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Seven Lectures on Statistical Parsing
Christopher Manning
LSA Linguistic Institute 2007
LSA 354
Lecture 5
Complexity of lexicalized PCFG
parsing
B[d 1 ] C[d 2 ]
i k j
d 1
A[d 2 ]
d 2
Running time is O ( g 3 × n 5 ) !!
Time charged :
• i, k, j ⇒ n 3
• A, B, C ⇒ g 3
• Naively, g becomes huge
• d 1 , d 2 ⇒ n 2
Complexity of lexicalized PCFG
parsing
• Work such as Collins (1997) and Charniak
(1997) is O(n 5 ) – but uses heuristic search to be
fast in practice
• Eisner and Satta (2000, etc.) have explored
various ways to parse more restricted classes of
bilexical grammars in O(n 4 ) or O(n 3 ) time
• Neat algorithmic stuff!!!
• See example later from dependency parsing
A bit more on lexicalized parsing
time
Complexity of exhaustive lexicalized
PCFG parsing
100000
10000
1000
100
10
1
y = c x 5.2019
10 100
length
Refining the node expansion
probabilities
BU naive
• Charniak (1997) expands each phrase structure tree
in a single step.
• This is good for capturing dependencies between
child nodes
• But it is bad because of data sparseness
• A pure dependency, one child at a time, model is
worse
• But one can do better by in between models, such as
generating the children as a Markov process on both
sides of the head (Collins 1997; Charniak 2000)
• Cf. the accurate unlexicalized parsing discussion
1

!
Collins (1997, 1999); Bikel (2004)
• Collins (1999): also a generative model
• Underlying lexicalized PCFG has rules of form
P " L jL j#1LL 1HR1LR k#1Rk • A more elaborate set of grammar transforms
and factorizations to deal with data sparseness
and interesting linguistic properties
• So, generate each child in turn: given P has been
generated, generate H, then generate modifying
nonterminals from head-adjacent outward with
some limited conditioning
Modifying nonterminals
generated in two steps
NP(NNP–John)
!
!
P M
P M w
!
S(VBD–sat)
P H
VP(VBD–sat)
Collins model … and linguistics
• Collins had 3 generative models: Models 1 to 3
• Especially as you work up from Model 1 to 3,
significant linguistic modeling is present:
• Distance measure: favors close attachments
• Model is sensitive to punctuation
• Distinguish base NP from full NP with post-modifiers
• Coordination feature
• Mark gapped subjects
• Model of subcategorization; arguments vs. adjuncts
• Slash feature/gap threading treatment of displaced
constituents
• Didn’t really get clear gains from this.
Overview of Collins’ Model
L i generated
conditioning on
Back-off level
10
21
32
L i
L i–1
… L1
Δ
subcat
P(t h ,w h )
{subcatL } H(th ,wh )
Smoothing for head words of
modifying nonterminals
P M w (w M i |…)
M i,t M i ,coord,punc,P,H,w h,t h," M ,subcat side
Mi,t M ,coord,punc,P,H,t i h," M ,subcatside !
t M i
!
• Other parameter classes have similar or more
elaborate backoff schemes
Bilexical statistics: Is use of
maximal context of P Mw useful?
• Collins (1999): “Most importantly, the model has
parameters corresponding to dependencies
between pairs of headwords.”
• Gildea (2001) reproduced Collins’ Model 1 (like
regular model, but no subcats)
• Removing maximal back-off level from P Mw resulted in
only 0.5% reduction in F-measure
• Gildea’s experiment somewhat unconvincing to the
extent that his model’s performance was lower than
Collins’ reported results
2

