HMM Forward Value

Problem

Perform one scaled forward step of a hidden Markov model. Given the previous forward vector alpha_prev, the row-stochastic transition matrix, and the emission probabilities for the new observation, compute alpha_new[j] = emission[j] * sum over i of alpha_prev[i] * A[i][j], then rescale the vector to sum to one.

Return a zero vector when the total is zero.

Hint

Propagate through the transition columns first, then weight by the emission.

Test cases

case 1

in: [[0.5,0.5],[[0.9,0.1],[0.2,0.8]],[0.6,0.4]]

expected: [0.6470588235294118,0.35294117647058826]

case 2

in: [[0.3,0.7],[[0.8,0.2],[0.1,0.9]],[0.5,0.5]]

expected: [0.31,0.69]

case 3

in: [[0.5,0.5],[[0.9,0.1],[0.2,0.8]],[0,0]]

expected: [0,0]

case 4

in: [[1,0],[[1,0],[0,1]],[0.3,0.7]]

expected: [1,0]

Starter codePython

def hmm_forward_value(alpha_prev, transition, emission):
    # Your code here
    pass

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