spkit.entropy_diff_joint_cond

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

Joint-Conditional Entropy \(H_{\partial}(X_{i+1},Y_{i+1}|X_i,Y_i)\)

Joint-Conditional Entropy

\[H_{\partial}(X_{i+1},Y_{i+1}|X_i,Y_i) = H(X_{i+1},Y_{i+1},X_i,Y_i) - H(X_i,Y_i)\]
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:
H_x1y: scaler

  • Conditional Joint Entropy

See also

entropy_diff_joint

Joint-Entropy

References

  • wiki

Examples

#sp.entropy_diff_joint_cond
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)
H_xy1 = sp.entropy_diff_joint_cond(X1,Y1)
H_xy2 = sp.entropy_diff_joint_cond(X1,Y2)
print('Conditional Entropy')
print(f'- H(X1(i+1),Y1(i+1) | X1(i),Y1(i)) = {H_xy1}')
print(f'- H(X1(i+1),Y2(i+1) | X1(i),Y2(i)) = {H_xy2}')