Natural Language Processing · M2 · mocks

Q5 (3 marks)

M2 Mock A · core calculations

M2 · confirmed 2 + 2 + any two of 3 + 3 + 3 · worked practice

Q5

For a two-sense Naive Bayes WSD model, P(F)=P(R)=0.5. After smoothing, P(loan|F)=0.4, P(money|F)=0.3, P(loan|R)=0.1 and P(money|R)=0.1. Classify “bank” using context {loan, money} and obtain the winning sense’s posterior. (3 marks)

Given

F=financial sense; R=river sense. Two exhaustive senses; conditional independence of the context words is assumed.

To find

Two scores, selected sense and normalised posterior.

Formula and why it applies

s(c)=P(c)P(\text{loan}\mid c)P(\text{money}\mid c)LaTeX: s(c)=P(c)P(\text{loan}\mid c)P(\text{money}\mid c)
P(c\mid x)=\frac{s(c)}{s(F)+s(R)}LaTeX: P(c\mid x)=\frac{s(c)}{s(F)+s(R)}

Multiply the prior by the two likelihoods, then normalise because a posterior is requested.

Solution

Step 1. Financial score

s(F)=0.5\times0.4\times0.3=0.06LaTeX: s(F)=0.5\times0.4\times0.3=0.06

Step 2. River score

s(R)=0.5\times0.1\times0.1=0.005LaTeX: s(R)=0.5\times0.1\times0.1=0.005

Step 3. Total evidence score

0.06+0.005=0.065LaTeX: 0.06+0.005=0.065

Step 4. Normalise winner

P(F\mid x)=\frac{0.06}{0.065}=\frac{12}{13}\approx0.923077LaTeX: P(F\mid x)=\frac{0.06}{0.065}=\frac{12}{13}\approx0.923077
Financial sense; posterior ≈0.923077.