HIDDEN MARKOV MODEL Application of the conditional probability.

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HIDDEN MARKOV MODEL Application of the conditional probability

Transcript of HIDDEN MARKOV MODEL Application of the conditional probability.

Page 1: HIDDEN MARKOV MODEL Application of the conditional probability.

HIDDEN MARKOV MODELApplication of the conditional probability

Page 2: HIDDEN MARKOV MODEL Application of the conditional probability.

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

Page 3: HIDDEN MARKOV MODEL Application of the conditional probability.

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

Page 4: HIDDEN MARKOV MODEL Application of the conditional probability.

Hidden Markov Model

We don’t know exactly what is the next state.

aij=P(j|i)

S1 S2 S5S4S3

1,2,3

Page 5: HIDDEN MARKOV MODEL Application of the conditional probability.

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)

Page 6: HIDDEN MARKOV MODEL Application of the conditional probability.

Application of HMM

Speech recognition

Page 7: HIDDEN MARKOV MODEL Application of the conditional probability.

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


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Hidden Markov Models

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