HIDDEN MARKOV MODEL Application of the conditional probability.
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Transcript of HIDDEN MARKOV MODEL Application of the conditional probability.
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HIDDEN MARKOV MODELApplication of the conditional probability
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Markov Chains
Weather forecast problemFrom 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?
Tomorrow
Today
Weather Sunny Cloudy Rainy
Sunny 0.7 0.2 0.1
Cloudy 0.05 0.8 0.15
Rainy 0.15 0.25 0.6
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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
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Hidden Markov Model
We don’t know exactly what is the next state.
aij=P(j|i)
S1 S2 S5S4S3
1,2,3
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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
2Go to S2….Repeat until finishing 4 ballsFor picking up the 5th ball, do the same exceptfinding next state because we need to finish at S5.
,R,G,Y,G,R
Random next state (aij)
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Application of HMM
Speech recognition
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Application of HMM
Silent
Consonant
A-Z
Vowel
A,E,I,O,U
Final
A-ZSilent
S1 S2 S3 S4 S5
a21
a11a22
a32 a43 a54
a33 a44