ling/c sc/psyc 438/538 -...

LING/CSC/PSYC438/538Lecture25

SandiwayFong

Today'sTopics

• Note:homeworks 12and13graded• OPTIONAL 2nd chancehomework(only ifyoudidbadlyontheProlog)• duenextMonday(bymidnight)

• 538Presentations• ChomskyNormalForm(CNF)revisited• GoogleandMisspellings

OPTIONAL Homework14Englishhasasetofverbsthataretransitivebutobligatorilytakeareflexivesobject,asin:

Johnperjuredhimself*JohnperjuredShevindicatedherself*ShevindicatedTheyingratiatedthemselves*TheyingratiatedYousunnedyourself*YousunnedIhelpedmyself*Ihelped

Theintransitivecounterpartsareconsideredungrammatical(*).Levin(1993)callssuchverbsObligatorilyReflexiveObject verbs.(Note:somemaytakenon-reflexiveobjectsbutwillhaveadifferentmeaning.)

• Question1:createatablesRo(S,RO) (S=subject,RO=reflexiveobject)thatliststhesubjectandreflexiveobjectsintheabovesentences:sRo(john, himself).sRo(she,herself).

• Question2:writeanaturallanguagegrammarusingProloggrammarrulestohandletheabovesentences.

• YourgrammarshouldreturnPrologtermsrepresentingtheparse.UsethePTBtagset andsyntactictags.Yourgrammarshouldbecapableofdealingwithexampleslikethefollowing.

Examples:JohnperjuredhimselfJohnperjured*Johnperjuredthemselves

Submityourgrammarandplentyofexamples,e.g.s(Parse,[john,perjured,himself],[]).Parse = s(np(nnp(john)),vp(vbd(perjured),np(prp(himself))))

538Presentations

• Assignments:Name Topic DateAndrewZupon 20.7WordSimilarity:DistributionalMethods 30-Nov

MariaAlexeeva24.1-2PropertiesofHumanConversation+BasicDialogueSystems 30-Nov

JiahengXie 22.1NamedEntityRecognition 5-Dec

BrendanMurphy 25.5-6AlignmentinMT+TrainingAlignmentModels 5-DecMohammadrezaEbrahimi 22.3TemporalandEventProcessing 5-DecRoyaKabiri 19.1-4WordSenses->EventParticipants 30-NovRebeccaCordes 17.3-4FirstOrderLogic 5-Dec

SeongjinPark17.1-2ComputationalDesiderataforRepresentation+Model-TheoreticSemantics 30-Nov

JohnCulnan 23.3-4SummarizationandMulti-textsummarization 30-NovRianneLyons 24.7Plan-BasedDialogAgents 5-DecChenChen 18.1-3ComputationalSemantics 30-NovYiyunZhao 20.1-5WordSenseDisambiguation 5-DecRaghebAl-Ghezi 21.7-8CoferenceResolutionandEvaluation 5-Dec

ChomskyNormalForm(CNF)

• Conversionsteps:1. newstartsymbols0 --> s.

(s originalstartsymbol)tocopewithpossibleemptyderivation.s0 istheonlynonterminalallowedtohaveforms0 --> s

1. x --> … [w] ... (|RHS|>1)transforminto: x --> ... xw ... andxw --> [w].(xw anewnonterminal)

3. x --> y1, ...,yn. (|RHS|>2)transformintoacascadingsequenceofbinarybranchingrules:x --> y1, x1. x1 --> y2, x2. ... xn-1 --> yn-1, yn.

4. foreachinstanceofx --> []. andy --> ... x ...addacopywithoutx,i.e. y --> ......thendeletex --> [].

5. removex --> y. (exception:x cannotbes0)Replacex byy inotherrules.


• Example:1. s --> [].2. s --> a.3. a --> a, b, b, a.4. a --> [a].5. b --> [b], c, [b].6. c --> [c].

1. [] 2. [a] 3. [a, b, c, b, b, c, b, a] 4. [a, b, c, b, b, c, b, a, b, c, b, b, c, b, a] 5. [a, b, c, b, b, c, b, a, b, c, b, b, c, b, a, b, c, b, b, c, b, a]6. …

• Let'sconvertthisgrammartoCNF.


• Example:1. s --> [].2. s --> a.3. a --> a, b, b, a.4. a --> [a].5. b --> [b], c, [b].6. c --> [c].

