Baum-Welch Gamma Step

Problem

Compute the Baum-Welch E-step state posteriors gamma for one time step: gamma[i] = alpha[i] * beta[i] / sum over j of alpha[j] * beta[j], where alpha and beta are the forward and backward probabilities.

Return a zero vector when the total is zero.

Hint

Gamma is the normalized product of the forward and backward messages.

Test cases

case 1

in: [[0.5,0.5],[0.4,0.6]]

expected: [0.4,0.6]

case 2

in: [[1,2,3],[1,1,1]]

expected: [0.16666666666666666,0.3333333333333333,0.5]

case 3

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

expected: [0,0]

case 4

in: [[2,1],[3,3]]

expected: [0.6666666666666666,0.3333333333333333]

Starter codePython

def baum_welch_gamma(alpha, beta):
    # Your code here
    pass

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