Solve the Soft Decoding Problem solved by 173

Soft Decoding Problem

Given: A string x, followed by the alphabet Σ from which x was constructed, followed by the states States, transition matrix Transition, and emission matrix Emission of an HMM (Σ, States, Transition, Emission).

Return: The probability Pr(π_i = k|x) that the HMM was in state k at step i (for each state k and each step i).

Sample Dataset

zyxxxxyxzz
--------
x   y   z
--------
A   B
--------
    A   B
A   0.911   0.089
B   0.228   0.772
--------
    x   y   z
A   0.356   0.191   0.453 
B   0.04    0.467   0.493

Sample Output

A   B 
0.5438  0.4562 
0.6492  0.3508 
0.9647  0.0353 
0.9936  0.0064 
0.9957  0.0043 
0.9891  0.0109 
0.9154  0.0846 
0.964   0.036 
0.8737  0.1263 
0.8167  0.1833

Extra Dataset

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