The Hidden Markov model

In the previous section, we discussed DBNs. In this section, we will discuss one particular variant of it, called the Hidden Markov model (HMM). Although named the Hidden Markov model, it is not a Markov network. Its etymology comes from the fact that the HMM satisfies the Markov property.

A Markov property basically indicates the memory-less property of a stochastic process, and any stochastic process satisfying this property is called as a Markov process. Let be a time-continuous process. Then, for every , time points with states . Then, . This means that the current state depends only on the previous state; any additional knowledge about the history doesn't add any extra information.

For example, if we sample the mood of a person once a minute, then it is fair to assume that the current mood of the person is only affected by his/her mood in the previous minute (unless that person is suffering from bipolar disorder). In the case of predicting the trajectory of a...