RenyiTEEstimator

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', **kwargs)

Bases: BaseRenyiTEEstimator, 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

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.