partitioning algorithms for improving efficiency of topic modeling parallelization

PartitioningAlgorithmsforImprovingEfficiency

ofTopicModelingParallelization

HungNghiepTran

UniversityofInformationTechnology

Vietnam

AtsuhiroTakasu

NationalInstituteofInformatics

Japan

Originalpaper:HungNghiepTran,AtsuhiroTakasu.PartitioningAlgorithmsforImprovingEfficiencyofTopicModelingParallelization.PacRim2015.Resource: Seethelastslide(SlideShareconvention.)

IntroductionTopicmodeling,e.g.,LDA.

Topicmodelingisslow.2

Imagesource:D.M.Blei,ProbabilisticTopicModels,Comm.ACM55,4(2012),77-84.

IntroductionTopicmodeling,e.g.,LDA.

Topicmodelingisslow.3

Imagesource:D.M.Blei,ProbabilisticTopicModels,Comm.ACM55,4(2012),77-84.

Introduction

Parallelization.CollapsedGibbsSamplingissequentialinnature.àDifficulttoparallelize.

4

Word

Document

Topic

Document

Word

Topic

Data

Params

Introduction

Parallelization.CollapsedGibbsSamplingissequentialinnature.àDifficulttoparallelize.

5

Word

Document

Topic

Document

Word

Topic

Data

Params

Introduction• Datapartitioning-basedapproach[1].

§ Howitworks:• Partitiondatabothhorizontallyandvertically.

• Nonconflictingparallelsampleoneachdiagonalline.

§ Howit‘sgood:• SharethesamecopyofDataandParams.

• Theoreticallylinearspeedup.

• Loadbalancing.§ Alltheotherprocessesmustwaitfor

theslowestone.à Difficulttoloadbalance.

6Do

cument

Word

[1]F.Yan,etal.,ParallelInferenceforLatentDirichletAllocationonGraphicsProcessingUnits,NIPS(2009).

Topic

Document

Word

Topic

Introduction• Datapartitioning-basedapproach[1].

§ Howitworks:• Partitiondatabothhorizontallyandvertically.

• Nonconflictingparallelsampleoneachdiagonalline.

§ Howit‘sgood:• SharethesamecopyofDataandParams.

• Theoreticallylinearspeedup.

• Loadbalancing.§ Alltheotherprocessesmustwaitfor

theslowestone.à Difficulttoloadbalance.

7Do

cument

Word

[1]F.Yan,etal.,ParallelInferenceforLatentDirichletAllocationonGraphicsProcessingUnits,NIPS(2009).

Topic

Document

Word

Topic

OurGoal

To develop data partitioning algorithmsthat achieve better load balance toimprove efficiency of topic modelingparallelization.

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RelatedWork• Topicmodeling:

§ LDA:thefirsttopicmodel.[Bleietal.,JMLR‘03]

• Advancedtopicmodeling:§ BagofTimestamps(BoT):time-

awaremodeling. [Masadaetal.,ADWM‘09]

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RelatedWork• Topicmodeling:

§ LDA:thefirsttopicmodel.[Bleietal.,JMLR‘03]

• Advancedtopicmodeling:§ BagofTimestamps(BoT):time-

awaremodeling. [Masadaetal.,ADWM‘09]

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RelatedWorkParallelizationapproach:1. CopyandSync:Samplingonmultiplecopiesofdatathen

synchronizeaftereachsamplingiteration.E.g.,[Newmanetal.,JMLR‘09].

àWeakness:Syncingoverhead.

2. Non-blockingaccess:Accesstoshareddatabyusingatomicoperation.E.g.,[SmolaandNarayanamurthy,VLDB‘10].

àWeakness:Moreconflictwhenincreasingparallelprocesses.

3. Datapartitioning-based:Accesstoshareddatabypartitioningdata.E.g.,[Yanetal.,NIPS‘09].

àWeakness:Loadbalancing.

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2. Non-blockingaccess:Accesstoshareddatabyusingatomicoperation.E.g.,[Smola&Narayanamurthy,VLDB‘10].




