Mutual Information

Mutual Information#

Mutual Information (MI) measures the amount of information obtained about one random variable through observing another random variable.

import delaynet as dn

# Calculate mutual information
result = dn.connectivity(
    ts1, ts2, metric="mutual_information", approach="kernel", lag_steps=5
)

or more involved with ordinal mutual information

import delaynet as dn

# Calculate transfer entropy
result = dn.connectivity(
    ts1,
    ts2,
    metric="mutual_information",
    approach='ordinal',
    lag_steps=5,
    embedding_dim=3
)

Parameters:

  • approach: The approach to use for estimating mutual information. For available approaches, find the string in infomeasure.mutual_information().

  • lag_steps: Time lags to consider. An integer will consider lags [1, …, lag_steps]. Passing a list will consider the specified values as lags.

  • hypothesis_type: Type of hypothesis test to use (‘permutation_test’ or ‘bootstrap’). Default is ‘permutation_test’.

  • n_tests: Number of iterations or resamples to perform within the hypothesis test. Default is 20.

  • Additional keyword arguments are passed directly to the mutual information estimator.

connectivities.mutual_information(ts2, approach: str = '', lag_steps: int | list = None, hypothesis_type: str = 'permutation_test', n_tests: int = 20, **mi_kwargs)

Mutual Information (MI) connectivity metric [ButhAZ25].

Parameters:

  • ts1 (numpy.ndarray) – First time series.

  • ts2 (numpy.ndarray) – Second time series.

  • approach (str) – Approach to use. See infomeasure.mutual_information() for available approaches.

  • lag_steps (int | list) – Time lags to consider. Can be a single integer or a list of integers. An integer will consider lags [1, …, lag_steps]. A list will consider the specified values as lags.

  • hypothesis_type (str) – Type of hypothesis test to use. Either ‘permutation_test’ or ‘bootstrap’. Default is ‘permutation_test’.

  • n_tests (int) – Number of iterations or resamples to perform within the hypothesis test.

  • mi_kwargs – Additional keyword arguments for the mutual information estimator.

Returns:

Best p-value and corresponding lag.

Return type:

tuple[float, int]

Raises:

ValueError – If approach is not given.