POS tagging using HMM solved exercise

Part-of-speech tagging using Hidden Markov Model solved exercise, find the probability value of the given word-tag 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(VB|start) * P(free|VB) * P(NNS|VB) * P(workers|NNS)

   * P(end|NNS)

= 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(JJ|start) * P(free|JJ) * P(NNS|JJ) * P(workers|NNS)

   * P(end|NNS)

          = 0.25 * 0.00158 * 0.6 * 0.000385 * 0.4

          = 0.0000000365

          = 3.65 * 10^-8

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