Home / Questions / In this problem, we would like to look at the Hidden Markov Model HMM Assume that we have...
In this problem, we would like to look at the Hidden Markov Model (HMM).
(a) Assume that we have the following data available for us to estimate the model parameters:
State sequence 
Observation sequence 
(X, Y, Z, X) 
(c, b, a, b) 
(X,Z,Y) 
(a, b, a) 
(Z,Y, X, Z,Y) 
(b, a, c,b,c) 
(Z, X,Y) 
(c, a,b) 
Clearly state what are the parameters associated with the HMM. Under the maximum likelihood estimation (MLE), what would be the optimal model parameters? Fill up the following emission probability table. Use the space below to clearly show how each emission parameter is estimated exactly.
bu(o) u/o 
a 
b 
c 
X 



Y 



Z 



(b) Now, consider you are given the following new observation sequence with two observations only (a, b), and the following model parameters, compute the following joint probability of the observation sequence using some algorithm that we have discussed in class. Clearly present the steps that lead to your final answer.
au,v u/v 
X 
Y 
Z 
STOP 
START 
0.1 
0.0 
0.9 
0.0 
X 
0.0 
0.5 
0.1 
0.4 
Y 
0.3 
0.0 
0.3 
0.4 
Z 
0.6 
0.4 
0.0 
0.0 
bu(o) u/o 
a 
b 
c 
X 
0.7 
0.3 
0.0 
Y 
0.8 
0.0 
0.2 
Z 
0.1 
0.5 
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