Hidden Markov model

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HiddenMarkovModel

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HMMGraph

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hmm temporal bayesian net

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HMMsequence

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A profile HMM modelling a multiple sequence alignment

Hidden Markov Model (HMM) is a statistical model that is used to describe the evolution of observable events that depend on internal factors, which are not directly observable. It is a powerful tool for pattern recognition and is widely used in various fields such as speech recognition, bioinformatics, weather forecasting, and finance.

Overview

A Hidden Markov Model is characterized by:

• A set of states, each of which is associated with a probability distribution. Transitions among these states are governed by a set of probabilities called transition probabilities.
• A sequence of observable events, where each event is a result of an internal state. These observable events are produced with certain probability distributions that depend on the current state of the model, known as emission probabilities.

The "hidden" part of the name comes from the fact that the state of the model is not directly visible to the observer; instead, the observer can only see the sequence of events produced by the model.

Components of HMM

An HMM can be fully described by the following components:

• States: The finite set of states of the Markov process. These states are not observable directly.
• Observations: The set of possible observations, which can be directly seen.
• Transition probabilities: The probabilities of transitioning from one state to another.
• Emission probabilities: The probabilities of an observation being generated from a state.
• Initial state probabilities: The probabilities of the system being in a certain state when the process starts.

Applications

• Speech Recognition: HMMs are used to model the sequence of speech signals and recognize spoken words or phrases.
• Bioinformatics: In bioinformatics, HMMs help in modeling the sequences of proteins and nucleic acids to predict their structure and function.
• Weather Forecasting: HMMs can model sequences of weather observations to predict future weather conditions.
• Finance: In finance, HMMs are applied to model and predict sequences of market conditions or stock prices.

Training HMMs

Training an HMM involves estimating the transition and emission probabilities based on observed sequences. The most common algorithm for training HMMs is the Baum-Welch algorithm, a special case of the Expectation-Maximization algorithm.

Decoding HMMs

Decoding involves determining the most likely sequence of states given a sequence of observations. The Viterbi algorithm is widely used for decoding, providing an efficient way to find the most likely sequence of hidden states.

Limitations and Extensions

While HMMs are powerful, they have limitations, such as the assumption of the Markov property and the independence of observations. Extensions like the Generalized Hidden Markov Model (GHMM) and the Hierarchical Hidden Markov Model (HHMM) have been developed to overcome some of these limitations.

Conclusion

Hidden Markov Models are a fundamental tool in the field of pattern recognition and have been successfully applied in numerous domains. Their ability to model time-dependent sequences makes them particularly useful in areas where understanding the underlying process is as crucial as observing the outcomes.

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