semi-supervised approaches for learning to parse natural languages

1

Semi-Supervised Approaches for Learning to Parse

Natural Languages

Slides are from Rebecca Hwa, Ray Mooney

2

The Role of Parsing in Language Applications…

• As a stand-alone application– Grammar checking

• As a pre-processing step– Question Answering– Information extraction

• As an integral part of a model– Speech Recognition– Machine Translation

3

Parsing

• Parsers provide syntactic analyses of sentences

VP

saw PN

her

VB

NP

S

PN

I

NP

Input: I saw her

4

Challenges in Building Parsers

• Disambiguation– Lexical disambiguation– Structural disambiguation

• Rule Exceptions– Many lexical dependencies

• Manual Grammar Construction– Limited coverage– Difficult to maintain

5

Meeting these Challenges:Statistical Parsing

• Disambiguation?– Resolve local ambiguities with global likelihood

• Rule Exceptions?– Lexicalized representation

• Manual Grammar Construction?– Automatic induction from large corpora– A new challenge: how to obtain training corpora?– Make better use of unlabeled data with machine

learning techniques and linguistic knowledge

6

Roadmap

• Parsing as a learning problem

• Semi-supervised approaches– Sample selection– Co-training– Corrected Co-training

• Conclusion and further directions

7

Parsing Ambiguities

T1: T2:

VP

saw

her

N

duck

PNS

VB

NP

S

PN

I

PP

with

P NP

a

NDET

NP

telescope

VP

saw

her

N

duck

PNS

VB

NP

S

PN

I PP

with

P NP

a

NDET

NP

telescope

Input: “I saw her duck with a telescope”

8

Disambiguation with Statistical Parsing

)|Pr()|Pr( 21 WTWT

T1: T2:

VP

saw

her

N

duck

PNS

VB

NP

S

PN

I

PP

with

P NP

a

NDET

NP

telescope

VP

saw

her

N

duck

PNS

VB

NP

S

PN

I PP

with

P NP

a

NDET

NP

telescope

W = “I saw her duck with a telescope”

9

A Statistical Parsing Model

• Probabilistic Context-Free Grammar (PCFG)

• Associate probabilities with production rules

• Likelihood of the parse is computed from the rules used

• Learn rule probabilities from training data

0.3 NP PN

0.5 DET a

0.1 DET anthe0.4 DET

Example of PCFG rules:

...

0.7 NP DET N

r rri

i

WTreesTi

WTreesT

LHSRHSWT

W

WTWT

ii

)|Pr(),Pr(

)Pr(

),Pr(maxarg)|Pr(maxarg

)()(

10

Sentence Probability• Assume productions for each node are chosen

independently.• Probability of derivation is the product of the

probabilities of its productions.

P(D1) = 0.1 x 0.5 x 0.5 x 0.6 x 0.6 x 0.5 x 0.3 x 1.0 x 0.2 x 0.2 x 0.5 x 0.8 = 0.0000216

D1SVP

Verb NP Det Nominal

Nominal PP

book

Prep NPthrough

HoustonProper-Noun

the

flightNoun

0.5

0.5 0.6

0.6 0.51.0

0.20.3

0.5 0.20.8

0.1

Syntactic Disambiguation• Resolve ambiguity by picking most probable parse

tree.

1111

D2

VPVerb NP

Det NominalbookPrep NP

throughHouston

Proper-Nounthe

flightNoun

0.5

0.5 0.6

0.6 1.0

0.20.3

0.5 0.20.8

S

VP0.1

PP

0.3

P(D2) = 0.1 x 0.3 x 0.5 x 0.6 x 0.5 x 0.6 x 0.3 x 1.0 x 0.5 x 0.2 x 0.2 x 0.8 = 0.00001296

Sentence Probability

• Probability of a sentence is the sum of the probabilities of all of its derivations.

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P(“book the flight through Houston”) = P(D1) + P(D2) = 0.0000216 + 0.00001296 = 0.00003456

13

PCFG: Supervised Training• If parse trees are provided for training sentences, a

grammar and its parameters can be can all be estimated directly from counts accumulated from the tree-bank (with appropriate smoothing).

.

.

.

