Hidden Markov Model vs. Markov Model

Attribute	Hidden Markov Model	Markov Model
Observations	Observations are not directly visible	Observations are directly visible
States	States are hidden	States are visible
Transition Probabilities	Transition probabilities between hidden states	Transition probabilities between visible states
Emission Probabilities	Emission probabilities for observations given hidden states	N/A
Applications	Speech recognition, bioinformatics, etc.	Text prediction, weather forecasting, etc.

Introduction

Hidden Markov Models (HMMs) and Markov Models are both powerful tools used in various fields such as speech recognition, bioinformatics, and natural language processing. While they share similarities in their underlying principles, they also have distinct attributes that make them suitable for different applications.

Definition

A Markov Model is a stochastic model that represents a sequence of events where the probability of each event depends only on the state attained in the previous event. In contrast, a Hidden Markov Model is an extension of the Markov Model where the states are not directly observable, but the observations are dependent on the underlying states.

State Representation

In a Markov Model, the states are directly observable and can be easily identified. Each state transition is associated with a probability distribution that determines the likelihood of moving from one state to another. On the other hand, in a Hidden Markov Model, the states are hidden or latent, making it more challenging to determine the underlying state at any given time.

Observations

One of the key differences between a Markov Model and a Hidden Markov Model lies in the observations. In a Markov Model, the observations are directly related to the states, meaning that the state can be inferred from the observation. In contrast, in a Hidden Markov Model, the observations are independent of each other and are only related to the underlying states.

Applications

Markov Models are commonly used in applications where the states are easily observable and the transitions between states are well-defined. For example, they are used in weather forecasting, speech recognition, and text generation. On the other hand, Hidden Markov Models are more suitable for applications where the underlying states are hidden or unknown, such as speech recognition with background noise, gene prediction, and part-of-speech tagging.

Training

Training a Markov Model involves estimating the transition probabilities between states based on a given sequence of observations. This process is relatively straightforward since the states are observable. In contrast, training a Hidden Markov Model involves estimating both the transition probabilities between hidden states and the emission probabilities of observations given the hidden states. This process is more complex and typically requires the use of algorithms like the Baum-Welch algorithm.

Flexibility

Markov Models are less flexible compared to Hidden Markov Models in terms of modeling complex systems with hidden states. Since Hidden Markov Models allow for the incorporation of hidden states, they are more versatile and can capture the underlying structure of the system more accurately. This flexibility makes Hidden Markov Models more suitable for applications where the underlying states are not directly observable.

Conclusion

In conclusion, both Hidden Markov Models and Markov Models have their own strengths and weaknesses. Markov Models are suitable for applications where the states are observable and well-defined, while Hidden Markov Models excel in modeling systems with hidden states. Understanding the differences between these two models is crucial in choosing the right tool for a given application.