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I don't know whether this is the correct forum for this but here goes:

I'm trying to implement a Hidden Markov Model to be able to predict and find the best sequence/path for a training file.

So far, I have the mel-frequency cepstral coefficients (MFCC) of a signal, and I am looking to train this so I can then compare (two data sets) using the Viterbi algorithm to find the best path. But I have some confusions:

  1. If I estimate $\Pi$, can I then use the backward-forward algorithm to find the probabilities at a given state?

  2. Instead of using the backward-forward algorithm, can I use the Viterbi algorithm to find the probability?

  3. If I'm trying to identify two probable things (two outcomes) and N = 2 what would M be? I assume that N = states and M = observations? But, the vector I have contains: N = 13, M = 450, so these values cannot therefore be used for N->M for the HMM.

  4. Do I therefore send the training data to the forward-backward algorithms, which predicts the probability for each state, then this will give me a final output... Which I can then compare with the Viterbi de-coder?

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Unless you want to see if you can implement training and decoding algorithms of HMMs, you can easily use existing toolkits such as the HTK (HMM toolkit for speech recognition). The advantage of using this is that it makes the job easier for you. Also it has very good documentation and examples for beginners.

However, if your goal is to implement these algorithms, it requires a very good understanding of HMMs and coding skills(trust me). In order to use HMMs for useful applications, 3 basic problems have to be solved:

  1. Evaluation problem: given a set of HMMs, how to determine the probable model that generated the test data. The solution is either the forward or backward algorithm. These are iterative algorithms that make this evaluation simpler.

  2. Determining the best state sequence: this is where the hidden state is uncovered and the solution is the Viterbi algorithm.

  3. Training problem: this deals with estimating the parameters of an HMM but unlike the previous 2 problems, there is no closed form solution for this. However, the Baum-Welch algorithm is commonly used. This is a variant of the well known Expectation-Maximation (EM) algorithm.

References

Rabiner, L. 1989. A tutorial on hidden Markov models and selected appli- cations in speech recognition.

Baum, L.E., T. Petrie, G. Soules and N. Weiss. 1970. A Maximization Technique Occurring in the Statistical Analysis of Probabilistic Functions of Markov Chains. The Annals of Mathematical Statistics Vol. 41, No. 1, pp. 164-171.

Dempster, A. P., N. M. Laird, and D. B. Rubin. 1977. Maximum likeli-hood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society. Series B (Methodological) 39 (1), pp. 1-38.

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