Text Classification and Naïve Bayes - Texas A&M...

TextClassificationandNaïveBayes

TheTaskofTextClassification

Many slides are adapted from slides by Dan Jurafsky

Isthisspam?

WhowrotewhichFederalistpapers?• 1787-8:anonymousessaystrytoconvinceNewYorktoratifyU.SConstitution: Jay,Madison,Hamilton.

• Authorshipof12ofthelettersindispute• 1963:solvedbyMosteller andWallaceusingBayesianmethods

JamesMadison AlexanderHamilton

Maleorfemaleauthor?1. By1925present-dayVietnamwasdividedintothreeparts

underFrenchcolonialrule.ThesouthernregionembracingSaigonandtheMekongdeltawasthecolonyofCochin-China;thecentralareawithitsimperialcapitalatHuewastheprotectorateofAnnam…

2. Claraneverfailedtobeastonishedbytheextraordinaryfelicityofherownname.Shefoundithardtotrustherselftothemercyoffate,whichhadmanagedovertheyearstoconverthergreatestshameintooneofhergreatestassets…

S.Argamon,M.Koppel,J.Fine,A.R.Shimoni,2003.“Gender,Genre,andWritingStyleinFormalWrittenTexts,”Text,volume23,number3,pp.321–346

Positiveornegativemoviereview?• unbelievablydisappointing• Fullofzanycharactersandrichlyappliedsatire,andsomegreatplottwists

• thisisthegreatestscrewballcomedyeverfilmed

• Itwaspathetic.Theworstpartaboutitwastheboxingscenes.

5

Whatisthesubjectofthisarticle?

• Antogonists andInhibitors

• BloodSupply• Chemistry• DrugTherapy• Embryology• Epidemiology• …

6

MeSH SubjectCategoryHierarchy

?

MEDLINE Article

TextClassification

• Assigningsubjectcategories,topics,orgenres• Spamdetection• Authorshipidentification• Age/genderidentification• LanguageIdentification• Sentimentanalysis• …

TextClassification:definition• Input:– adocumentd– afixedsetofclassesC= {c1,c2,…,cJ}

• Output:apredictedclassc Î C

ClassificationMethods:Hand-codedrules

• Rulesbasedoncombinationsofwordsorotherfeatures– spam:black-list-addressOR(“dollars”AND“have beenselected”)

• Accuracycanbehigh– Ifrulescarefullyrefinedbyexpert

• Butbuildingandmaintainingtheserulesisexpensive

ClassificationMethods:SupervisedMachineLearning

• Input:– adocumentd– afixedsetofclassesC= {c1,c2,…,cJ}– Atrainingsetofm hand-labeleddocuments(d1,c1),....,(dm,cm)

• Output:– alearnedclassifierγ:dà c

10

ClassificationMethods:SupervisedMachineLearning

• Anykindofclassifier– Naïve Bayes– Logisticregression,maxent– Support-vectormachines– k-NearestNeighbors

– …


TheTaskofTextClassification


FormalizingtheNaïve BayesClassifier

NaïveBayesIntuition

• Simple(“naïve”)classificationmethodbasedonBayesrule

• Reliesonverysimplerepresentationofdocument– Bagofwords

Bayes’RuleAppliedtoDocumentsandClasses

•Foradocumentd andaclassc

P(c | d) = P(d | c)P(c)P(d)

Naïve BayesClassifier(I)

cMAP = argmaxc∈C

P(c | d)

= argmaxc∈C

P(d | c)P(c)P(d)

= argmaxc∈C

P(d | c)P(c)

MAP is “maximum a posteriori” = most likely class

Bayes Rule

Dropping the denominator

Naïve BayesClassifier(II)

cMAP = argmaxc∈C

P(d | c)P(c)

Document d represented as features x1..xn

= argmaxc∈C

P(x1, x2,…, xn | c)P(c)

Naïve BayesClassifier(IV)

How often does this class occur?

cMAP = argmaxc∈C

P(x1, x2,…, xn | c)P(c)

O(|X|n•|C|)parameters

We can just count the relative frequencies in a corpus

Couldonlybeestimatedifavery,verylargenumberoftrainingexampleswasavailable.

