Grammar Correction

7/24/2019 Grammar Correction

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Learner Error Corpora

Grammatical Error Detection

Grammatical Error Correction

Evaluation of Error Detection/CorrectionSystem


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A learner corpus is a computerized textual database of

the language produced by foreign language learners Benefits Researchers will have access to leaners interlanguage

May lead to development of language learning tools

NativeLanguage

ForeignLanguage

Transformation

Interlanguage


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Error tagged corpora Deals with real errors made by language learners

Well formed corpora

Language corpora with well formed constructs BNC, WSJ N-gram corpora

Artificial error corpora

Error tagged corpora are expensive Well formed corpora do not deal with errors Artificially modify well formed corpora to become

error corpora


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NUCLE : NUS Corpus of Learner English

About 1,400 essays from university-level students

with 1.2 million words. Completely annotated with error categories and

corrections.

Annotation performed by English instructors at

NUS Centre for English Language Communication

(CELC).


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Annotation Task Select arbitrary, contiguous text spans using the

cursor to identify grammatical errors.

Classifyerrors by choosing an error tag from a drop-down menu. Correcterrors by typing the correction into a text box. Comment to give additional explanations if necessary.

Writing, Annotation, and Marking Platform (WAMP)


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NICT-JLE

Error Annotation for Corpus of Japanese Learner

English Izumi et al. CoNLL shared task data

http://www.comp.nus.edu.sg/~nlp/conll13st.html

HOO data

http://clt.mq.edu.au/research/projects/hoo/hoo2012/index.html


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Precision Grammar: formal grammardesigned to distinguish ungrammatical from

grammatical sentences. Constraint Dependency Grammar (CDG)

every grammatical rule is given as a constrainton word-to-word modifications

Resource: Structural disambiguation with constraint propagation, Hiroshi Maruyama,ACL90


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CDG grammar < , , , > finite set of terminal symbols (words) * , , finite set of role-ids * , , finite set of labels constraint that an assignmentA should

satisfy


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A sentence , , is a finite stringon

Each word in a sentence s has k roles , , , () Roles are variables that can take < , >as its

value where

and modifiee is

either

1 or special symbol .


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-

-

-

Analysis of a sentenceassigning values to the roles.


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Definitions

Assuming is an role of word .


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A constraint

. where . range over the set of roles in an assignment. Each is a subformula with vocabulary

Variables: . Constants: * , 1 , 2 , Function symbols: , , , Predicate symbols: ,, Logical connectors: ,,,


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Definitions

The arity of a subformula depends on thenumber of variables that it contains

The degree of grammar is the size of set of role

ids (). A non-null string

over the alphabet is

generated iff there exists an assignment that satisfies the constraint .


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1 1 , , 1 * 1 , , 1 :;11131

: A determiner (D) modifies a noun (N) on the right with the label DET ( , , < ( ))

:A noun modifies a verb (V) on the right with the label SUBJ

: A verb modifies nothing and its label should be ROOT

: No two words can modify the same word with the same label.


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1 1 , , 1 * 1 , , 1 :;11131

: A determiner (D) modifies a noun (N) on the right with the label DET ( , , < ( ))

:A noun modifies a verb (V) on the right with the label SUBJ

, , < ( )

: A verb modifies nothing and its label should be ROOT ,

: No two words can modify the same word with the same label. ,


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[A1]D[dog2]N[runs3]V


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CDG parsing Assigning values to roles from a finite set

* ,1,2,

A constraint satisfaction problem (CSP)

Use constraint propagation or filteringto solveCSP

Form an initial constraint network using a coregrammar.

Remove local inconsistencies by filtering.

If any ambiguity remains, add new constraints and go toStep 2.


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Put the block on the floor on the table in the room

3

2 2 , , 2 * 2 , , , 2 :;


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Constraints


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mod(x) mod(y) x y

mod(x) mod(y) y x


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Total number of possible parse trees?

Catallan number

Explicit representation is not feasible Constraint networkfor implicit representation of

the parse trees


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*

*

*,

*, , 3

*, , 3 ,

,


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A constraint network is said to be arc consistentif, for any constraint matrix, there are no rowsand no columns that contain only zeros

A node corresponding to all zero row or columnis removed from solution

Removing one value makes others inconsistent

The process is propagated until the networkbecomes arc consistent.