Tree Bank

SupervisedPCFGTraining

S → NP VPS → VPNP → Det A NNP → NP PPNP → PropNA → εA → Adj APP → Prep NPVP → V NPVP → VP PP

0.90.10.50.30.20.60.41.00.70.3

English

S

NP VP

John V NP PP

put the dog in the pen

S

NP VP

John V NP PP


Estimating Production Probabilities

• Set of production rules can be taken directly from the set of rewrites in the treebank.

• Parameters can be directly estimated from frequency counts in the treebank.

14

)count(

)count(

)count(

)count()|(

P

15

Vanilla PCFG Limitations

• Since probabilities of productions do not rely on specific words or concepts, only general structural disambiguation is possible (e.g. prefer to attach PPs to Nominals).

• Consequently, vanilla PCFGs cannot resolve syntactic ambiguities that require semantics to resolve, e.g. ate with fork vs. meatballs.

• In order to work well, PCFGs must be lexicalized, i.e. productions must be specialized to specific words by including their head-word in their LHS non-terminals (e.g. VP-ate).

Example of Importance of Lexicalization

• A general preference for attaching PPs to NPs rather than VPs can be learned by a vanilla PCFG.

• But the desired preference can depend on specific words.

16


0.90.10.50.30.20.60.41.00.70.3

English

PCFG Parser

S

NP VP

John V NP PP


John put the dog in the pen.

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Example of Importance of Lexicalization

• A general preference for attaching PPs to NPs rather than VPs can be learned by a vanilla PCFG.

• But the desired preference can depend on specific words.


0.90.10.50.30.20.60.41.00.70.3

English

PCFG Parser

S

NP VP

John V NP

put the dog in the penXJohn put the dog in the pen.

Head Words

• Syntactic phrases usually have a word in them that is most “central” to the phrase.

• Linguists have defined the concept of a lexical head of a phrase.

• Simple rules can identify the head of any phrase by percolating head words up the parse tree.– Head of a VP is the main verb– Head of an NP is the main noun– Head of a PP is the preposition– Head of a sentence is the head of its VP

Lexicalized Productions• Specialized productions can be generated by

including the head word and its POS of each non-terminal as part of that non-terminal’s symbol.

S

VPVBD NP

DT NominalNominal PP

liked

IN NPin

the

dogNN

DT Nominal

NNthepen

NNP

NP

John

pen-NN

pen-NN

in-INdog-NN

dog-NN

dog-NN

liked-VBD

liked-VBD

John-NNP

Nominaldog-NN → Nominaldog-NN PPin-IN

Lexicalized Productions

S

VPVP PP

DT NominalputIN NP

in

thedogNN

DT Nominal

NNthepen

NNP

NP

Johnpen-NN

pen-NN

in-IN

dog-NN

dog-NN

put-VBD

put-VBD

John-NNP

NPVBD

put-VBD

VPput-VBD → VPput-VBD PPin-IN

Parameterizing Lexicalized Productions

• Accurately estimating parameters on such a large number of very specialized productions could require enormous amounts of treebank data.

• Need some way of estimating parameters for lexicalized productions that makes reasonable independence assumptions so that accurate probabilities for very specific rules can be learned.

Collins’ Parser

• Collins’ (1999) parser assumes a simple generative model of lexicalized productions.

• Models productions based on context to the left and the right of the head daughter.– LHS → LnLn1…L1H R1…Rm1Rm

• First generate the head (H) and then repeatedly generate left (Li) and right (Ri) context symbols until the symbol STOP is generated.

Count(PPin-IN right of head in a VPput-VBD production)

Estimating Production Generation Parameters• Estimate PH, PL, and PR parameters from treebank data.

PR(PPin-IN | VPput-VBD) =Count(symbol right of head in a VPput-VBD)

Count(NPdog-NN right of head in a VPput-VBD production)PR(NPdog-NN | VPput-VBD) =

• Smooth estimates by linearly interpolating with simpler models conditioned on just POS tag or no lexical info.

smPR(PPin-IN | VPput-VBD) = 1 PR(PPin-IN | VPput-VBD) + (1 1) (2 PR(PPin-IN | VPVBD) + (1 2) PR(PPin-IN | VP))

Count(symbol right of head in a VPput-VBD)

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Parsing Evaluation Metrics• PARSEVAL metrics measure the fraction of the

constituents that match between the computed and human parse trees. If P is the system’s parse tree and T is the human parse tree (the “gold standard”):– Recall = (# correct constituents in P) / (# constituents in T)

– Precision = (# correct constituents in P) / (# constituents in P)

• Labeled Precision and labeled recall require getting the non-terminal label on the constituent node correct to count as correct.

