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Hidden markov model ppt

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Hidden markov model ppt

  1. 1. CONTENTS • Introduction • Markov Model • Hidden Markov model (HMM) • Three central issues of HMM – Model evaluation – Most probable path decoding – Model training • Application Areas of HMM • References
  2. 2. Hidden Markov Models  Hidden Markow Models: – A hidden Markov model (HMM) is a statistical model,in which the system being modeled is assumed to be a Markov process (Memoryless process: its future and past are independent ) with hidden states.
  3. 3. Hidden Markov Models  Hidden Markow Models: – Has a set of states each of which has limited number of transitions and emissions, – Each transition between states has an assisgned probability, – Each model strarts from start state and ends in end state,
  4. 4. Hidden Markov Models
  5. 5. Hidden Markov Models  Markow Models :  Talk about weather,  Assume there are three types of weather: – Sunny, – Rainy, – Foggy.
  6. 6. Markov Models  Weather prediction is about the what would be the weather tomorrow, – Based on the observations on the past.
  7. 7. Markov Models  Weather at day n is – qn depends on the known weathers of the past days (qn-1, qn-2,…) },,{ foggyrainysunnyqn∈
  8. 8. Markov Models  We want to find that: – means given the past weathers what is the probability of any possible weather of today.
  9. 9. Markov Models  Markow Models:  For example:  if we knew the weather for last three days was:  the probability that tomorrow would be is: P(q4 = | q3 = , q2 = , q1 = )
  10. 10. Markov Models  Markow Models and Assumption (cont.): – Therefore, make a simplifying assumption Markov assumption:  For sequence:  the weather of tomorrow only depends on today (first order Markov model)
  11. 11. Markov Models  Markow Models and Assumption (cont.): Examples:  HMM:
  12. 12. Markov Models  Markow Models and Assumption (cont.): Examples:  If the weather yesterday was rainy and today is foggy what is the probability that tomorrow it will be sunny?
  13. 13. Markov Models  Markow Models and Assumption (cont.): – Examples:  If the weather yesterday was rainy and today is foggy what is the probability that tomorrow it will be sunny? Markov assumption
  14. 14. Hidden Markov Models  Hidden Markov Models (HMMs): – What is HMM:  Suppose that you are locked in a room for several days,  you try to predict the weather outside,  The only piece of evidence you have is whether the person who comes into the room bringing your daily meal is carrying an umbrella or not.
  15. 15. Hidden Markov Models  Hidden Markov Models (HMMs): – What is HMM (cont.):  assume probabilities as seen in the table:
  16. 16. Hidden Markov Models  Hidden Markov Models (HMMs): – What is HMM (cont.):  Finding the probability of a certain weather  is based on the observations xi: },,{ foggyrainysunnyqn∈
  17. 17. Hidden Markov Models  Hidden Markov Models (HMMs): – What is HMM (cont.):  Using Bayes rule:  For n days:
  18. 18. Hidden Markov Models  Hidden Markov Models (HMMs): – Examples:  Suppose the day you were locked in it was sunny. The next day, the caretaker carried an umbrella into the room.  You would like to know, what the weather was like on this second day.
  19. 19. 20 Discrete Markov Processes (Markov Chains)
  20. 20. 21 Hiddden Markov Models
  21. 21. 22 Hidden Markov Models
  22. 22. 23 Hidden Markov Models
  23. 23. 24 Hidden Markov Model Examples
  24. 24. 25 Hidden Markov Models
  25. 25. 26 Hidden Markov Models
  26. 26. 27 Hidden Markov Models
  27. 27. 28 Three Fundamental Problems for HMMs
  28. 28. 29 HMM Evaluation Problem
  29. 29. 30 HMM Evaluation Problem
  30. 30. 31 HMM Evaluation Problem
  31. 31. 32 HMM Evaluation Problem
  32. 32. 33 HMM Evaluation Problem
  33. 33. 34 HMM Decoding Problem
  34. 34. 35 HMM Decoding Problem
  35. 35. 36 HMM Decoding Problem
  36. 36. 37 HMM Learning Problem
  37. 37. 38 HMM Learning Problem
  38. 38. 39 HMM Learning Problem
  39. 39. 40 HMM Learning Problem
  40. 40. Application Areas of HMM • On-line handwriting recognition • Speech recognition • Gesture recognition • Language modeling • Motion video analysis and tracking • Stock price prediction and many more….
  41. 41. References  R.O. Duda, P.E. Hart, and D.G. Stork, Pattern Classification, New York: John Wiley, 2001.  Selim Aksoy, “Pattern Recognition Course Materials”, Bilkent University, 2011.

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