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2. Non-blockingaccess:Accesstoshareddatabyusingatomicoperation.E.g.,[Smola&Narayanamurthy,VLDB‘10].




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ProblemDefinition

• Loadbalancingproblem:§ E.g.,require:

|A1|≈ |B1| ≈ |C1||A2|≈ |B2| ≈ |C2||A3|≈ |B3| ≈ |C3|

§ Equivalenttoanintegerprogrammingproblem:NP-hard.

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A1 A2 A3

B3 B1 B2

C2 C3 C1Document

Word

ProblemDefinition

• Loadbalancingratio𝜂:§ Optimalcost:dividingworkequally.

• E.g.,C#$% ='#%()+#,-%#./0

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§ Actualcost:costoftheslowestpartitiononeachdiagonalline.• E.g.,𝐶 = 𝐴1 + 𝐵2 + |𝐵3|

§ Loadbalancingratio𝜂 = :;<=:

àMinimizeloadbalancingratio𝜂.

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A1 A2 A3

B3 B1 B2

C2 C3 C1Document

Word

E.g.,A1,B2,B3arethepartitionsthathavethemostwordtokensoneachdiagonalline,respectively.

ProblemDefinition

• Loadbalancingratio𝜂:§ Optimalcost:dividingworkequally.

• E.g.,C#$% ='#%()+#,-%#./0

1

§ Actualcost:costoftheslowestpartitiononeachdiagonalline.• E.g.,𝐶 = 𝐴1 + 𝐵2 + |𝐵3|

§ Loadbalancingratio𝜂 = :;<=:

àMinimizeloadbalancingratio𝜂.

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A1 A2 A3

B3 B1 B2

C2 C3 C1Document

Word

E.g.,A1,B2,B3arethepartitionsthathavethemostwordtokensoneachdiagonalline,respectively.

ProposedApproach

• Toachievebetterloadbalance:Step1:DistributewordtokensevenlyinDocument-Wordmatrix.

à Bypermutingrowsandcolumns.

Step2:DivideDocument-Wordmatrix into𝑃×𝑃 approx.equalpartitions.

àSimplybycountingwordtokensinrows,thendividingrowsintoPconsecutivegroups,eachcontainsapprox.𝐶#$% wordtokens.

àSimilarlyforcolumns.

• Note:Eachstepisdoneseparatelyforrowsandcolumns.

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ProposedApproach







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ProposedApproach







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ProposedApproach







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PermutationExample(Forrows,similarlyforcolumns)

• Input:§ Darkerdenotesmoreword

tokens.§ Assumethereareonly5

documentsand5words.• Output:

§ Heuristic1(alsoAlgorithmA1):Darkestandlightestrowsareinterposed.

§ Heuristic2 (alsoAlgorithmA2):SimilarlytoHeuristic1butdofrombothends.

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Input







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Input

Heuristic1’sOutput







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Input




• Input:§ Darkerdenotesmorewordtokens.§ Assumetherearealotofrows.

• Output:§ Heuristic3 (alsoAlgorithmA3):

• First,createPrangesofrows,eachcontainsalldarkandlightrows.

• ThenuniformlyrandomlypermuteeachofthosePrangesofrows.

à Theoutputisarandomlyshuffledmatrixwiththeconditionthatrowcolor(numberofwordtokensineachrow)aredistributedevenly.

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Input







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Input

Intermediate







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Input

Intermediate

Output







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Input

Intermediate

Output

ExtendingtoParallelBoT

• BagofTimestamps(BoT)[Masadaetal.,ADWM‘09]:§ Time-awaremodeling.§ BettertopicqualitythanLDA,but

trainingisslower.§ Timestampsaretreatedaswords.

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HowtoExtendtoParallelBoT

• TreatDocument-Timestamp(D-TS)matrixsimilarlyasDocument-Word (D-W) matrix.à Whenpartitioning:PartitionD-Wmatrix

normallyasinLDA,partitionD-TSmatrixthesamewayasD-Wmatrix.

