Dear Future Jeff: Doing this by hand is a bad idea. Next time, have them do a spreadsheet or a Python script. Love, Past Jeff. (Alternatively, a smaller example would be better.)
For this assignment, you will answer a few questions about a specific Hidden Markov Model. Hand in your answers on paper, and show your work.
Using the notation from Chapter 9 of Manning and Schütze, answer the following questions for the HMM μ shown below. Showing your work will include displaying diagrams of the alphas, betas, etc.
Here's the HMM in question:
S = {1, 2, 3} -- the set of states
K = {@, #, $} -- the output alphabet
π1 = 0.7
π2 = 0.2
π3 = 0.1
a11 = 0.3
a12 = 0.3
a13 = 0.4
a21 = 0.4
a22 = 0.6
a23 = 0.0
a31 = 0.0
a32 = 0.5
a33 = 0.5
b11@ = 0.6
b11# = 0.2
b11$ = 0.2
b12@ = 0.2
b12# = 0.2
b12$ = 0.6
b13@ = 0.9
b13# = 0.1
b13$ = 0.0
b21@ = 0.5
b21# = 0.5
b21$ = 0.0
b22@ = 0.1
b22# = 0.8
b22$ = 0.1
b23@ = 0.3
b23# = 0.3
b23$ = 0.4
b31@ = 0.5
b31# = 0.3
b31$ = 0.2
b32@ = 0.0
b32# = 0.1
b32$ = 0.9
b33@ = 0.0
b33# = 0.0
b33$ = 1.0
By the way, I recognize that this assignment will be somewhat tedious. However, I believe that by going through these computations a couple times by hand, you will have a much better understanding of the algorithms than you can get by watching me do it. Feel free to work with other people to check your answers, but please do dig through the details yourself.