Natural Language Processing solved MCQ - Bigram language model

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Natural Language Processing MCQ - Bigram probability calculation - solved Exercise

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1. Let us suppose that we are given a mini-corpus consisting of four sentences. Here <s> and </s> are special symbols used to mark the beginning and end of the sentences respectively.

Arrange the sentences of the corpus in ascending order of their probabilities as per bigram model.

s1: <s>Paris is beautiful</s>

s2: <s>Is Paris in Europe</s>

s3: <s>Paris is in France</s>

s4: <s>Paris is a city</s>

	Paris	is	beautiful	in	Europe	France	city	a	</s>
<s>	0.1	0.15			0.17
Paris		0.15		0.25			0
is	0.1		0.5	0.15				0.15
beautiful									0.25
in			0		0.15	0.75
Europe									0.2
France			0				0.005		0.25
city	0.04	0.15	0	0.12	0	0.15	0		0.5
a	0	0	0.1	0	0	0	0.15	0	0

a)   s1, s2, s3, s4

b)   s3, s2, s1, s4

c)    s2, s4, s3, s1

d)  s3, s2, s4, s1

 

Answer: (c) s2, s4, s3, s1 s1 : <s>Paris is beautiful</s> P(<s>Paris is beautiful</s>) = P(Paris|<s>) * P(is|Paris) * P(beautiful|is) * P(</s>|beautiful) P(<s>Paris is beautiful</s>) = 0.10 *  0.15 * 0.50 * 0.25 =  1.875 * 10-3 = 0.001875   s2 : <s>Is Paris in Europe</s> P(<s>Is Paris in Europe</s>) = P(Is|<s>) * P(Paris|Is) * P(in|Paris) * P(Europe|in) * P(</s>|Europe) P(<s>Is Paris in Europe</s>) =  0.15 *  0.10 * 0.25 * 0.15 * 0.20 = 0.1125 * 10-3 = 0.0001125   s3 :  <s>Paris is in France</s> P(<s>Paris is in France</s>) =P(Paris|<s>) * P(is|Paris) * P(in|is) * P(France|in) * P(</s>|France) P(<s>Paris is in France</s>) = 0.10 * 0.15 * 0.15 * 0.75 * 0.25 = 0.421875 * 10-3 = 0.000421875   s4 : <s>Paris is a city</s> P(<s>Paris is a city</s>) = P(Paris|<s>) * P(is|Paris) * P(a|is) *  P(city|a) * P(</s>|city) P(<s>Paris is a city</s>) = 0.10 * 0.15 * 0.15 * 0.15 * 0.50 = 0.16875 * 10-3 = 0.00016875

 

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