Source code for neurokit2.complexity.information_fisher

import numpy as np
import pandas as pd

from .utils_complexity_embedding import complexity_embedding

[docs] def fisher_information(signal, delay=1, dimension=2): """**Fisher Information (FI)** The Fisher information was introduced by R. A. Fisher in 1925, as a measure of "intrinsic accuracy" in statistical estimation theory. It is central to many statistical fields far beyond that of complexity theory. It measures the amount of information that an observable random variable carries about an unknown parameter. In complexity analysis, the amount of information that a system carries "about itself" is measured. Similarly to :func:`SVDEn <entropy_svd>`, it is based on the Singular Value Decomposition (SVD) of the :func:`time-delay embedded <complexity_embedding>` signal. The value of FI is usually anti-correlated with other measures of complexity (the more information a system withholds about itself, and the more predictable and thus, less complex it is). See Also -------- entropy_svd, information_mutual, complexity_embedding, complexity_delay, complexity_dimension Parameters ---------- signal : Union[list, np.array, pd.Series] The signal (i.e., a time series) in the form of a vector of values. delay : int Time delay (often denoted *Tau* :math:`\\tau`, sometimes referred to as *lag*) in samples. See :func:`complexity_delay` to estimate the optimal value for this parameter. dimension : int Embedding Dimension (*m*, sometimes referred to as *d* or *order*). See :func:`complexity_dimension` to estimate the optimal value for this parameter. Returns ------- fi : float The computed fisher information measure. info : dict A dictionary containing additional information regarding the parameters used to compute fisher information. Examples ---------- .. ipython:: python import neurokit2 as nk signal = nk.signal_simulate(duration=2, frequency=5) fi, info = nk.fisher_information(signal, delay=10, dimension=3) fi """ # Sanity checks if isinstance(signal, (np.ndarray, pd.DataFrame)) and signal.ndim > 1: raise ValueError( "Multidimensional inputs (e.g., matrices or multichannel data) are not supported yet." ) embedded = complexity_embedding(signal, delay=delay, dimension=dimension) W = np.linalg.svd(embedded, compute_uv=False) W /= np.sum(W) # normalize singular values FI_v = (W[1:] - W[:-1]) ** 2 / W[:-1] return np.sum(FI_v), {"Dimension": dimension, "Delay": delay, "Values": FI_v}