POS tagging using Hidden Markov Model 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:

For the given HMM, show the transition and emission probability matrices. Also, calculate the probability of P(she|PRON can|NOUN run|NOUN).

Solution:

As per the HMM, the following are the transition and emission (observation) probabilities;

Transition probabilities	Emission probabilities
PRON NOUN AUX VERB Start 0.4 0.4 0.2 PRON 0.001 0.2 NOUN 0.1 0.2 AUX 0.001 0.5 VERB 0.5	she can run PRON 0.1 NOUN 0.001 0.001 AUX 0.2 VERB 0.2

Following graph shows the portion of HMM to solve the given problem;

P(she|PRON can|NOUN run|NOUN)

= P(PRON|Start) * P(she|PRON) * P(NOUN|PRON) * P(can|NOUN) * P(NOUN|NOUN) * P(run|NOUN)

= 0.4 * 0.1 * 0.001 * 0.001 * 0.1 * 0.001

= 0.000000000004

= 4*10^-12

We arrived at this value by multiplying the transition and emission probabilities.

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