The hidden Markov model

The hidden Markov model has numerous applications related to speech recognition, face identification (biometrics), and pattern recognition in pictures and videos [7:3].

A hidden Markov model consists of a Markov process (also known as a Markov chain) for observations with a discrete time. The main difference with the Markov processes is that the states are not observable. A new observation is emitted with a probability known as the emission probability each time the state of the system or model changes.

There are two sources of randomness, which are as follows:

• Transition between states

• Emission of an observation when a state is given

Let's reuse the boxes and balls example. If the boxes are hidden states (nonobservable), then the user draws the balls whose color is not visible. The emission probability is the probability b_ik =p(o_t = colork|q_t =S_i) to retrieve a ball of the color k from a hidden box I, as shown in the following diagram:

The hidden Markov model for the balls...