• F1 is the harmonic mean of precision and recall.

26

Treebank Results• Results of current state-of-the-art systems on the

English Penn WSJ treebank are slightly greater than 90% labeled precision and recall.

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Supervised Learning Avoids Manual Construction

• Training examples are pairs of problems and answers• Training examples for parsing: a collection of

sentence, parse tree pairs (Treebank)– From the treebank, get maximum likelihood estimates for

the parsing model

• New challenge: treebanks are difficult to obtain– Needs human experts

– Takes years to complete

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Learning to Classify Learning to Parse

Train a model to decide: should a prepositional phrase modify the verb before it or the noun?

Train a model to decide: what is the most likely parse for a sentence W?

Training examples:(v, saw, duck, with, telescope)

(n, saw, duck, with, feathers)

(v, saw, stars, with, telescope)

(n, saw, stars, with, Oscars)

…

[S [NP-SBJ [NNP Ford] [NNP Motor] [NNP Co.]] [VP [VBD acquired] [NP [NP [CD 5] [NN %]] [PP [IN of] [NP [NP [DT the] [NNS shares]] [PP [IN in] [NP [NNP Jaguar] [NNP PLC]]]]]]] . ]

[S [NP-SBJ [NNP Pierre] [NNP Vinken]] [VP [MD will] [VP [VB join] [NP [DT the] [NN board]] [PP [IN as] [NP [DT a] [NN director]]] .]

…

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Hwa’s Approach

• Sample selection– Reduce the amount of training data by picking

more useful examples

• Co-training– Improve parsing performance from unlabeled

data

• Corrected Co-training– Combine ideas from both sample selection and

co-training

30

Roadmap


• Semi-supervised approaches– Sample selection

• Overview

• Scoring functions

• Evaluation

– Co-training– Corrected Co-training


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Sample Selection

• Assumption– Have lots of unlabeled data (cheap resource)

– Have a human annotator (expensive resource)

• Iterative training session– Learner selects sentences to learn from

– Annotator labels these sentences

• Goal: Predict the benefit of annotation– Learner selects sentences with the highest Training

Utility Values (TUVs)

– Key issue: scoring function to estimate TUV

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Algorithm

InitializeTrain the parser on a small treebank (seed data) to get the

initial parameter values.

RepeatCreate candidate set by randomly sample the unlabeled pool.Estimate the TUV of each sentence in the candidate set with

a scoring function, f.Pick the n sentences with the highest score (according to f).Human labels these n sentences and add them to training set.Re-train the parser with the updated training set.

Until (no more data).

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Scoring Function

• Approximate the TUV of each sentence– True TUVs are not known

• Need relative ranking

• Ranking criteria– Knowledge about the domain

• e.g., sentence clusters, sentence length, …

– Output of the hypothesis• e.g., error-rate of the parse, uncertainty of the parse, …

….

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Proposed Scoring Functions

• Using domain knowledge– long sentences tend to be complex

• Uncertainty about the output of the parser– tree entropy

• Minimize mistakes made by the parser– use an oracle scoring function find

sentences with the most parsing inaccuraciesferror

fte

flen

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Entropy

• Measure of uncertainty in a distribution– Uniform distribution very uncertain– Spike distribution very certain

• Expected number of bits for encoding a probability distribution, X

x

xpxpXH )(log)()(

36

Tree Entropy Scoring Function

))(log(

)(

WTrees

WTEfte

)(

1)|Pr(WTreesT

i

i

WT

• Distribution over parse trees for sentence W:

• Tree entropy: uncertainty of the parse distribution

• Scoring function: ratio of actual parse tree entropy to that of a uniform distribution

)|Pr(log)|Pr()()(

WTWTWTE iWTreesT

i

i

38

Experimental Setup

• Parsing model: – Collins Model 2

• Candidate pool– WSJ sec 02-21, with the annotation stripped

• Initial labeled examples: 500 sentences• Per iteration: add 100 sentences• Testing metric: f-score (precision/recall)• Test data:

