Can any one clear me the concept of hidden markov model?

[dexterdev]

Hi friends,
I have an idea what a markov chain is. But when it comes to HMM (hidden markov model) I have a doubt regarding emission matrix. What is emission matrix? I have an idea of transition matrix , current states etc. when coming to simulation (using Matlab) I don't have a choice of ordinary markov chains, only HMM is available. why is it so?

I would like to learn markov chains because of its applications in prediction and music etc.

-Devanand T

 

[MarneMath]

The emission matrix is one of the parameter for a hidden markov. Basically, you have the transition matrix with N possible states that at time t, the hidden variable can take. The transition from t to t + 1 the variable can take on N possible choices for each state, thus there exist N^2 'transition possibilities'. The key rule for the transition matrix is that for each transition, the transitions probability must sum to 1 and this must hold for every transition. What we end up with is a N X N stochastic matrix with a total of N(N-1) transition parameter.

The emission matrix is collection of emission probabilities. Each state is given an emission probability, where each state has a possible emission probability. This is a bit more tricky to handle. The set is determined by the size of the observable data, you typically have to relate them to a distribution. The common ways would be the categorical distribution and Gaussian distribution.

All this becomes more clear with an example. The most common one would be weather forecast. If no one else comes to clear up my muddy explanation, I'll post a concrete example.

As for why matlab, I imagine the reason why they format it as a HMM is because in one way you can view a typical markov chain is an hidden markov model without the uncertainty of the output.

 

[dexterdev]

Thank you for the reply , I will wait for the example... :)