1. Ambiguity in POS Tagging

Sentence:

They can fish in the can.

• Task: Identify ambiguous words and list all possible POS tags for each.
• Explain: How does context help determine the correct POS sequence?

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2. Emission and Transition Probabilities

Training Corpus:

Sentence
The/DET dog/NOUN barks/VERB loudly/ADV
A/DET cat/NOUN sleeps/VERB peacefully/ADV
The/DET cat/NOUN barks/VERB
Dogs/NOUN sleep/VERB

Questions:

A. Calculate:

• P(dog | NOUN)
• P(cat | NOUN)

B. Calculate:

• P(VERB | NOUN)
• P(ADV | VERB)

C. Which transition is more likely:

• NOUN → VERB
• VERB → ADV?

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3. Viterbi Algorithm Application

Sentence:

The dog sleeps

Probability Matrices:

Transition Probabilities:

• P(NOUN | DET) = 0.8
• P(VERB | NOUN) = 0.6
• P(END | VERB) = 0.9

Emission Probabilities:

• P(the | DET) = 0.7
• P(dog | NOUN) = 0.4
• P(sleeps | VERB) = 0.5

Task:
Show your step-by-step calculations to find the most likely POS tag sequence using the Viterbi algorithm.

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4. POS Tag Ambiguity

POS-tagged Sentences:

          Sentence 1: I/PRON will/AUX park/VERB the/DET car/NOUN
          Sentence 2: The/DET park/NOUN is/VERB beautiful/ADJ
          Sentence 3: Park/PROPN Avenue/PROPN is/VERB busy/ADJ
          

• Task: Are there any words that appear with different POS tags?
• Explain: How does an HMM handle such ambiguities?

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5. HMM Design and Probability Calculation

Mini Tagset:
{DET, NOUN, VERB}

Training Sentences:

• The/DET boy/NOUN runs/VERB
• A/DET girl/NOUN walks/VERB
• The/DET dog/NOUN sleeps/VERB
• The/DET cat/NOUN jumps/VERB

Tasks:

• Calculate all transition probabilities:
  A = {a_i,j}
• Calculate all emission probabilities for the word "the"
• Calculate initial state probabilities:
  π = {π_i}

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