Information Plane Point

Problem

Return the information plane coordinates [H(T), I(T; Y)] in bits for a representation T defined by the encoder pt_given_x[x][t] on the joint pxy. H(T) is the entropy of the marginal over t and I(T; Y) is computed from the coarsened joint p(t, y).

Hint

The information plane tracks how much a layer remembers and how much it predicts.

Test cases

case 1

in: [[[0.5,0],[0,0.5]],[[1,0],[0,1]]]

expected: [1,1]

case 2

in: [[[0.5,0],[0,0.5]],[[0.5,0.5],[0.5,0.5]]]

expected: [1,0]

case 3

in: [[[0.4,0.1],[0.1,0.4]],[[0.9,0.1],[0.1,0.9]]]

expected: [1,0.1732536275073823]

case 4

in: [[[1,0],[0,1]],[[0,1],[1,0]]]

expected: [0,0]

Starter codePython

import math
def information_plane_point(pxy, pt_given_x):
    # Your code here
    pass

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