spkit.mutual_info_diff

spkit.mutual_info_diff(X, Y, present_first=True)

Mutual Information \(I_{\partial}(X_{i+1}; X_i, Y_i)\)

Mutual Information

Predictibility of \(X(i+1)\) given \(X(i)\) and \(Y(i)\)

\[I_{\partial}(X_{i+1}; X_i, Y_i) = H_{\partial}(X_{i+1}) - H_{\partial}(X_{i+1} | X_i, Y_i)\]
\[H_{\partial}(X_{i+1}|X_i,Y_i) = H_{\partial}(X_{i+1},X_i,Y_i) - H_{\partial}(X_i,Y_i)\]
Parameters:
X: 2d-array,

  • multi-dimentional signal space, where each column (axis=1) are the delayed signals

Y: 2d-array,

  • multi-dimentional signal space, where each column (axis=1) are the delayed signals

present_first: bool, default=True

  • if True, X[:,0] is present, and X[:,1:] is past, in incresing order

  • if True, X[:,-1] is present, and X[:,:-1] is past

Returns:
I_x1y: scaler

  • Mutual Information

See also

mutual_info_diff_self

Self-Mutual Information

entropy_diff_joint

Joint-Entropy

References

  • wiki

Examples

#sp.mutual_info_diff
import numpy as np
import matplotlib.pyplot as plt
import spkit as sp
X, fs, ch_names = sp.data.eeg_sample_14ch()
X = X - X.mean(1)[:, None]
# Example 1
X1 = sp.signal_delayed_space(X[:,0].copy(),emb_dim=5,delay=2)
Y1 = sp.signal_delayed_space(X[:,2].copy(),emb_dim=5,delay=2)
Y2 = sp.add_noise(Y1,snr_db=0)
I_xy1 = sp.mutual_info_diff(X1,Y1)
I_xy2 = sp.mutual_info_diff(X1,Y2)
print('Mutual-Information')
print(f'- I(X1,Y1) = {I_xy1}')
print(f'- I(X1,Y2) = {I_xy2}')