MultinomialNaïve BayesIndependenceAssumptions

• BagofWordsassumption:Assumepositiondoesn’tmatter

• ConditionalIndependence:AssumethefeatureprobabilitiesP(xi|cj)areindependentgiventheclassc.

P(x1, x2,…, xn | c)

P(x1,…, xn | c) = P(x1 | c)•P(x2 | c)•P(x3 | c)•...•P(xn | c)

ThebagofwordsrepresentationI love this movie! It's sweet, but with satirical humor. The dialogue is great and the adventure scenes are fun… It manages to be whimsical and romantic while laughing at the conventions of the fairy tale genre. I would recommend it to just about anyone. I've seen it several times, and I'm always happy to see it again whenever I have a friend who hasn't seen it yet.

γ(

)=c

Thebagofwordsrepresentation

γ(

)=cgreat 2love 2

recommend 1

laugh 1happy 1

... ...

Planning GUIGarbageCollection

Machine Learning NLP

parsertagtrainingtranslationlanguage...

learningtrainingalgorithmshrinkagenetwork...

garbagecollectionmemoryoptimizationregion...

Test document

parserlanguagelabeltranslation…

Bagofwordsfordocumentclassification

...planningtemporalreasoningplanlanguage...

?

ApplyingMultinomialNaiveBayesClassifierstoTextClassification

cNB = argmaxc j∈C

P(cj ) P(xi | cj )i∈positions∏

positions ¬ allwordpositionsintestdocument


FormalizingtheNaïve BayesClassifier


Naïve Bayes:Learning

LearningtheMultinomialNaïve BayesModel

• Firstattempt:maximumlikelihoodestimates– simplyusethefrequenciesinthedata

Sec.13.3

P̂(wi | cj ) =count(wi,cj )count(w,cj )

w∈V∑

P̂(cj ) =doccount(C = cj )

Ndoc

Parameterestimation

• Createmega-documentfortopicj byconcatenatingalldocsinthistopic– Usefrequencyofw inmega-document

fractionoftimeswordwi appearsamongallwordsindocumentsoftopiccj

P̂(wi | cj ) =count(wi,cj )count(w,cj )

w∈V∑

ProblemwithMaximumLikelihood• Whatifwehaveseennotrainingdocumentswiththewordfantastic and

classifiedinthetopicpositive (thumbs-up)?

• Zeroprobabilitiescannotbeconditionedaway,nomattertheotherevidence!

P̂("fantastic" positive) = count("fantastic", positive)count(w, positive

w∈V∑ )

= 0

cMAP = argmaxc P̂(c) P̂(xi | c)i∏

Sec.13.3

Laplace(add-1)smoothing:unknownwords

P̂(wu | c) = count(wu,c)+1

count(w,cw∈V∑ )

#

$%%

&

'(( + V +1

Addoneextrawordtothevocabulary,the“unknownword”wu

=1

count(w,cw∈V∑ )

#

$%%

&

'(( + V +1

UnderflowPrevention:logspace• Multiplyinglotsofprobabilitiescanresultinfloating-pointunderflow.• Sincelog(xy)=log(x)+log(y)

– Bettertosumlogsofprobabilitiesinsteadofmultiplyingprobabilities.• Classwithhighestun-normalizedlogprobabilityscoreisstillmost

probable.

• Modelisnowjustmaxofsumofweights

cNB = argmaxc j∈C

logP(cj )+ logP(xi | cj )i∈positions∑

TextClassificationandNaïve Bayes

Naïve Bayes:Learning


MultinomialNaïve Bayes:AWorkedExample

Choosingaclass:P(c|d5)

P(j|d5) 1/4*(2/10)3 *2/10 *2/10≈0.00008

Doc Words Class

Training 1 Chinese BeijingChinese c

2 ChineseChineseShanghai c3 ChineseMacao c4 TokyoJapanChinese j

Test 5 ChineseChineseChineseTokyo Japan ?

