Hidden Markov Model

Question

I am trying to construct a Hidden Markov Model to predict the next state to go to.

I am doing an example system, or, a test system that contains the following:

Ok so the training I have used is:

training = "HTTHTTTHHTTHTTTHHTTHTTTHHTTHTTTHHTTHTTTHHTTHTTTHHTTHTTTHHTTHTTTH"

and the test case is:

"HTHTTHTHTTHTHTHTHTTHHTHTHTTHTHTTHHT"

I assign the values to these, so like:

1, 'H', 0.5

2, 'H', 0.75

3, 'H', 0.25

1, 'T', 0.5

2, 'T', 0.25

3, 'T', 0.75

I compute the forward probability, this gives a result of: 0.25

And the viberti algorithm is used to find the best path:

 2 , 3 , 3 , 2 , 3 , 3 , 3 , 2 , 2 , 3 , 3 , 2 , 3 , 3 , 3 , 2 , 2 , 3 , 3 , 2 
 , 3 , 3 , 3 , 2 , 2 , 3 , 3 , 2 , 3 , 3 , 3 , 2 , 2 , 3 , 3 , 2 , 3 , 3 , 3 , 
 2 , 2 , 3 , 3 , 2 , 3 , 3 , 3 , 2 , 2 , 3 , 3 , 2 , 3 , 3 , 3 , 2 , 2 , 3 , 3 
 , 2 , 3 , 3 , 3 , 2

The confusion is how to do I determine which is the next sequence from the Viberti Algorithm? It gives values of (2, 3) BUT, I do not know whether these are H, or T.

Anyone offer any help?

Answer 1

You don't need to use the Viterbi algorithm to do what you want to do.

You have only two possible outcomes: T or H. So train a model on your training sequence (not sure if this is the numbers you give - it looks like emission probabilities for 3 states, but you don't mention a transition matrix and how you derived these probabilities...), and then compute the probability of the observation sequence test + 'H' and test + 'T' - whichever has the highest score is the prediction. Cf "problem 1" in the classic Rabiner tutorial.