A Brief Introduction To The Hidden Markov Model

 Hidden Markov Model is a markov model that is used for systems which can be interpreted as a Markov Process whose states are unobservable. A markov process is a continuous markov chain. In a Markov chain the next state only depends on the current state and not on the previous states. Generally the system is assumed to be a markov process to avoid intractability which comes with the high complexity of real life problems.

Here is an example of such a system. Here the unobserved markov chain is X, and the markov process which depends on the unobserved markov process is Y.

A Markov process is a stochastic process which follows the markov principle, i.e, the next state of the system should depend only on the current state of the system. As the name suggests stochastic process is a random process, where the next state of a system cannot be predicted just by the current state and/or the system parameters. But mathematically speaking it’s a collection of random variables that are indexed uniquely. The index set (mathematical set used to index the random variables) can be either finite or infinite. Each value in the indexed set can be interpreted as a point in time. In the case of a finite index set, the process can be classified as a discrete stochastic process. Else, if the index set is an infinite set it can be classified as a continuous stochastic process. As it is a random process, it can have multiple outcomes. A single outcome is known as realization.

Let the Markov Chain representing the system be A. Then, Hidden Markov Model assumes another markov process, say B, whose states depend on the markov process representing the system being modelled, that is, A. The objective is to learn about A using B.

For learning, in the Hidden Markov Model, several algorithms like Baum–Welch algorithm or Forward-Backward Algorithm can be used. These learning alogorithms deserves a blog of their own. 

Here are some of the applications of HMM

• Cryptanalysis
• Speech Synthesis
• Handwriting Recognition

Hope you find this blog useful. If you have any queries related to the subject, please let us know in the comments section below.