HIDDEN MARKOV MODEL Application of the conditional probability.

HIDDEN MARKOV MODELApplication 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

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

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

Hidden Markov Model

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

aij=P(j|i)

S1 S2 S5S4S3

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)

Application of HMM

Speech recognition

Application of HMM

Silent

Consonant

A,E,I,O,U

A-ZSilent

S1 S2 S3 S4 S5

a11a22

a32 a43 a54

a33 a44

HIDDEN MARKOV MODEL Application of the conditional probability.

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