33

ConditionalProbabilities:P(Chinese|c)=P(Tokyo|c)=P(Japan|c)=P(Chinese|j)=P(Tokyo|j)=P(Japan|j)=

Priors:P(c)=P(j)=

34 1

4

P̂(w | c) = count(w,c)+1count(c)+ |V |

P̂(c) = Nc

N

(5+1)/(8+7)=6/15(0+1)/(8+7)=1/15

(1+1)/(3+7)=2/10(0+1)/(8+7)=1/15

(1+1)/(3+7)=2/10(1+1)/(3+7)=2/10

3/4*(6/15)3 *1/15 *1/15≈0.0002

µ

µ

+1

Summary:NaiveBayesisNotSoNaive• RobusttoIrrelevantFeatures

IrrelevantFeaturescanceleachotherwithoutaffectingresults

• Verygoodindomainswithmanyequallyimportantfeatures

DecisionTreessufferfromfragmentation insuchcases– especiallyiflittledata

• Optimaliftheindependenceassumptionshold:Ifassumedindependenceiscorrect,thenitistheBayesOptimalClassifierforproblem

• Agooddependablebaselinefortextclassification– Butwewillseeotherclassifiersthatgivebetteraccuracy


MultinomialNaïve Bayes:AWorkedExample


TextClassification:Evaluation

The2-by-2contingencytable

correct notcorrectselected tp fp

notselected fn tn

Precisionandrecall• Precision:%ofselecteditemsthatarecorrectRecall:%ofcorrectitemsthatareselected

correct notcorrectselected tp fp

notselected fn tn

Acombinedmeasure:F• AcombinedmeasurethatassessestheP/RtradeoffisFmeasure(weightedharmonicmean):

• PeopleusuallyusebalancedF1measure– i.e.,withb =1(thatis,a =½): F =2PR/(P+R)

RPPR

RP

F+

+=

−+= 2

2 )1(1)1(1

1ββ

αα

Confusionmatrixc• Foreachpairofclasses<c1,c2>howmanydocumentsfromc1 wereincorrectlyassignedtoc2?– c3,2:90wheatdocumentsincorrectlyassignedtopoultry

40

Docsintestset AssignedUK

Assignedpoultry

Assignedwheat

Assignedcoffee

Assignedinterest

Assignedtrade

TrueUK 95 1 13 0 1 0

Truepoultry 0 1 0 0 0 0

Truewheat 10 90 0 1 0 0

Truecoffee 0 0 0 34 3 7

Trueinterest - 1 2 13 26 5

Truetrade 0 0 2 14 5 10

PerclassevaluationmeasuresRecall:Fractionofdocsinclassi classifiedcorrectly:

Precision:Fractionofdocsassignedclassi thatareactually

aboutclassi:

Accuracy:(1- errorrate)Fractionofdocsclassifiedcorrectly: 41

ciii∑

ciji∑

j∑

ciic ji

j∑

ciicij

j∑

Sec. 15.2.4

Micro- vs.Macro-Averaging– Ifwehavemorethanoneclass,howdowecombinemultipleperformancemeasuresintoonequantity?

• Macroaveraging:Computeperformanceforeachclass,thenaverage.Averageonclasses

• Microaveraging:Collectdecisionsforeachinstancefromallclasses,computecontingencytable,evaluate.Averageoninstances

42

Sec. 15.2.4

Micro- vs.Macro-Averaging:Example

Truth:yes

Truth:no

Classifier:yes 10 10

Classifier:no 10 970

Truth:yes

Truth:no



Truth:yes

Truth:no



43

Class1 Class2 MicroAve.Table

Sec.15.2.4

• Macroaveraged precision:(0.5+0.9)/2=0.7• Microaveraged precision:100/120=.83• Microaveraged scoreisdominatedbyscoreoncommonclasses

DevelopmentTestSetsandCross-validation

• Metric:P/R/F1orAccuracy• Unseentestset– avoidoverfitting (‘tuningtothetestset’)– moreconservativeestimateofperformance

– Cross-validationovermultiplesplits• Handlesamplingerrorsfromdifferentdatasets

– Poolresultsovereachsplit– Computepooleddev setperformance

Trainingset Development Test Set TestSet

TestSet

TrainingSet

TrainingSetDev Test

TrainingSet

Dev Test

Dev Test


TextClassification:Evaluation

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