probabilistic lexicalized context-free grammars - METU Computer ...

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PROBABILISTIC LEXICALIZED CONTEXT
-
FREE GRAMMARS



İbrahim Alız




Department of Computer Engineering ,

Middle East Technical University ( METU)

ibrahim_aliz@yahoo.com






“With enough knowledge we can

figure out the probability of just about anything.”

Referring to the moral here, it didn’t get to much time for computer linguists to use the
power of probability for parsing, to deal with the
ambiguities in natural language
understanding task.

Probabili
stic parsing is a key contribution to disambiguation. Choose the
most probable parse as the answer, so simple. However, additionally, using the help of
subcategorization and lexical dependency information and so of probabilistic lexicalized
context
-
free gr
ammars (PLCFG) which is

an extension to the probabilis
t
i
c

context free
grammars (PCFG) one

can get better results. This pa
per gives a brief description on

the
principles of PLCFG, and then g
ives a suggestion, for an implementation

on
a PLCFG
within

a l
imited Turkish lexicon and grammar.


An easy way to think of a lexicalized grammar is as a context free grammar with a lot
more rules; it is as if we created many copies of each rule, one copy for each possible
headword for each constituent. In general, i
t will be to costly to keep all these rules around
but thinking lexicalized grammars this way makes it clearer that we can parse them with
standard CFG parsing algorithms. As an example for a sentence like “what does your student
want to write” we have the

following parsing results.


Lexicalized parse tree

(write, what
, S

write
S
)
,

(write, does
, S


does
S
)
,

(write, student
, S


NP VP
)
,

(student, your
, NP


your student)
,

(write, want
, VP

want
VP
)
,

(write, to
, VP

to write),



Usage of a lexical head (most
important item for the constituent) for each constituent
is the main idea while extending a PCFG to a lexicalized PCFG. For example the head of a
noun phrase is the main noun typically the rightmost one

(e.g. student for “your student”)
.
More generally, he
ads are computed bottom up and the head of a constituent c is a
deterministic function of the rule used to expand c. For example the c is expanded using

s


np vp, the function would indicate that one should find the head of the c by looking for
the head

of the vp.











Lexicalized statistical parsers collect, to a first approximation, two kinds of

statistics. One relates the head of a phrase to the rule used to expand the phrase, which we
denote p(r | h), and the other relates the head of a phras
e to the head of a subphrase, which we
denote p(h | m, t), where h is the head of the subphrase, m the head of the mother phrase, and t
the type of subphrase. Therefore , for a lexicalized parser to find the probability of a
corresponding parse we use the
following formula, i
f s is the entire sentence, π

is a particular
parse of s, c range
s over the constituents of π
, and r(c) is the rule used to expand c, then



p
(s,

π
) =

c
p(h(c)|m(c)) * p(r(c)|h(c))


Here we first find the probability of the head of t
he constituent h(c) given the head of the
mother m(c) and then the probability of the rule r(c) given the head
of c.



However, before

parsing we
have to train the parser using a pre

p
arsed training corpus,
referring to the Charniak’s work
*

on statistical

parsing

which also uses two more equations
on calculating the probability for individual rules and on their dependencies
, meanin
g to give
the necessary probabilities to the rules
.



Thus,
having the primitive probabilities approximated by

the lexical dep
endencies
between the

words in the training corpus
, subcategorized on the word affinities,

we can
calcul
ate

the probability of each parse

using the above

formula. H
aving enough information
on the basics of
PLCFG
, my aim is

to develop a LPCFG parser on a s
pecified Turkish
grammar
&

lexicon
.




As it is a natural tendency to calculate the probabilities

with the proven phsycological
results on human parsing,
both with the lexical dependency another determining factor in
human parsing,
it is not shocking that
parsers that are implementations of lexicalized PCFG
have a success rate 88%. With more intelligent machines
pushing the tight limits every day on
Natural Language Processing topics, the LPCFG’s are an importmant phase on getting the
moral of understand
ing human speech recognition and parsing.




References



Statistical Techniques for Natural Language Parsing

Eugene Charniak, Department of Computer Science, Brown University



*
Statistical Parsing with a Context Free Grammar and Word Statistics

Eugene Charniak, Department of Computer Science, Brown University



Speech and Language Processing, Jurafsky and Martino, Prentice Hall 2000



A Model of Syntactic Disambiguation Based on Lexicalized Grammars

Yusuke Miyao, Deparment of Computer Science, Unive
rsity of Tokyo

Jun’ichi Tsujii, Department of Computer Science, University of Tokyo