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Forward-backward algorithm

Forward-backward algorithm. CS 5368 Yin Lu 10/28/2010. Outline. HMM Definition Problem Forward probability Backward probability. HMM Definition. Set of N states: Set of M observations: State transition probabilities: Observation/emission probabilities in state j: Initial state:

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Forward-backward algorithm

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  1. Forward-backward algorithm CS 5368 Yin Lu 10/28/2010

  2. Outline • HMM Definition • Problem • Forward probability • Backward probability

  3. HMM Definition Set of N states: Set of M observations: State transition probabilities: Observation/emission probabilities in state j: Initial state: Entire tuple:

  4. Problem Given: Estimate: - Ot is one of the symbols from V. T is the number of observations in the sequence - Given a model and a sequence of observations, how to compute the probability that the observed sequence was produced by the model

  5. Forward probability The probability of producing O1…t while ending up in state Si

  6. Calculating forward probability Initialization: Induction: Termination:

  7. Calculating forward probability • Induction Step: - To calculate the probability of getting to a state through all paths, we can calculate the probability of each path to that state and sum them

  8. Calculating forward probability • Induction Step:

  9. Calculating forward probability • Termination :

  10. Backward probability • The probability of producing the sequence from t+1 to the end, given that at time t, we are at state Si.

  11. Calculating backward probability Initialization: Induction:

  12. Calculating backward probability • Induction Step:

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