The network in example is arc consistent


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Two more constraints

(())extracts semanticfeatures of


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3


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*

*

*,

*, , 3

*, , 3 ,


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*

*

*,

*,

*, , 3 ,


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*

*

*,

*,

*, , 3 ,


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Two more constraints


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*

*

*,

*,

*, ,


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*

*

*

*,

*, ,


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3


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*

*

*

*

*


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LOC

POSTMOD POSTMODOBJ


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All constraints are treated with same priority failure to adhere to the set of specified

constraints mark an utterance to beungrammatical Gradationin natural language

Can model robustness, the ability to deal with

unexpected and possibly erroneous input .

Weighted Constraint Dependency Grammar(WCDG)


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Different error detection tasks

Grammatical vs Ungrammatical

Detecting errors for targeted categories Preposition errors

Article errors

Agnostic to error category

Approaches

Error detection as classification

Error detection as sequence labelling


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Generic steps Decide on the error category Pick up a learning algorithm

Identify discriminative features Train the algorithm with training data

Error corpora Model encodes the error contexts

flags error detecting a matchof context in learner response

Well-formed corpora Learns the ideal models for the targeted categories

Flags error in case of mismatch

Artificial error corpora


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Type of preposition errors

Selection error [They arrived tothe town]

Extraneous use [They came tooutside]

Omission error [He is fond this book]

Tasks

Classifier prediction

Training a model

What are the features?

Resource: The Ups and Downs of Preposition Error Detection in ESL Writing, Tetreault andChodorow, COLING08


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Cast error detection task as a classification problem Given a model classifier and a context:

System outputs a probability distribution over all prepositions

Compare weight of systems top preposition with writerspreposition

Error occurs when:

Writers preposition classifiers prediction

And the difference in probabilities exceeds a threshold


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Develop a training set of error-annotated ESLessays (millions of examples?):

Too labor intensive to be practical

Alternative:

Train on millions of examples of proper usage

Determining how close to correct writerspreposition is


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Prepositions are influenced by:

Words in the local context, and how they interact

with each other (lexical)

Syntactic structure of context

Semantic interpretation


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1. Extract lexical and syntactic features fromwell-formed (native) text

2. Train MaxEnt model on feature set to outputa probability distribution over a set of preps3. Evaluate on error-annotated ESL corpus by:

Comparing systems prep with writers prep

If unequal, use thresholds to determine

correctness of writers prep


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Feature Description

PV Prior verb

PN Prior noun

FH Headword of the following phrase

FP Following phrase

TGLR Middle trigram (pos + words)

TGL Left trigram

TGR Right trigram

BGL Left bigram

He will take our place inthe line


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Feature Description

PV Prior verb

PN Prior noun

FH Headword of the following phraseFP Following phrase


TGL Left trigram

TGR Right trigramBGL Left bigram

He will take our place inthe line

FHPNPV


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Feature Description

PV Prior verb

PN Prior noun

FH Headword of the following phrase

FP Following phrase


TGL Left trigram

TGR Right trigram

BGL Left bigram

He will take our place inthe line.

TGLR


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MaxEnt does not model the interactionsbetween features

Build combination features of the headnouns and commanding verbs

PV, PN, FH

3 types: word, tag, word+tag

Each type has four possible combinations

Maximum of 12 features


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Class Components +Combo:word

p-N FH line

N-p-N PN-FH place-line

V-p-N PV-PN take-line

V-N-p-N PV-PN-FH take-place-line

He will take our place in the line.


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Typical way that non-native speakers check ifusage is correct: Google the phrase and alternatives

Google N-gram corpus Queries provided frequency data for the

+Combo features

Top three prepositions per query were usedas features for ME model Maximum of 12 Google features


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Class Combo:word Google Features

p-N line P1= onP2= in

P3= of

N-p-N place-line P1= inP2= on

P3= of

V-p-N take-line P1= on

P2= toP3= into

V-N-p-N take-place-line P1= inP2= on

P3= after

He will take our lace in the line


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Thresholds allow the system to skip caseswhere the top-ranked preposition and what

the student wrote differ by less than a pre-specified amount


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0

10

20

30

40

50

60

70

80

90

100

of in at by with

He is fond withbeer

FLAG AS ERROR

FLAG ERROR


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0

10

20

30

40

50

60

of in around by with

My sister usually gets home around3:00

FLAG AS OK

FLAG OK


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Errors consist of a sub-sequence of tokens ina longer token sequence.

