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Questions and Answers
A statistical model used to model systems that are assumed to be ______ processes with unobservable states.
A statistical model used to model systems that are assumed to be ______ processes with unobservable states.
Markov
The ______ state sequence can be recovered from the observable outputs.
The ______ state sequence can be recovered from the observable outputs.
hidden
The ______ are unobservable states that the system can be in.
The ______ are unobservable states that the system can be in.
hidden states
The ______ are observable outputs of the system.
The ______ are observable outputs of the system.
The ______ are probabilities of transitioning from one hidden state to another.
The ______ are probabilities of transitioning from one hidden state to another.
HMMs are used to model the ______ patterns of speech and recognize spoken words.
HMMs are used to model the ______ patterns of speech and recognize spoken words.
HMMs are used to model the ______ of language and perform tasks such as part-of-speech tagging.
HMMs are used to model the ______ of language and perform tasks such as part-of-speech tagging.
The ______ algorithm is used to compute the posterior probabilities of the hidden states given the observations.
The ______ algorithm is used to compute the posterior probabilities of the hidden states given the observations.
The ______ algorithm is used to find the most likely hidden state sequence given the observations.
The ______ algorithm is used to find the most likely hidden state sequence given the observations.
HMMs are used to model the ______ of DNA and protein sequences.
HMMs are used to model the ______ of DNA and protein sequences.
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Study Notes
Hidden Markov Models (HMMs)
Definition
- A statistical model used to model systems that are assumed to be Markov processes with unobservable states.
- The model can be used to recover the hidden state sequence from the observable outputs.
Key Components
- Hidden States (Q): unobservable states that the system can be in
- Observations (O): observable outputs of the system
- Transition Probabilities (A): probabilities of transitioning from one hidden state to another
- Emission Probabilities (B): probabilities of observing a particular output given a hidden state
- Initial State Probabilities (Ï€): probabilities of starting in a particular hidden state
Types of HMMs
- Basic HMM: simplest form of HMM, where the hidden states and observations are discrete
- Continuous HMM: hidden states and observations are continuous
- Hierarchical HMM: multiple levels of hidden states
Applications
- Speech Recognition: HMMs are used to model the acoustic patterns of speech and recognize spoken words
- Natural Language Processing: HMMs are used to model the patterns of language and perform tasks such as part-of-speech tagging
- Bioinformatics: HMMs are used to model the patterns of DNA and protein sequences
Algorithms
- Forward-Backward Algorithm: used to compute the posterior probabilities of the hidden states given the observations
- Viterbi Algorithm: used to find the most likely hidden state sequence given the observations
- Baum-Welch Algorithm: used to re-estimate the HMM parameters given a set of observations
Hidden Markov Models (HMMs) Definition
- A statistical model used to model systems that are assumed to be Markov processes with unobservable states.
- Used to recover the hidden state sequence from the observable outputs.
Key Components
- Hidden States (Q): unobservable states that the system can be in.
- Observations (O): observable outputs of the system.
- Transition Probabilities (A): probabilities of transitioning from one hidden state to another.
- Emission Probabilities (B): probabilities of observing a particular output given a hidden state.
- Initial State Probabilities (Ï€): probabilities of starting in a particular hidden state.
Types of HMMs
- Basic HMM: simplest form of HMM, where the hidden states and observations are discrete.
- Continuous HMM: hidden states and observations are continuous.
- Hierarchical HMM: multiple levels of hidden states.
Applications
- Speech Recognition: HMMs are used to model the acoustic patterns of speech and recognize spoken words.
- Natural Language Processing: HMMs are used to model the patterns of language and perform tasks such as part-of-speech tagging.
- Bioinformatics: HMMs are used to model the patterns of DNA and protein sequences.
Algorithms
- Forward-Backward Algorithm: used to compute the posterior probabilities of the hidden states given the observations.
- Viterbi Algorithm: used to find the most likely hidden state sequence given the observations.
- Baum-Welch Algorithm: used to re-estimate the HMM parameters given a set of observations.
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