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:
Consider
the HMM given below to solve the sequence labeling problem of POS tagging. With
that HMM, calculate the probability that the sequence of words “free workers”
will be assigned the following parts of speech;
(a)
VB NNS
(b)
JJ NNS
HMM as stochastic automata
Emission/Observation
probabilities
free

workers


JJ

0.00158

0

NNS

0

0.000385

VB

0.00145

0

VBP

0.00081

0

VBZ

0

0.00005

Solution:
(a)
Here, the word sequence “free workers” is tagged with tags VB
NNS with the meaning “to let the workers free”. The HMM
can be expressed as Bayes network for the given problem of finding the
probability P(free workers, VB NNS) as follows;
P(free
workers, VB NNS)
= P(VBstart) * P(freeVB) * P(NNSVB) * P(workersNNS)
* P(endNNS)
= 0.25 * 0.00145 * 0.85 *
0.000385 * 0.4
= 0.0000000475
= 4.75 * 10^{8}
(b)
Here, the word sequence “free workers” is tagged with tags JJ
NNS to mean that the workers those work for free. The
HMM can be expressed as Bayes network for the given problem of finding the
probability P(free workers, JJ NNS) as follows;
P(free
workers, JJ NNS)
= P(JJstart) * P(freeJJ)
* P(NNSJJ) * P(workersNNS)
* P(endNNS)
= 0.25 * 0.00158 * 0.6 * 0.000385 *
0.4
= 0.0000000365
= 3.65
* 10^{8}
*************
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