####
G22.2590 - Natural Language Processing -- Spring 2005 -- Prof. Grishman

###
Assignment #9

1. [2 points] With the grammar
`s = np vp`

`vp = v np pp`

`vp = v np`

`np = n`

`np = n pp`

`pp = p np`

the sentence “Delis serve pizza with relish.” gets two parses.
Suppose
we were given a training corpus of 5 sentences, with their parses:
`(s (np (n Men) (pp (p of) (np (n distinction)))) (vp (v
like) (np (n broccoli))))`

`(s (np (n Men)) (vp (v like) (np (n ham) (pp (p
with) (np (n eggs))))))`

`(s (np (n Men)) (vp (v serve) (np (n ham) (pp (p
with) (np (n eggs))))))`

`(s (np (n Men)) (vp (v serve) (np (n eggs)) (pp (p with) (np (n
gusto)))))`

`(s (np (n Men)) (vp (v serve) (np (n eggs)) (pp (p
to) (np (n customers)))))`

Suppose we used these five parses to train a probabilistic CFG.
What probability would be assigned to each production? What
probability
would be assigned to the two parses for “Delis serve pizza with
relish.”?
In your calculation, consider only the probabilities of the
productions;
we are not concerned with the probabilities of generating specific
lexical
items.
2. [2 points] (a) Would the conclusion change if the
probability of the expansion of the vp
node were conditioned on the head of the vp? In other words, if we used
the conditional probability p(r(n) | n,
h(n)) only for the productions expanding vp. Show how you obtained your
conclusion (show the revised probabilities for the **vp**
productions and the two parses).

(b) Make the same comparison (between non-lexicalized and lexicalized
probabilities) for the two parses of the sentence "Men like pizza with
relish."

**Due April 18**^{th}.