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HMM Evaluation

  1. Sep 13, 2010 #1
    Hi, all:

    about HMM Evaluation question:

    There are 3 methods to carry out HMM evaluation.
    1) forward algorithm
    2) backward algorithm
    3) forward-backward algorithm

    Sometimes, forward algorithm and backward algorithm may not give out the same result.
    Can anybody (mathematician) help to explain it clearly?

    I designed my data as: 2 hidden states, 3 observations, and the sequence if of length 4

    1) initial state probability of state 1 and 2: 0.6, 0.4 sequentially

    2) transition probability :
    from state 1 to state 1: 0.7
    from state 1 to state 2: 0.3
    from state 2 to state 1: 0.4
    from state 2 to state 2: 0.6

    3) observation probability:
    from state 1 to observation 1: 0.1
    from state 1 to observation 2: 0.4
    from state 1 to observation 3: 0.5
    from state 2 to observation 1: 0.6
    from state 2 to observation 2: 0.3
    from state 2 to observation 3: 0.1

    4) the observation sequence is known as: 0->1->2->
    that is
    observation 1 to observation 2 to observation 3 to observation 1

    According to my implementation, forward algorithm got the probability as: 0.0090887999999999993
    while backward algorithm got the probability as: 0.0090888000000000010

    I'm wondering if this is the precision problem during the computation?
    Or there are some other problems hidden in my wrong coding???
    (Sorry that I didn't afford my coding at this moment,
    I'm guessing Julius has its own HMM to have the above simple example computed)

    The difference between two probabilities using my HMM looks like a precision issue,
    but I'm just not certain about this.

    Can anybody give a hand to confirm this?

    Cheers
    JIA
     
  2. jcsd
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