Q$1$: The following sentence is partially tagged with POS Tags, where "bear" can be either a VB $($verb$)$ or a NN $($noun$)$:

Your$/$Which formulas can calculate the most probable tag sequence for "bear"?

$1)$ P$($bear$|$NN$)*$ P$($NN$|$VB$)*$P$($VB$|$NN$)$

$2)$ P$($bear$|$VB$)*$P$($VB$|$MD$)*$P$($NN$|$VB$)$

$3)$ P$($will$|$MD$)*$P$($bear$|$VB$)*$ P$($fruit$|$NN$)$

$4)$ P$($NN$|$NN$)*$ P$($NN$|$MD$)*$P$($bear$|$NN$)$

$5)$ P$($bear$|$VB$)*$P$($VB$|$NN$)*$P$($VB$|$MD$)$PPR$ efforts$/$NN will$/$MD bear$/?$ fruit$/$NN$.$

A$.2,4$

B$.1,5$

C$.3,5$

D$.1,2$

E$.4,5$

Q$2$: The following sentence is partially tagged with POS Tags, where "race" can be either a VB $($verb$)$ or a NN $($noun$)$:

Secretariat$/$NNP is$/$VBZ expected$/$VBN to$/$TO race$/?$ tomorrow$/$NR$.$

Which formulas can calculate the most probable tag sequence for "race"?

Q$3$: What is cosine similarity? How to calculate it$?$

Q$4$: TF$-$IDF helps to establish how important a particular word is in the context of the document corpus. TF$-$IDF takes into account the number of times the word appears in the document and is offset by the number of documents that appear in the corpus.

$$ TF is the frequency of terms divided by the total number of terms in the document.

$$ IDF is obtained by dividing the total number of documents by the number of documents containing the term and then taking the logarithm of that quotient.

$$ TF$-$IDF is then the multiplication of two values TF and IDF.

Suppose that we have term count tables of a corpus consisting of only two documents, as in the picture $($table$)$:

Calcuate TF$-$IDFs for the term $$example$$ for Document $1$ and Document $2,$ respectively.

Q$5$: Describe Yarowsky's $(1995)$ technique for word sense disambiguation and illustrate how it would disambiguate the following two senses of "sake":

Sense $1$: sake, interest $($a reason for wanting something done: "for your sake", "died for the sake of his country"$)$

Sense $2$: sake, saki, rice beer $($Japanese alcoholic beverage made from fermented rice, usually served hot$)$

Q$6$: Suppose you want to develop a new approach to summarization that extracts phrases rather than full sentences and puts together the phrases to form a sentence for the summary. Many summarization systems use language models. Please clearly explain your algorithm. You can draw a diagram of the summarization system architecture to help you answer this question.