1. s0 --> s.2. s --> [].3. s --> a.4. a --> a, bba.5. bba --> b, ba.6. ba --> b, a.7. a --> [a].8. b --> b2, cb.9. b2 --> [b].10. cb --> c, b2.11. c --> [c].

1. s0 --> [].2. s0 --> a.3. a --> a, bba.4. bba --> b, ba.5. ba --> b, a.6. a --> [a].7. b --> b2, cb.8. b2 --> [b].9. cb --> c, b2.10. c --> [c].

GoogleandMisspellings

MinimumEditDistance

• Anotheralgorithmusingdynamicprogramming:• Textbook:section3.11• File:eds.xls

10

MinimumEditDistance

• generalstringcomparison

• editoperationsareinsertion,deletionandsubstitution

• notjustlimitedtodistancedefinedbyasingleoperationaway

• wecanaskhowdifferentisstringa fromb bytheminimumeditdistance

11

MinimumEditDistance

• applications• couldbeusedformulti-typocorrection• usedinMachineTranslationEvaluation(MTEval)• example

• Source:⽣産⼯程改善について• Translations:• (Standard)Forimprovementoftheproductionprocess• (MT-A)Aboutaproductionprocessbetterment• (MT-B)Abouttheproductionprocessimprovement• method

• computeeditdistancebetweenMT-AandStandardandMT-BandStandardintermsofwordinsertion/substitutionetc.

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MinimumEditDistance

• costmodels• Levenshtein

• insertion,deletionandsubstitutionallhaveunitcost

• Levenshtein (alternate)• insertion,deletionhaveunitcost• substitutionistwiceasexpensive• substitution=oneinsertfollowedbyone

delete

• Typewriter• insertion,deletionandsubstitutionall

haveunitcost• modifiedbykeyproximity

MinimumEditDistance

• DynamicProgramming• divide-and-conquer

• tosolveaproblemwedivideitintosub-problems• sub-problemsmayberepeated

• don’twanttore-solveasub-problemthe2ndtimearound• idea:putsolutionstosub-problemsinatable

• andjustlookupthesolution2ndtimearound,therebysavingtime• memoization

we’lluseanExcelspreadsheet…

MinimumEditDistance• Considerasimplecase:xy ⇄ yx

• Minimum#ofoperations:• insertanddelete• cost=2

• Minimum#ofoperations:• swap• cost=?

MinimumEditDistance

• Generally

MinimumEditDistance• ProgrammingPractice:couldbeeasilyimplementedinPythonorPerl

MinimumEditDistance

• Generally

MinimumEditDistanceComputation

• OrinMicrosoftExcel,file:eds.xls (oncoursewebpage)

$inacellreferencemeansdon’tchangewhencopiedfromcelltocelle.g.inC$11staysthesamein$A3Astaysthesame

MinimumEditDistance

• Task:transformstrings1..si intostringt1..tj• each sn and tn are letters• string s is of length i, t is of length j

• Example:• s=leader,t=adapter• i =6,j=7• Let’ssayyou’reallowedjustthreeoperations:(1)deletealetter,(2)insertaletter,or(3)substitutealetterforanotherletter• Whatisonepossiblewaytogeneratet froms?

MinimumEditDistance

• Example:• s=leader,t=adapter• Whatisonepossiblewaytogeneratet froms?• leader

• adapter• costis2deletesand3inserts,total5operations• Question:isthistheminimumpossible?

leader◄leade◄lead◄lea◄le◄l◄◄a◄ad◄ada◄adap◄adapt◄adapte◄adapter◄

Simplestmethodcost:13operations

MinimumEditDistance0 1 2 3 4 5 6 7

a d a p t e r0

1 l2 e3 a4 d5 e6 r


a d a p t e r0

1 l2 e3 a4 d5 e6 r

cell(2,3)costof

transformingleintoada


a d a p t e r0

1 l2 e3 a4 d5 e6 r

cell(2,3)costof


cell(6,7)costof

transformingleader intoadapter


a d a p t e r0

1 l2 e3 a4 d5 e6 r

cell(3,0)costof

transformingleainto(empty)