à Whensampling:AlternatelysamplingeachdiagonallineofD-WmatrixandeachdiagonallineofD-TSmatrix.

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ExperimentalData

• OrdinarydatasetsNIPSandNYTimes:§ Source:http://archive.ics.uci.edu/ml/datasets/Bag+of+Words

• NewdatasetMAS:§ Dataaboutscientificpapers,withpublishedyearinformation.§ Tobereleasedfromhttps://sites.google.com/site/tranhungnghiep

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Evaluation• Tomeasuretheefficiencyofpartitioningdata:

§ Loadbalancingratio𝜂.• Thehigherthebetter.𝑆𝑝𝑒𝑒𝑑𝑢𝑝𝑓𝑎𝑐𝑡𝑜𝑟 ≈ 𝜂×|𝑃𝑎𝑟𝑎𝑙𝑙𝑒𝑙𝑝𝑟𝑜𝑐𝑒𝑠𝑠𝑒𝑠|.

• Tomeasurethequalityofextractedtopics:§ Abilitytodescribedata:Perplexity.

• Thelowerthebetter.

𝑃𝑒𝑟𝑝 𝑥 = exp − ST log𝑝 𝑥 ,

withlog𝑝 𝑥 = ∑ 𝑙𝑜𝑔∑ 𝜃.|[𝜙]^_|..[` .

• Baselinealgorithm:[Yanetal.,NIPS‘09]§ Randomlypermutedocumentsandwordsinthedatamatrix.§ Usethepermutationwiththehighest𝜂.

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ImprovementonLoadBalancing

Loadbalancingratio𝜼 onNIPS.

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• A3givesthehighestresults.• A1andA2areverycompetitive.

Note:𝑆𝑝𝑒𝑒𝑑𝑢𝑝𝑓𝑎𝑐𝑡𝑜𝑟 ≈ 𝜂×|𝑃𝑎𝑟𝑎𝑙𝑙𝑒𝑙𝑝𝑟𝑜𝑐𝑒𝑠𝑠𝑒𝑠|.

ImprovementonLoadBalancing

Loadbalancingratio𝜼 onNYT.

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• A3givesthehighestresults.• A1andA2arequitegood,especiallywithlarge𝑃.

Note:𝑆𝑝𝑒𝑒𝑑𝑢𝑝𝑓𝑎𝑐𝑡𝑜𝑟 ≈ 𝜂×|𝑃𝑎𝑟𝑎𝑙𝑙𝑒𝑙𝑝𝑟𝑜𝑐𝑒𝑠𝑠𝑒𝑠|.

TheQualityofTopicModelingusingParallelBoTAlgorithm

PerplexityoftheBoTmodellearnedbytheparallelBoTalgorithmonMASdataset.

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• Parallelalgorithmdoesnotaffectthequalityoftopics.• WhenPislarge,qualityisslightlybetter.

Conclusion

• Wehavedevelopeddatapartitioningalgorithmsthatachievebetterloadbalancetoimproveefficiencyoftopicmodelingparallelization.

• WehavealsodemonstratedtheextensibilityofthesealgorithmsonBoTmodel.

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Conclusion



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Conclusion



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Futurework

• Weplantodevelopmethodsforimprovingparallelizationefficiencyonadvancedtopicmodels.

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Thankyouverymuch!

Futurework

• Weplantodevelopmethodsforimprovingparallelizationefficiencyonadvancedtopicmodels.

Thankyouverymuch!

Originalpaper:HungNghiepTran,Atsuhiro Takasu.PartitioningAlgorithmsforImprovingEfficiencyofTopicModelingParallelization.PacRim 2015.Code&Data:https://github.com/tranhungnghiep/Parallel_Topic_Modeling.Otherresource:https://sites.google.com/site/tranhungnghiep/code-data/time-aware-topic-modeling-parallelization.

partitioning algorithms for improving efficiency of topic modeling parallelization

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