Some of the sub-sequences are errors while theothers not

Advantage: Error category independent

Sequence modelling tasks in NLP

Parts-of-speech tagging

Information Extraction

Resource: High-Order Sequence Modeling for Language Learner Error Detection, MichaelGamon, 6th Workshop on Innovative Use of NLP for Building Educational Applications


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Many NLP problems can be viewed as sequencelabeling.

Each token in a sequence is assigned a label.

Labels of tokens are dependent on the labels ofother tokens in the sequence, particularly theirneighbors (not i.i.d).

foo bar blam zonk zonk bar blam

Slides from Raymond J. Mooney


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Annotate each word in a sentence with apart-of-speech.

Lowest level of syntactic analysis.

Useful for subsequent syntactic parsing

and word sense disambiguation.

John saw the saw and decided to take it to the table.

PN V Det N Con V Part V Pro Prep Det N


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Identify phrases in language that refer to specific types ofentities and relations in text.

Named Entity Recognition (NER) is task of identifyingnames of people, places, organizations, etc. in text.

people organizations places Michael Dellis the CEO of Dell Computer Corporationand lives in

Austin Texas.

Extract pieces of information relevant to a specificapplication, e.g. used car ads:

make model year mileage price For sale, 2002ToyotaPrius, 20,000 mi, $15K or best offer.Available starting July 30, 2006.


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Classify each token independently but use as input features,information about the surrounding tokens (sliding window).


classifier

PN


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classifier

V


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classifier

Det


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classifier

N


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classifier

Conj


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classifier

V


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classifier

Part


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classifier

V


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classifier

Pro


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classifier

Prep


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classifier

Det


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classifier

N


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Better input features are usually thecategoriesof the surrounding tokens, butthese are not available yet.

Can use category of either the preceding orsucceeding tokens by going forward or backand using previous output.


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classifier

N


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PN


classifier

V


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PN V


classifier

Det


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PN V Det


classifier

N


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PN V Det N


classifier

Conj


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PN V Det N Conj


classifier

V


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PN V Det N Conj V


classifier

Part


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PN V Det N Conj V Part


classifier

V


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PN V Det N Conj V Part V


classifier

Pro


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PN V Det N Conj V Part V Pro


classifier

Prep


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PN V Det N Conj V Part V Pro Prep


classifier

Det


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PN V Det N Conj V Part V Pro Prep Det


classifier

N


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Hidden Markov Model

Finite state automation with stochastic state

transitions and observations

Start from a stateemitting an observation

transiting to new stateemitting observation

..Final state

State transition probability (|) Observation probability (|) Initial state distribution ()


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Maximum Entropy Markov Model (MEMM)

Combines transition and observation functions

together with a single function

(|, )


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NER annotation convention

Ooutside NE

Bbeginning of NE

Iinside NE

Learner error annotation

O and I

Most of the error spans are short

Michael Dellis the CEO of Dell Computer Corporationand lives in Austin Texas.B I O O O O B I I O O O B I


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Language model features How close or far is the learners utterance from

ideal language usage?

String features whether a token is capitalized (initial

capitalization or all capitalized)?

token length in characters

number of tokens in the sentence

Linguistic analysis feature Features from constituency parse tree


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All features are calculated for each token ofthe tokens , , in a sentence

Basic LM features

Unigram probability of average n-gram probability of all n-grams in the

sentence that contain ( +) = += 1 = +=


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Ratio features

( > )

tokens that are part of an unlikely combination of

otherwise likely smaller n-gramserror

Drop features

drop or increase in n-gram probability across token

. + ()


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good n-gram is likely to have a much higherprobability than an n-gram with the sametokens in random order

( ) Minimum ratio to random

Average ratio to random

Overall ratio to random = 1 2 1 ( +) = += 2


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Overlap to adjacent ratio

an erroneous word may cause n-grams that containthe word to be less likely than adjacent but non-

overlapping n-grams


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Features extracted from syntactic parse trees

