Partofspeech tagging using Hidden Markov Model solved exercise, find the probability value of the given wordtag sequence, how to find the probability of a word sequence for a POS tag sequence
POS Tagging using Hidden Markov Model  Solved Exercise
Question:
A
Hidden Markov Model (HMM) is given in the table below;
Transition probabilities

Emission probabilities

P(NOUNPRON)=0.001
P(PRONSTART)=0.5
P(VERBAUX)=0.5
P(AUXPRON)=0.2
P(NOUNAUX)=0.001
P(VERBNOUN)=0.2
P(NOUNNOUN)=0.1

P(shePRON)=0.1
P(runVERB)=0.01
P(canAUX)=0.2
P(canNOUN)=0.001
P(runNOUN)=0.001

Calculate
the probability P(shePRON canAUX runVERB). [ Or, calculate the probability
P(she can run, PRON AUX VERB)]
Solution:
The following graph is extracted from the given HMM, to calculate the required probability;
The
probability of the given sentence can be calculated using the given bigram
probabilities as follow;
P(shePRON
canAUX runVERB)
= P(PRONSTART) *
P(shePRON) * P(AUXPRON) * P(canAUX) * P(VERBAUX) * P(runVERB)
= 0.5 * 0.1 * 0.2 * 0.2 *
0.5 * 0.01
= 0.00001
= 10^{5}
We
arrived at this value by multiplying the transition and emission probabilities.
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Go to Hidden Markov Model Formal Definition page