Which expression corresponds to the 'Bigram calculation' for P(w1,w2,w3) as described?

Which expression corresponds to the 'Bigram calculation' for P(w1,w2,w3) as described?

• A. P(w1,w2,w3)=P(w1)⋅P(w2∣w1)⋅P(w3∣w2)
• B. P(w1,w2,w3)=P(w1)⋅P(w2∣w1)⋅P(w3)
• C. P(w1,w2,w3)=P(w1)⋅P(w2)⋅P(w3)
• D. P(w1,w2,w3)=P(w1) + P(w2∣w1) + P(w3∣w2)

Answer: (A)

Bigram calculation in language modeling uses the idea that each word mostly depends on the one before it. To find the chance of a three-word sequence w1, w2, w3, you start with the chain rule: P(w1) × P(w2|w1) × P(w3|w1, w2). But in a bigram model, you approximate P(w3|w1, w2) with P(w3|w2), treating only the immediate predecessor as relevant. Multiplying the terms gives P(w1) × P(w2|w1) × P(w3|w2), which is the expression shown. This is the correct bigram form because it uses the immediate prior word for conditioning, rather than ignoring context or conditioning on both previous words.

Bigram calculation in language modeling uses the idea that each word mostly depends on the one before it. To find the chance of a three-word sequence w1, w2, w3, you start with the chain rule: P(w1) × P(w2|w1) × P(w3|w1, w2). But in a bigram model, you approximate P(w3|w1, w2) with P(w3|w2), treating only the immediate predecessor as relevant. Multiplying the terms gives P(w1) × P(w2|w1) × P(w3|w2), which is the expression shown. This is the correct bigram form because it uses the immediate prior word for conditioning, rather than ignoring context or conditioning on both previous words.