Comparing Viterbi & Kalman Filters for Dynamic HMM

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SUMMARY

The discussion clarifies the differences between the Viterbi algorithm and the Kalman filter when modeling dynamic hidden Markov models (HMMs). The Viterbi algorithm provides the Maximum A Posteriori (MAP) estimate of hidden state variables, yielding the most likely state sequence. In contrast, the Kalman filter offers the Minimum Mean Square Error (MMSE) estimates of states based on observations, which can be concatenated for a comprehensive view. The performance of each algorithm is contingent on the nature of the underlying process, particularly when the Kalman filter assumes a discrete state space while the actual process is continuous.

PREREQUISITES
  • Understanding of Hidden Markov Models (HMMs)
  • Familiarity with the Viterbi algorithm
  • Knowledge of Kalman filtering techniques
  • Concept of Maximum A Posteriori (MAP) and Minimum Mean Square Error (MMSE) estimates
NEXT STEPS
  • Research the implementation of the Viterbi algorithm in Python using libraries like NumPy or SciPy
  • Study the Kalman filter's application in continuous state spaces
  • Explore the impact of discrete approximations on real-world processes in dynamic systems
  • Examine case studies comparing Viterbi and Kalman filter performance in various applications
USEFUL FOR

Data scientists, machine learning engineers, and researchers working with dynamic systems and hidden Markov models will benefit from this discussion.

EmmaSaunders1
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HI All,

Would someone be-able to clarify the key differences between the kalman filter (including smoothing) and Viterbi algorithm when modelling a dynamic hidden Markov chain from a results point of view.

I understand that the Viterbi algorithm will give the MAP estimate of hidden state variables given all observations, resulting in the single most likely state sequence. The kalman filter will give the individual most probable states given all observables which can be concatenated to give the most likely (in a MMSE sense) states given observations.

I am slightly confused as to which algorithm performs the best. The Viterbi algorithm is used in a discrete model, the Kalman will approach the same result as the Viterbi if the system is continuous, what if however the kalman filter you are using assumes a discrete state space but the underlying physical process is continuous?

Thanks for any help
 
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It's just like anything else. How well does the discrete approximation represent the real process? You must answer that question first and foremost.

But also look at these related PF threads.
https://www.physicsforums.com/search/25857/?q=Viterbi++Kalman&o=relevance
 

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