– ~2000 unseen sentences (from WSJ sec 00)

• Baseline– Annotate data in sequential order

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Training Examples Vs. Parsing Performance

80

82

84

86

88

90

0 10000 20000 30000 40000

Number of Training Sentences

Pa

rsin

g p

erfo

rma

nce

on

Tes

t S

ente

nce

s (f

-sco

re)

sequential

length

tree entropy

oracle

40

Parsing Performance Vs. Constituents Labeled

0

100000

200000

300000

400000

500000

600000

700000

800000

87.5 88 88.7

Parsing Performance on Test Sentences (f-score)

Num

ber

of C

onst

itue

nts

in T

rain

ing

Sent

ence

s

baseline

length

tree entropy

oracle

41

Co-Training [Blum and Mitchell, 1998]

• Assumptions– Have a small treebank– No further human assistance– Have two different kinds of

parsers• A subset of each parser’s

output becomes new training data for the other

• Goal: – select sentences that are

labeled with confidence by one parser but labeled with uncertainty by the other parser.

42

AlgorithmInitialize

Train two parsers on a small treebank (seed data) to get the initial models.

RepeatCreate candidate set by randomly sample the unlabeled pool.Each parser labels the candidate set and estimates the accuracy

of its output with scoring function, f.Choose examples according to some selection method, S (using

the scores from f).Add them to the parsers’ training sets.Re-train parsers with the updated training sets.


43

Scoring Functions

• Evaluates the quality of each parser’s output

• Ideally, function measures accuracy– Oracle fF-score

• combined prec./rec. of the parse

• Practical scoring functions– Conditional probability fcprob

• Prob(parse | sentence)

– Others (joint probability, entropy, etc.)

44

Selection Methods

• Above-n: Sabove-n

– The score of the teacher’s parse is greater than n

• Difference: Sdiff-n

– The score of the teacher’s parse is greater than that of the student’s parse by n

• Intersection: Sint-n

– The score of the teacher’s parse is one of its n% highest while the score of the student’s parse for the same sentence is one of the student’s n% lowest

45

Experimental Setup

• Co-training parsers:– Lexicalized Tree Adjoining Grammar parser [Sarkar, 2002]

– Lexicalized Context Free Grammar parser [Collins, 1997]

• Seed data: 1000 parsed sentences from WSJ sec02• Unlabeled pool: rest of the WSJ sec02-21, stripped• Consider 500 unlabeled sentences per iteration• Development set: WSJ sec00• Test set: WSJ sec23• Results: graphs for the Collins parser

49

79.5

79.8

80.1

80.4

80.7

81

81.3

0 1000 2000 3000 4000 5000

Number of training sentences

Pa

rsin

g P

erf

orm

an

ce

o

f th

e t

es

t s

et

above-70%

diff-30%

int-30%

Co-Training using fcprob

50

Roadmap


• Semi-supervised approaches– Sample selection– Co-training– Corrected Co-training


51

Corrected Co-Training

• Human reviews and corrects the machine outputs before they are added to the training set

• Can be seen as a variant of sample selection [cf. Muslea et al., 2000]

• Applied to Base NP detection [Pierce & Cardie, 2001]

52

AlgorithmInitialize:

Train two parsers on a small treebank (seed data) to get the initial models.

RepeatCreate candidate set by randomly sample the unlabeled pool.Each parser labels the candidate set and estimates the accuracy

of its output with scoring function, f.Choose examples according to some selection method, S (using

the scores from f).Human reviews and corrects the chosen examples.Add them to the parsers’ training sets.Re-train parsers with the updated training sets.


53

Selection Methods and Corrected Co-Training

• Two scoring functions: fF-score , fcprob

• Three selection methods: Sabove-n , Sdiff-n , Sint-n

56

Corrected Co-Training using fcprob

(Reviews)

79

81

83

85

87

0 5000 10000 15000

Number of training sentences

Pa

rsin

g P

erf

orm

an

ce

o

f th

e t

es

t s

et

above-70%

diff-30%

int-30%

No selection

semi-supervised approaches for learning to parse natural languages

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