Label of the parent and grandparent node (some

of the labels denote complex constructs , e.g.,

SBAR )

number of sibling nodes

number of siblings of the parent

length of path to the root


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GEC Approaches

Rule-based Classification LanguageModelling

SMT Hybrid


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Whole sentence error correction

Pipeline based approach

Design classifiers for different error categories

Deploy classifiers independently

Relations between errors are ignored

Example:A cats runs

An article classifier may propose to delete a

A noun number classifier may propose to change cats to cat

Resource: Grammatical Error Correction Using Integer Linear Programming, Yuanbin Wuand Hwee Tou Ng


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Joint Inference

Errors are most of the cases interacting

Errors needs to be correctedjointly

Steps

For every possible correction, a score(how muchgrammatical) is assigned to the corrected sentence

A set of corrections resulting in maximum score isselected


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Integer Linear Programming

0

GECGiven an input sentence, choose a setof correctionswhich results in the bestoutputsentence


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ILP formulation of GEC Encode the output space using integer variables.

Corrections that a word needs

Express inference objective as a linear objectivefunction. Maximize the grammaticality of corrections

Introducing constraints to refine feasible output

space Constraints guarantee that the corrections do not

conflict with each other


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What corrections at which positions?

Location of error

Error type

Correction

First order variables, 0,1

1,2, , is an error type 1,2, , is a correction of type


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, 1 The word at position should be corrected to

that is of error type

.

, 0 The word at position is not applicable for

correction

, 1 Deletion of a word


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Objective: To find best correction Exponential in combinations of corrections

Approximate by decomposable assumption

Measuring the output quality of multiple corrections canbe decomposed into measuring quality of the individualcorrections

Let

,

and

,, measure the

grammaticality of max ,, ,

,,


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For individual correction , , the quality of isdepends on Language model score: , Classifier confidence: , Disagreement score: ,

Difference between maximum confidence score and thescore of the word that is being corrected

,, , (, ) (, )


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Constraint to avoid conflict

For each error type , only one output is allowedat any applicable position

, 1 applicable ,

Final ILP formulation

m a x ,, ,,,

. . , 1 applicable ,

,

*0 1


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A cats sat on the mat

Possible corrections and related variables


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Constraint, , , 1

Computing weights

Language model score, classifier confidence

score, disagreement score

Classifiers: article (ART), preposition (PREP), noun

number (NOUN)

Correction: ,

.


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Weight for ,: ,, ,

, , ,

,

,

,

, 1 , 1, 5 , 5, 12 , 1, ,5,

, max , , 1, ,1, , 5, ,5,


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,, , 2 , 1, ,5, ,4,

2 , 2, ,6, , , ,


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A motivating case A cat sat on the mat ()Cats sat on the mat ()

,

,

,,will be small due to missing article ,, will be small due to low LM score of A

cats Relaxing decomposable assumption Combine multiple corrections to a single correction

Instead of considering corrections A/and /separately consider /together

Higher order variables


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Let , , , , be the set offirst order variables

Let ,,be the weight of ,

A second order variable:

, , , , ,

, , , , .


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Weight for second order variable is similar asthat for first order variables

Why?

, , ( , ) (, )


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New constraints for enforcing consistencybetween first and second order variables

New objective function


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Statistical Machine Translation for GEC

arg max

(|)

Model GEC as SMT E=L1 and F=L2

Parallel corpora: Learner error corpora


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GEC is as good as SMT

Increase size of parallel corpora covering targeted

types of errorsExpensive

A hack through SMT systems considered to be meaning

preserving

Generate alternate surface renderings of themeaning expressed in L2 sentence

Select the most fluent oneResource: Exploring Grammatical Error Correction with Not-So-Crummy Machine Translation,

Madnani et al.