Choice of heads
• If not bilexical statistics, then surely choice of
heads is important to parser performance…
• Chiang and Bikel (2002): parsers performed
decently even when all head rules were of form
“if parent is X, choose left/rightmost child”
• Parsing engine in Collins Model 2–emulation
mode: LR 88.55% and LP 88.80% on §00
(sent. len. ≤40 words)
• compared to LR 89.9%, LP 90.1%
Use of maximal context of P Mw
Back-off level
0
1
2
Total
Number of
accesses
3,257,309
24,294,084
191,527,387
219,078,780
Percentage
1.49
11.0
87.4
100.0
Number of times parsing engine was able to deliver a probability
for the various back-off levels of the mod-word generation model, P Mw ,
when testing on §00 having trained on §§02–21
Charniak (2000) NAACL:
A Maximum-Entropy-Inspired Parser
• There was nothing maximum entropy about it. It was a
cleverly smoothed generative model
• Smoothes estimates by smoothing ratio of conditional
terms (which are a bit like maxent features):
P(
t | l,
l , t , l )
• Biggest improvement is actually that generative model
predicts head tag first and then does P(w|t,…)
• Like Collins (1999)
• Markovizes rules similarly to Collins (1999)
• Gets 90.1% LP/LR F score on sentences ≤ 40 wds
p
P(
t | l,
l , t )
p
p
p
g
Full
model
No
bigrams
Use of maximal context of P Mw
[Bikel 2004]
LR
89.9
89.5
LP
90.1
90.0
CBs
0.78
0.80
0 CBs
68.8
68.0
Performance on §00 of Penn Treebank
on sentences of length ≤40 words
≤2 CBs
89.2
88.8
Bilexical statistics are used often
[Bikel 2004]
• The 1.49% use of bilexical dependencies suggests they don’t
play much of a role in parsing
• But the parser pursues many (very) incorrect theories
• So, instead of asking how often the decoder can use bigram
probability on average, ask how often while pursuing its topscoring
theory
• Answering question by having parser constrain-parse its own output
• train as normal on §§02–21
• parse §00
• feed parse trees as constraints
• Percentage of time parser made use of bigram statistics shot up to
28.8%
• So, used often, but use barely affect overall parsing accuracy
• Exploratory Data Analysis suggests explanation
• distributions that include head words are usually sufficiently similar to those
that do not as to make almost no difference in terms of accuracy
Petrov and Klein (2006):
Learning Latent Annotations
Can you automatically find good symbols?
� Brackets are known
� Base categories are known
� Induce subcategoriesInduce subcategories
� Clever split/merge category refinement
EM algorithm, like Forward-Backward for
HMMs, but constrained by tree.
X 2
X 3
Outside
X 5
X 1
X4
X 6
He was right
Inside
X 7
.
3

40
35
30
25
20
15
10
5
0
NP
VP
Number of phrasal subcategories
PP
ADVP
S
ADJP
SBAR
QP
WHNP
PRN
NX
SINV
PRT
WHPP
SQ
CONJP
FRAG
NAC
UCP
WHADVP
INTJ
SBARQ
RRC
The Latest Parsing Results…
Parser
Klein & Manning unlexicalized
2003
Matsuzaki et al. simple EM
latent states 2005
Charniak generative (“maxent
inspired”) 2000
Petrov and Klein NAACL 2007
Charniak & Johnson
discriminative reranker 2005
Treebanks
F1
≤ 40 words
86.3
86.7
90.1
90.6
92.0
WHADJP
X
ROOT
F1
all words
85.7
86.1
89.5
90.1
91.4
• Treebank and parsing experimentation has been
dominated by the Penn Treebank
• If you parse other languages, parser
performance generally heads, downhill, even if
you normalize for treebank size:
• WSJ small 82.5%
• Chinese TB 75.2%
• What do we make of this? We’re changing
several variables at once.
• “Is it harder to parse Chinese, or the Chinese
Treebank?” [Levy and Manning 2003]
• What is the basis of the structure of the Penn
English Treebank anyway?
LST
POS tag splits, commonest words:
effectively a class-based model
� Proper Nouns (NNP):
NNP-14
NNP-12
NNP-2
NNP-1
NNP-15
NNP-3
Oct.
John
Bush
New
York
� Personal pronouns (PRP):
PRP-0
PRP-1
PRP-2
J.
It
it
it
Nov.
Robert
E.
Noriega
San
Francisco
He
he
them
Sept.
James
L.
Peters
Wall
Street
I
they
him
Treebanks and linguistic theory
TiGer Treebank
crossing branches for
discontinuous constituency types
Im
APPRART
Dat
in
MO
PP
nächsten
ADJA
Sup.Dat.
Sg.Neut
nahe
Jahr
NN
Dat.
Pl.Neut
Jahr
HD SB OC
AC NK NK NK NK NK NK
will
VMFIN
3.Sg.
Pres.Ind
wollen
die
ART
Nom.
Sg.Fem
die
S
edge labels:
syntactic functions
NP
VP
Regierung ihre
NN PPOSAT
Nom. Acc.
Sg.Fem Pl.Masc
Regierung ihr
annotation on word level:
part-of-speech,
morphology, lemmata
node labels:
phrase categories
OA
NP
Reformpläne
NN
Acc.
Pl.Masc
Plan
HD
umsetzen
VVINF
Inf
umsetzen
.
$.
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