Markov models and Hidden Markov Models (HMMs)

1. What is Markov model?

It consists of a set of states and a set of transition probabilities from one state to another.

2. How does it work? We represent the state transition probabilities in matrix form and compute the probability of the sequence as follows.

P(s1s2s3)=P(s3|s2)P(s2|s1)P(s1|start_state)

* Note: the conditional probabilities are the transition probabilities.

3. Where is it applied?

When we are given a Markov model, we can compute the probability of the sequence occurred, for example, P(s1s2s3). If we are given two models and each model represents for each class, then we can compute the probability of the sequence occurred for each class. After that, we can decide which class the sequence s1s2s3 belongs to based on the comparison of these two probabilities. The MM can be applied in speech recognition, classification of gene (DNA).

1. What is HMM?

It consists of transition probabilities; and states with the probability for each value belong to states.

2. Where is it applied? It can be applied in speech recognition.

3. How does it work?