a d a p t e r0

1 l2 e3 a4 d5 e6 r

cell(0,4)costof

transforming(empty)intoadap


a d a p t e r0

1 l2 e3 a4 d5 e k

6 r

cell(5,6)costof

transformingleadeintoadapte


a d a p t e r0

1 l2 e3 a4 d5 e k

6 r k

cell(5,6)costof

transformingleadeintoadapte


a d a p t e r0

1 l2 e k

3 a4 d5 e6 r

cell(2,3)costof



a d a p t e r0

1 l2 e k

3 a4 d5 e6 r

cell(2,3)costof


cell(2,4)costof

transformingleintoadap

➡


a d a p t e r0

1 l2 e k k+1

3 a4 d5 e6 r

cell(2,3)costof


cell(2,4)costof

transformingleintoadap

➡

l e

a d a p


a d a p t e r0

1 l k

2 e3 a4 d5 e6 r

cell(1,4)costof

transforminglintoadap

➡


a d a p t e r0

1 l k

2 e k+1

3 a4 d5 e6 r

cell(1,4)costof

transforminglintoadap

➡

l e

a d a p


a d a p t e r0

1 l k

2 e3 a4 d5 e6 r

cell(1,3)costof

transforminglintoada


a d a p t e r0

1 l k

2 e k+2

3 a4 d5 e6 r

cell(1,3)costof

transforminglintoada

assumingthecostofswappinge forp

is2

l e

a d a p


a d a p t e r0

1 l k1,3 k1,4

2 e k2,3 ?

3 a4 d5 e6 r

➡

➡

cell(2,4)minimumofthethreecoststogethereinonestep


a d a p t e r0

1 l2 e3 a4 d5 e6 r

cell(3,0)costof

transformingleainto(empty)


a d a p t e r0 0

1 l2 e3 a4 d5 e6 r


a d a p t e r0 0

1 l 1

2 e3 a4 d5 e6 r


a d a p t e r0 0

1 l 1

2 e 2

3 a4 d5 e6 r

➡ costofle à=costofl à ,plusthecostofdeletingthee


a d a p t e r0 0

1 l 1

2 e 2

3 a 3

4 d 4

5 e 5

6 r 6


a d a p t e r0 0

1 l2 e3 a4 d5 e6 r


a d a p t e r0 0 1

1 l2 e3 a4 d5 e6 r


a d a p t e r0 0 1 2 3 4 5 6 7

1 l2 e3 a4 d5 e6 r


a d a p t e r0 0 1 2 3 4 5 6 7

1 l 1

2 e 2

3 a 3

4 d 4

5 e 5

6 r 6


a d a p t e r0 0 1 2 3 4 5 6 7

1 l 1

2 e 2

3 a 3

4 d 4

5 e 5

6 r 6

➡

➡


a d a p t e r0 0 1 2 3 4 5 6 7

1 l 1 2

2 e 2

3 a 3

4 d 4

5 e 5

6 r 6

➡

➡


a d a p t e r0 0 1 2 3 4 5 6 7

1 l 1

2 e 2

3 a 3

4 d 4 5 6

5 e 5 6

6 r 6


a d a p t e r0 0 1 2 3 4 5 6 7

1 l 1

2 e 2

3 a 3

4 d 4 5 6

5 e 5 6 5

6 r 6


a d a p t e r0 0 1 2 3 4 5 6 7

1 l 1

2 e 2 6 7

3 a 3 5

4 d 4

5 e 5

6 r 6


a d a p t e r0 0 1 2 3 4 5 6 7

1 l 1

2 e 2 6 7

3 a 3 5

4 d 4

5 e 5

6 r 6

➡


a d a p t e r0 0 1 2 3 4 5 6 7

1 l 1

2 e 2 6 7

3 a 3 5 6

4 d 4

5 e 5

6 r 6

➡


a d a p t e r0 0 1 2 3 4 5 6 7

1 l 1

2 e 2

3 a 3

4 d 4

5 e 5 6 5

6 r 6 7


a d a p t e r0 0 1 2 3 4 5 6 7

1 l 1

2 e 2

3 a 3

4 d 4

5 e 5 6 5

6 r 6 7

➡


a d a p t e r0 0 1 2 3 4 5 6 7

1 l 1

2 e 2

3 a 3

4 d 4

5 e 5 6 5

6 r 6 7 6

➡

MinimumEditDistance

ling/c sc/psyc 438/538 -...

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