Transfer Entropy (Lag 1)

Problem

Compute the lag-1 transfer entropy in bits from X to Y given the joint joint[x_prev][y_prev][y_t]:

T = H(Y_t | Y_prev) - H(Y_t | X_prev, Y_prev)

Build the needed marginals and use entropy in bits for every term.

Hint

Transfer entropy is zero when the past of X adds nothing beyond Y's own past.

case 1

in: [[[[0.125,0.125],[0.125,0.125]],[[0.125,0.125],[0.125,0.125]]]]

expected: 0

case 2

in: [[[[0.25,0],[0.25,0]],[[0,0.25],[0,0.25]]]]

expected: 1

case 3

in: [[[[0.4,0.1],[0.1,0.4]],[[0.4,0.1],[0.1,0.4]]]]

expected: 0

case 4

in: [[[[0.15,0.1],[0.1,0.15]],[[0.05,0.2],[0.2,0.05]]]]

expected: 0.12451124978365313

Starter codePython

import math
def transfer_entropy(joint):
    # Your code here
    pass

4 test cases · run your code against them in the editor