Natural Language Processing · M2 · mocks

Q4 (3 marks)

M2 Mock A · core calculations

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

Q4

An HMM has P(N|start)=0.6, P(V|N)=0.5, P(end|V)=0.4, P(dogs|N)=0.5 and P(run|V)=0.8. Find the joint probability of words “dogs run” with tag path N,V, including the end transition. (3 marks)

Given

The five required transition/emission factors are supplied.

To find

P(dogs run, N V, end).

Formula and why it applies

P(w,t)=P(t_1\mid start)P(w_1\mid t_1)P(t_2\mid t_1)P(w_2\mid t_2)P(end\mid t_2)LaTeX: P(w,t)=P(t_1\mid start)P(w_1\mid t_1)P(t_2\mid t_1)P(w_2\mid t_2)P(end\mid t_2)

Transitions move between tags. Emissions generate words from tags. Include both types of factor.

Solution

Step 1. Place the factors along the path

start → N: 0.6
emit dogs: 0.5
N → V: 0.5
emit run: 0.8
V → end: 0.4

Step 2. First word contribution

0.6\times0.5=0.3LaTeX: 0.6\times0.5=0.3

Step 3. Enter V and emit run

0.3\times0.5=0.15LaTeX: 0.3\times0.5=0.15
0.15\times0.8=0.12LaTeX: 0.15\times0.8=0.12

Step 4. End the sentence

0.12\times0.4=0.048LaTeX: 0.12\times0.4=0.048
Joint path-and-word probability = 0.048. This is not a normalised posterior over tag paths.