Hidden Markov Models

ByMaravar Kannan

Markov Chain

• A Markov chain named after Andrey Markov, is a mathematical system that undergoes transitions from one state to another, between a finite or countable number of possible states.

• It is a random process usually characterized as memoryless:

• the next state depends only on the current state and not on the sequence of events that preceded it. This specific kind of "memorylessness" is called the Markov property.

Discrete –Time Markov Process

• Discrete –Time Markov Process (discrete-time Markov chain or DTMC) is When a Markov Chain result is considered at a finite interval.

• What is the probality that the weather for 8 consecutive days is“Sun-Sun-Sun-Rain-Rain-Sun-Cloudy-Sun”

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Discrete –Time Markov Process

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Extension to Hidden Markov Model

• Now, we extend the concept of Markov models to include the case in which the observation is a probabilistic function of the state-that is, the resulting model (which is Hidden Markov model) is a doubly embedded stochastic process with an underlying stochastic process that is not directly Observed only through another set of stochastic processes that produce the sequence of observations.

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Extension to Hidden Markov Model

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The Urn-and-Ball Model

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Elements of an HMM

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Types of HMMs

Implementation Issues for HMMs

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Scaling

Multiple Observation Sequences

Initial Estimates of HMM Parameters

Effect of Insufficient Training Data

Choice of Model

Conclusion• The conclusion of this study of recognition and hidden

markov model has been carried out to develop a voice based user machine interface system. In various applications we can use this user machine system and can take advantages as real interface, these application can be related with disable persons those are unable to operate computer through keyboard and mouse, these type of persons can use computer with the use of Automatic Speech Recognition system, with this system user can operate computer with their own voice commands (in case of speaker dependent and trained with its own voice samples). Second application for those computer users which are not comfortable with English language and feel good to work with their native language i.e. English, Punjabi, Hindi

Thank You

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