In a bigram language model, which expression represents the probability of the word following the previous word?

In a bigram language model, which expression represents the probability of the word following the previous word?

• A. p(the | dog)
• B. p(dog)
• C. p(dog | the)
• D. p(the, dog)

Answer: (C)

In a bigram language model, you model the probability of a word given the immediately preceding word. That means for the word that comes after the previous word, you use the conditional probability P(next_word | previous_word). Here, the previous word is "the" and the next word is "dog," so the expression is P(dog | the). This captures how likely "dog" is to follow "the" based on observed word pairs. The other options either condition on the wrong word (P(the | dog) would be the probability of "the" after "dog"), represent the unconditional likelihood of the next word P(dog) without any context, or represent the joint probability of the two-word sequence P(the, dog) without conditioning on the preceding word.

In a bigram language model, you model the probability of a word given the immediately preceding word. That means for the word that comes after the previous word, you use the conditional probability P(next_word | previous_word). Here, the previous word is "the" and the next word is "dog," so the expression is P(dog | the). This captures how likely "dog" is to follow "the" based on observed word pairs.

The other options either condition on the wrong word (P(the | dog) would be the probability of "the" after "dog"), represent the unconditional likelihood of the next word P(dog) without any context, or represent the joint probability of the two-word sequence P(the, dog) without conditioning on the preceding word.