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Bilingual MT

System 1

Bilingual MT

System 2

Bilingual MT

System n

ErroneousSentence

PL1Translation

PL2Translation

PLnTranslation

RT1 RT2 RTn Select

Combine


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Find the most fluent alternative Use an n-gram language model

Issue Language model does not care about preserving sentence

meaning

No single translation is error free in general


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To increase the likelihood of whole-sentencecorrection

Combine evidence of corrections produced by

each independent translation model

Steps: Combination based approach

Align(original, round translation) pairs

Combinealigned pairs to form word lattice Decode for best candidate


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The task: Align each sentence pair

Alignment:

For a (hypothesis, reference) pair perform some editoperations that transform a hypothesis sentence to areference one

Each edit operation involves a cost

Best alignment is that with minimal cost

Also used as machine translation metric


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Word order rate (WER)

Levenstein distance between pair

Edit operations: Match, Insertionand Substitution

Fails to model reordering of words or phrases in

translation

Translation Edit Rate (TER) Introduce shiftoperation

Resource: TERp System Description, Snover et al.


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Shift operation in TER Allow block movement of words A number of constraints on shift operations

Shifts are selected by a greedy algorithm that selects the shift

that most reduces the WER between the reference and thehypothesis.

The shifted words must exactly match the reference words inthe destination position.

The words to be shifted must contain at least one error to

prevent the shifting of words that currently correctlymatched.

The word sequence of the reference that corresponds to thedestination position must be misaligned before the shift


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TER-Plus (TERp)

Three more edit operations

Stem match, synonym match, phrase substitution

allows shifts if the words being shifted are exactly

the same, are synonyms, stems or paraphrases of

each other, or any such combination


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both experience and books are very important about living .

related to the life experiences and the books are very imp0rtant .

[I] Insertion[S] Substitution[M] Match[T] Stemming[Y] Wordnet Synonym

* Shiftin


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---- both experience and books are very important about living .


[I]


* Shiftin


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---- ---- both experience and books are very important about living .


[I] [I]


* Shiftin


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---- ---- both experience and books are very important about living

related to the life experiences and the books are very imp0rtant

[I] [I] [S]


* Shiftin


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related to the experiences and the books are very imp0rtant life

[I] [I] [S] [Y]*


* Shiftin


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[I] [I] [S] [Y]*


* Shiftin


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[I] [I] [S] [T] [Y]*


* Shiftin


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[I] [I] [S] [T] [M] [Y]*


* Shiftin


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---- ---- both experience and --- books are very important about living


[I] [I] [S] [T] [M] [I] [Y]*


* Shiftin


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[I] [I] [S] [T] [M] [I] [Y]*


* Shiftin


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related to the experiences and the books are very imp0rtant ----- life

[I] [I] [S] [T] [M] [I] [M] [M] [M] [M] [S] [Y]*


* Shiftin


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---- both experience --- and books are very important about living

and the experience , and book a very important about life

[I] [S] [M] [I] [M] [T]* [S] [M] [M] [M] [Y]


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The task: Combine every translations usingtheir alignments to the original sentence We need a data structure for combination: Word

Lattice Word Lattice a directed acyclic graph with a single start point

and edges labeled with a word and weight.

every path must pass through every node. a word lattice can represent an exponential

number of sentences in polynomial space


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Create backbone of the lattice using theoriginal sentence

1 2 3 4both/1 experience/1and/1


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For all round trip translations, map thealignments to the lattice

each insertion, substitution, stemming, synonymy

and paraphrase operation lead to creation of newnodes

Duplicate nodes are merged (match operation)

Edges produced by different translations betweensame pair of nodes are merged and their weightsare added (two consecutive match operation)


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Original: Both experience and books are very important about living.Russian: And the experience, and a very important book about life.

---- both experience --- and books are very important about living

and the experience , and book a very important about life

[I] [S] [M] [I] [M] [T]* [S] [M] [M] [M] [Y]


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Greedy best first

Both experience and books are very important about life


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1-Best

Convert TREp lattice edge weights to edge costs

by multiplying the weights by -1

Find the output as the shortest path in TERplattice.

Both experience and the books are very important about life (cost: -59)


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Language Model ranked

Find n-best (lowest cost) list from TERp lattice

Rank the list using n-gram language model

Suggest top ranked candidate as correction


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Language Model Composition Convert edge weights in the TERp lattice into

probabilities

Weighted Finite State Transducer (WFST)representation () Train an n-gram finite state language model in

WFST () Compose: shortest path through is suggested as

correction


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Learner error corpora

Grammatical error detection

Grammatical error correction

Evaluating error detection and correctionsystem

Grammar Correction

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Grammar Correction

Text of Grammar Correction