1. Bayan Turki Bagasi

2.  Introduction  Generating a Test Sequence  Estimating the State Sequence  Estimating Transition and Emission Matrices  Estimating Posterior State Probabilities

3.  Observe a sequence of emissions  Do not know the sequence of states the model went through to generate the emissions.

4.  Analyses of hidden Markov models seek to recover the sequence of states from the observed data.

5.  The model uses:  A red die, having six sides, labeled 1 through 6.  A green die, having twelve sides, five of which are labeled 2 through 6, while the remaining seven sides are labeled 1.

6.  A weighted red coin, for which the probability of heads is.9 and the probability of tails is.1.  A weighted green coin, for which the probability of heads is.95 and the probability of tails is.05.  a Markov model with two states and six possible emissions.

8.  The model creates a sequence of numbers from the set {1, 2, 3, 4, 5, 6} with the following rules:  Begin by rolling the red die and writing down the number that comes up, which is the emission.  Toss the red coin and do one of the following:  If the result is heads, roll the red die and write down the result.  If the result is tails, roll the green die and write down the result.

9.  At each subsequent step, you flip the coin that has the same color as the die you rolled in the previous step.  If the coin comes up heads, roll the same die as in the previous step.  If the coin comes up tails, switch to the other die.

10. Green coinRed coin 0.10.9Red coin 0.950.05green coin

11. 4 32 1 56

12.  The model is not hidden because you know the sequence of states from the colors of the coins and dice

13.  Given a sequence of emissions  what is the most likely state path?  how can you estimate transition and emission probabilities of the model?  What is the forward probability that the model generates a given sequence?  What is the posterior probability that the model is in a particular state at any point in the sequence

14.  hmmgenerate — Generates a sequence of states and emissions from a Markov model hmmgenerate  hmmestimate — Calculates maximum likelihood estimates of transition and emission probabilities from a sequence of emissions and a known sequence of states hmmestimate  hmmtrain — Calculates maximum likelihood estimates of transition and emission probabilities from a sequence of emissions hmmtrain  hmmviterbi — Calculates the most probable state path for a hidden Markov model hmmviterbi  hmmdecode — Calculates the posterior state probabilities of a sequence of emissions hmmdecode

15. TRANS = [.9.1;.05.95;]; EMIS = [1/6, 1/6, 1/6, 1/6, 1/6, 1/6;... 7/12, 1/12, 1/12, 1/12, 1/12, 1/12]; [seq,states] = hmmgenerate(100,TRANS,EMIS);  hmmgenerate begins in state 1 at step 0  Seq is 100 element from 1-6 randomly  States is 100 element 1 or 2 dependent on Seq

16.  useing the Viterbi algorithm to compute the most likely sequence of states  given sequence seq of emissions likelystates = hmmviterbi(seq, TRANS, EMIS);  likelystates is a sequence the same length as seq.

17.  compute the percentage of the actual sequence states that agrees with the sequence likelystates. sum(states==likelystates)/100 ans = 0.8200

18.  Using hmmestimate  requires that you know the sequence of states States that the model went through to generate seq. [TRANS_EST, EMIS_EST] = hmmestimate(seq, states)

19. TRANS_EST =[ 0.8989 0.1011 0.0585 0.9415] EMIS_EST = [0.1721 0.1721 0.1749 0.1612 0.1803 0.1393 0.5836 0.0741 0.0804 0.0789 0.0726 0.1104]  You can compare the outputs with the original transition and emission matrices, TRANS and EMIS

20.  Using hmmtrain If you do not know the sequence of states states, but you have initial guesses for TRANS and EMIS TRANS_GUESS = [.85.15;.1.9]; EMIS_GUESS = [.17.16.17.16.17.17;.6.08.08.08.08 08]; [TRANS_EST2, EMIS_EST2] = hmmtrain(seq, TRANS_GUESS, EMIS_GUESS)

21. Two factors reduce the reliability of the output matrices of hmmtrain:  guesses for the matrices TRANS_EST and EMIS_EST. use different  The sequence seq. use long

22.  The posterior state probabilities of an emission sequence seq are the conditional probabilities that the model is in a particular state when it generates a symbol in seq, given that seq is emitted.

23. PSTATES = hmmdecode(seq,TRANS,EMIS)  The output PSTATES is an M-by-L matrix, where M is the number of states and L is the length of seq.  PSTATES(i,j) is the conditional probability that the model is in state i when it generates the jth symbol of seq, given that seq is emitted.

24.  The most important methods can be used on recognition are :  Hmmgenrate : to test the model  Hmmtrain : to estmaite transition and emission probility from initial transtion and emission

25.  http://www.mathworks.com/help/stats/hidden -markov-models-hmm.html. (n.d.). Retrieved 11 17, 2013, from Hidden Markov Models (HMM).