Acoustic Model and Language Model

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SUMMARY

The discussion focuses on the relationship between acoustic models and language models in the context of maximizing the conditional probability P(V|O) for vowels. The acoustic model P_AM(O|V) and language model P_LM(V) are utilized to derive the vowel V that maximizes this probability. Participants questioned the interpretation of argmax and the application of log likelihoods from a provided table, suggesting that the approach taken may be incorrect. The consensus indicates that a more thorough understanding of the argmax function and the role of log likelihoods is essential for accurate calculations.

PREREQUISITES
  • Understanding of conditional probability, specifically P(V|O)
  • Familiarity with acoustic models and language models in speech recognition
  • Knowledge of log likelihoods and their application in statistical models
  • Basic understanding of the argmax function and its significance in optimization
NEXT STEPS
  • Research the concept of argmax and its application in probability maximization
  • Study the principles of acoustic modeling and language modeling in speech recognition systems
  • Learn about the role of log likelihoods in statistical inference and model evaluation
  • Explore practical examples of maximizing conditional probabilities in machine learning contexts
USEFUL FOR

Students and professionals in the fields of machine learning, speech recognition, and natural language processing who seek to understand the interplay between acoustic and language models for optimizing vowel recognition.

nao113
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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:
Screenshot 2023-04-25 at 19.26.03.png


My Answer:
WhatsApp Image 2023-04-25 at 19.32.30.jpeg


Is it correct? Thank you
 
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nao113 said:
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?
 
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)).
Screenshot 2023-04-26 at 17.05.46.png

Screenshot 2023-04-26 at 17.06.12.png

Screenshot 2023-04-26 at 17.05.55.png
 
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.
 

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