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Hidden Markov model

Hidden Markov model. Application of the conditional probability. Markov Chains. Weather forecast problem From history, P( weather tomorrow |weather today ): Given today as sunny (S) what is the probability that the next following five days are S , C , C , R and S, having the above model?.

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Hidden Markov model

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  1. Hidden Markov model Application of the conditional probability

  2. Markov Chains • Weather forecast problem From history, P(weathertomorrow|weathertoday): • Given today as sunny (S) what is the probability that the next following five days are S , C , C , R and S, having the above model?

  3. Markov Chains • We are looking for is the weather conditional probability P(Tomorrow/Today). • Assumption: tomorrow’s weather depends only on today’s condition => first order Markov chain. • P(q1=S,q2=S ,q3= C ,q4= C ,q5= R ,q6=S)= P(S)*P(S|S)*P(C|S) *P(C|C)*P(R|C)*P(S|R) =1*0.7*0.2*0.8*0.15*0.15 =0.0052

  4. Hidden Markov Model • We don’t know exactly what is the next state. • aij=P(j|i) S1 S2 S3 S4 S5 1,2,3

  5. Hidden Markov Model • Start at S1, end at S5. Pick balls 6 times. What is the sequence of ball’s color? • Pick 1: S1 Sequence={ } ,R,G,Y,G,R R Go to S2….Repeat until finishing 4 balls For picking up the 5th ball, do the same except finding next state because we need to finish at S5. Random next state (aij) 2

  6. Application of HMM • Speech recognition

  7. Application of HMM S1 S2 S3 S4 S5 Silent Consonant A-Z Vowel A,E,I,O,U Final A-Z Silent a21 a32 a43 a54 a22 a33 a44 a11

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