q) = \frac{1}{2} KL(P \| M) + \frac{1}{2} KL(Q \| M)\]

where \(M = \frac{1}{2} (P + Q)\).

Parameters:

parray_like

The first data.

qarray_like

The second data.

…array_like

Further data to compare.

approachstr

The name of the entropy estimator to use.

**kwargsdict

Additional keyword arguments to pass to the entropy estimator.

Returns:

float

The Jensen-Shannon Divergence.

Raises:

ValueError

If the approach is not supported or the entropy estimator is not compatible with the Jensen-Shannon Divergence.

ValueError

If any of the given data is not an array-like object.

infomeasure.jsd(*data, approach: str | None = None, **kwargs)

Calculate the Jensen-Shannon Divergence between two or more distributions.

The Jensen-Shannon Divergence is a symmetrized and smoothed version of the Kullback-Leibler Divergence. It is calculated as the average of the Kullback-Leibler Divergence between each distribution and the average distribution.

\[JSD(P \| Q) = \frac{1}{2} KL(P \| M) + \frac{1}{2} KL(Q \| M)\]

where \(M = \frac{1}{2} (P + Q)\).

Parameters:

parray_like

The first data.

qarray_like

The second data.

…array_like

Further data to compare.

approachstr

The name of the entropy estimator to use.

**kwargsdict

Additional keyword arguments to pass to the entropy estimator.

Returns:

float

The Jensen-Shannon Divergence.

Raises:

ValueError

If the approach is not supported or the entropy estimator is not compatible with the Jensen-Shannon Divergence.

ValueError

If any of the given data is not an array-like object.

infomeasure.kld(data_p, data_q, approach: str = '', **kwargs)

Calculate the Kullback-Leibler Divergence between two distributions.

The Kullback-Leibler Divergence is a measure of the difference between two probability distributions. It is calculated as the expectation of the logarithm of the ratio of the probability of two events. To calculate, we use the identity of combining the joint and marginal entropies:

\[KL(P \| Q) = \sum_{x \in X} P(x) \log \left( \frac{P(x)}{Q(x)} \right) = H_Q(P) - H(P)\]

Parameters:

data_parray_like

The first data.

data_qarray_like

The second data.

approachstr

The name of the entropy estimator to use.

**kwargsdict

Additional keyword arguments to pass to the entropy estimator.

Returns:

float

The Kullback-Leibler Divergence.

Raises:

ValueError

If the approach is not supported or the entropy estimator is not compatible with the Kullback-Leibler Divergence.

infomeasure.kullback_leiber_divergence(data_p, data_q, approach: str = '', **kwargs)

Calculate the Kullback-Leibler Divergence between two distributions.

The Kullback-Leibler Divergence is a measure of the difference between two probability distributions. It is calculated as the expectation of the logarithm of the ratio of the probability of two events. To calculate, we use the identity of combining the joint and marginal entropies:

\[KL(P \| Q) = \sum_{x \in X} P(x) \log \left( \frac{P(x)}{Q(x)} \right) = H_Q(P) - H(P)\]

Parameters:

data_parray_like

The first data.

data_qarray_like

The second data.

approachstr

The name of the entropy estimator to use.

**kwargsdict

Additional keyword arguments to pass to the entropy estimator.

Returns:

float

The Kullback-Leibler Divergence.

Raises:

ValueError

If the approach is not supported or the entropy estimator is not compatible with the Kullback-Leibler Divergence.

infomeasure.mi(*data, approach: str, **kwargs: any)

Calculate the mutual information using a functional interface of different estimators.

Supports the following approaches:

1. ansb: Asymptotic NSB mutual information estimator.

2. bayes: Bayesian mutual information estimator.

3. bonachela: Bonachela mutual information estimator.

4. chao_shen: Chao-Shen mutual information estimator.

5. chao_wang_jost: Chao Wang Jost mutual information estimator.

6. discrete: Discrete mutual information estimator.

7. grassberger: Grassberger mutual information estimator.

8. kernel: Kernel mutual information estimator.

9. [metric, ksg]: Kraskov-Stoegbauer-Grassberger mutual information estimator.

10. [miller_madow, mm]: Miller-Madow mutual information estimator.

11. nsb: NSB (Nemenman-Shafee-Bialek) mutual information estimator.

12. [ordinal, symbolic, permutation]: Ordinal mutual information estimator.

13. renyi: Renyi mutual information estimator.

14. shrink: Shrinkage (James-Stein) mutual information estimator.

15. tsallis: Tsallis mutual information estimator.

16. zhang: Zhang mutual information estimator.

Parameters:

*dataarray_like

The data used to estimate the (conditional) mutual information.

condarray_like, optional

The conditional data used to estimate the conditional mutual information.

approachstr

The name of the estimator to use.

normalizebool, optional

If True, normalize the data before analysis. Default is False. Not available for the discrete estimator.

**kwargs: dict

Additional keyword arguments to pass to the estimator.

Returns:

float

The calculated mutual information.

Raises:

ValueError

If the estimator is not recognised.

infomeasure.mutual_information(*data, approach: str, **kwargs: any)

Calculate the mutual information using a functional interface of different estimators.

