Acoustic Model and Language Model

[nao113]

Homework Statement

Suppose 𝑉 is a vowel and 𝑂 is a feature vector.
Suppose that 𝑃 AM (𝑂|𝑉) is an acoustic model and 𝑃 𝐿M (𝑉) is a language model. Obtain a vowel 𝑉 that maximizes 𝑃(𝑉|𝑂) when the acoustic and language model log likelihoods are given in the following table.

Relevant Equations

W: a vowel v (v ∊ {a,i,u,e,o})
O: a feature vector

Question:

My Answer:

Is it correct? Thank you

 

[Mark44]

Homework Statement: Suppose 𝑉 is a vowel and 𝑂 is a feature vector.
Suppose that 𝑃 AM (𝑂|𝑉) is an acoustic model and 𝑃 𝐿M (𝑉) is a language model. Obtain a vowel 𝑉 that maximizes 𝑃(𝑉|𝑂) when the acoustic and language model log likelihoods are given in the following table.
Relevant Equations: W: a vowel v (v ∊ {a,i,u,e,o})
O: a feature vector

Question:
View attachment 325473

My Answer:
View attachment 325474

Is it correct? Thank you

No idea without some more context.
Is P(V|O) a conditional probability?
What does argmax mean?
How did you go from $P(V|O)$ to $\frac{P(O|V)P(V)}{P(O)}$ in the 2nd line of your work and similar for the 3rd line?
What role do the numbers in the log table play?

 

[nao113]

This is the reference that I got, I don t know about what argmax mean here, so I assumed it has the same meaning as log e (P(V|O)).

 

[Mark44]

What you've posted so far doesn't give any definition of "argmax". In your work that you showed in post #1, you added the numbers in the first row of the table to get one sum, and then added the numbers in the second row to get another sum. You then multiplied the two sums.

Given that I know nothing more about this than what you posted, I think your work is incorrect. My guess, and this is only a guess, is that to maximize $P(O|W)P(O)$ what you need to do is to look at the five separate products of the numbers in the five columns, and pick whichever one is the largest. You might get better advice by contacting your instructor.