Quiz 2: Reduce 3-gram to 2-gram

Quiz 2: Reduce 3-gram to 2-gram

by Pingsheng Li -
Number of replies: 8

Hi,

I have a question for the following question. Since the question asks about all possible ways we can compute the prob. I think 3-gram can be reduced to 2-gram by marginalization. So the marked choice might also be valid? Since other correct options also consider marginalization sometimes.


In reply to Pingsheng Li

Re: Quiz 2: Reduce 3-gram to 2-gram

by Jean-Cédric Chappelier -
Here it's a 3-gram model, so you can not get rid of w_{i-2} in the conditioning. (marginalization deals with the part BEFORE the conditioning, not after)
In reply to Jean-Cédric Chappelier

Re: Quiz 2: Reduce 3-gram to 2-gram

by Pingsheng Li -

Sorry for not explaining clearer. I simply mean here in the slide, since the 3 gram parameters P(aaa)...P(zzz) already give us the ability to compute parameters of 2-gram parameters P(aa)...P(zz) by marginalization. So it is possible to compute the probability in a 2-gram fashion when we have the parameters of 3-grams. It's also possible to rewrite the 2-gram form to the 3-gram form by just adding more conditions too. Since the question states: select all ways to compute the max likelihood. Here I am suggesting a way to do so.


In reply to Jean-Cédric Chappelier

Re: Quiz 2: Reduce 3-gram to 2-gram

by Pingsheng Li -
Dear Professor,

Do you mind elaborating more on my question?
In reply to Pingsheng Li

Re: Quiz 2: Reduce 3-gram to 2-gram

by Jean-Cédric Chappelier -
Sorry but it's the same answer: your selected wrong answer removes values from the conditioning part (i.e. AFTER the bar), which is incorrect (and has nothing to do with marginalization).
Maybe it's better we discuss that on the blackboard.
In reply to Jean-Cédric Chappelier

Re: Quiz 2: Reduce 3-gram to 2-gram

by Pingsheng Li -

Sorry but I still think you misunderstand my point. I mean it is possible to compute the prob in 2-gram fashion in 3-gram model setting because we can first reduce the 3-gram model to 2-gram by marginalization. and the question did not constrain the way to compute this prob.

In reply to Pingsheng Li

Re: Quiz 2: Reduce 3-gram to 2-gram

by Jean-Cédric Chappelier -
I'm sorry but you don't understand my answers.

> we can first reduce the 3-gram model to 2-gram by marginalization

No, by no means!
In reply to Jean-Cédric Chappelier

Re: Quiz 2: Reduce 3-gram to 2-gram

by Pingsheng Li -
In that case, sorry I'm unsure about the trigram & bigram probability parameters mean here in this slide. Do you mind elaborate a bit more? So the parameters are only conditionals?

In reply to Pingsheng Li

Re: Quiz 2: Reduce 3-gram to 2-gram

by Jean-Cédric Chappelier -
Can't we discuss that on the board? I think it'll be more appropriate.

But in short words (maybe...; actually I'm not sure what you don't understand):
1. you cannot sum on things that are given. P(ro) above as nothing to do with e.g. P(rob), where b is given
2. don't confuse probabilities in general and parameters of the model. P(ro) above is **NOT** a parameter; P(rob) would be, for a 3-gram model