Supports the following approaches:

1. ansb: Asymptotic NSB mutual information estimator.

2. bayes: Bayesian mutual information estimator.

3. bonachela: Bonachela mutual information estimator.

4. chao_shen: Chao-Shen mutual information estimator.

5. chao_wang_jost: Chao Wang Jost mutual information estimator.

6. discrete: Discrete mutual information estimator.

7. grassberger: Grassberger mutual information estimator.

8. kernel: Kernel mutual information estimator.

9. [metric, ksg]: Kraskov-Stoegbauer-Grassberger mutual information estimator.

10. [miller_madow, mm]: Miller-Madow mutual information estimator.

11. nsb: NSB (Nemenman-Shafee-Bialek) mutual information estimator.

12. [ordinal, symbolic, permutation]: Ordinal mutual information estimator.

13. renyi: Renyi mutual information estimator.

14. shrink: Shrinkage (James-Stein) mutual information estimator.

15. tsallis: Tsallis mutual information estimator.

16. zhang: Zhang mutual information estimator.

Parameters:

*dataarray_like

The data used to estimate the (conditional) mutual information.

condarray_like, optional

The conditional data used to estimate the conditional mutual information.

approachstr

The name of the estimator to use.

normalizebool, optional

If True, normalize the data before analysis. Default is False. Not available for the discrete estimator.

**kwargs: dict

Additional keyword arguments to pass to the estimator.

Returns:

float

The calculated mutual information.

Raises:

ValueError

If the estimator is not recognised.

infomeasure.te(*data, approach: str, **kwargs: any)

Calculate the transfer entropy using a functional interface of different estimators.

Supports the following approaches:

1. ansb: Asymptotic NSB transfer entropy estimator.

2. bayes: Bayesian transfer entropy estimator.

3. bonachela: Bonachela transfer entropy estimator.

4. chao_shen: Chao-Shen transfer entropy estimator.

5. chao_wang_jost: Chao Wang Jost transfer entropy estimator.

6. discrete: Discrete transfer entropy estimator.

7. grassberger: Grassberger transfer entropy estimator.

8. kernel: Kernel transfer entropy estimator.

9. [metric, ksg]: Kraskov-Stoegbauer-Grassberger transfer entropy estimator.

10. [miller_madow, mm]: Miller-Madow transfer entropy estimator.

11. nsb: NSB (Nemenman-Shafee-Bialek) transfer entropy estimator.

12. [ordinal, symbolic, permutation]: Ordinal transfer entropy estimator.

13. renyi: Renyi transfer entropy estimator.

14. shrink: Shrinkage (James-Stein) transfer entropy estimator.

15. tsallis: Tsallis transfer entropy estimator.

16. zhang: Zhang transfer entropy estimator.

Parameters:

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.

approachstr

The name of the estimator to use.

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.

prop_timeint, optional

Number of positions to shift the data arrays relative to each other. Delay/lag/shift between the variables. Default is no shift. Assumed time taken by info to transfer from source to destination. Not compatible with the cond parameter / conditional TE. Alternatively called offset.

*args: tuple

Additional arguments to pass to the estimator.

**kwargs: dict

Additional keyword arguments to pass to the estimator.

Returns:

float

The calculated transfer entropy.

Raises:

ValueError

If the estimator is not recognised.

infomeasure.transfer_entropy(*data, approach: str, **kwargs: any)

Calculate the transfer entropy using a functional interface of different estimators.

Supports the following approaches:

1. ansb: Asymptotic NSB transfer entropy estimator.

2. bayes: Bayesian transfer entropy estimator.

3. bonachela: Bonachela transfer entropy estimator.

4. chao_shen: Chao-Shen transfer entropy estimator.

5. chao_wang_jost: Chao Wang Jost transfer entropy estimator.

6. discrete: Discrete transfer entropy estimator.

7. grassberger: Grassberger transfer entropy estimator.

8. kernel: Kernel transfer entropy estimator.

9. [metric, ksg]: Kraskov-Stoegbauer-Grassberger transfer entropy estimator.

10. [miller_madow, mm]: Miller-Madow transfer entropy estimator.

11. nsb: NSB (Nemenman-Shafee-Bialek) transfer entropy estimator.

12. [ordinal, symbolic, permutation]: Ordinal transfer entropy estimator.

13. renyi: Renyi transfer entropy estimator.

14. shrink: Shrinkage (James-Stein) transfer entropy estimator.

15. tsallis: Tsallis transfer entropy estimator.

16. zhang: Zhang transfer entropy estimator.

Parameters:

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.

approachstr

The name of the estimator to use.

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.

prop_timeint, optional

Number of positions to shift the data arrays relative to each other. Delay/lag/shift between the variables. Default is no shift. Assumed time taken by info to transfer from source to destination. Not compatible with the cond parameter / conditional TE. Alternatively called offset.

*args: tuple

Additional arguments to pass to the estimator.

**kwargs: dict

Additional keyword arguments to pass to the estimator.

Returns:

float

The calculated transfer entropy.

Raises:

ValueError

If the estimator is not recognised.