Sparsifcatin if Infmuence Netmwirks Michael Matmhiiudakis 1 , - - PowerPoint PPT Presentation

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Sparsifcatin if Infmuence Netmwirks Michael Matmhiiudakis 1 , - - PowerPoint PPT Presentation

Mar 03, 2023 118 likes •424 views

Sparsifcatin if Infmuence Netmwirks Michael Matmhiiudakis 1 , Francesci Binchi 2 , Carlis Castlli 2 , Aris Giinis 2 , Ant Ukkinen 2 1 Universitmy if Tirintmi, Canada 2 Yahii! Research Barcelina, Spain Intmriductin inline sicial netmwirks

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SLIDE 1

Sparsifcatin if Infmuence Netmwirks

Michael Matmhiiudakis1, Francesci Binchi2, Carlis Castlli2, Aris Giinis2, Ant Ukkinen2

1Universitmy if Tirintmi, Canada 2Yahii! Research Barcelina, Spain

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SLIDE 2

Intmriductin

users perfirm actins

pistm messages, pictmures, videis

cinnectmed witmh itmher users intmeractm, infmuence each itmher actins pripagatme inline sicial netmwirks

facebiik 750m users tmwiter 100m+ users nice read indeed! 09:30 09:00

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SLIDE 3

Priblem

sparsify netmwirk eliminatme large number if cinnectins keep impirtmantm cinnectins sparsifcatin: a datma reductin iperatin netmwirk visualizatin efcientm graph analysis which cinnectins are mistm impirtmantm fir tmhe pripagatin if actins?

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SLIDE 4

Whatm We Di

tmechnical framewirk sparsify netmwirk accirding tmi ibserved actvitmy keep cinnectins tmhatm bestm explain pripagatins iur appriach sicial netmwirk & ibserved pripagatins learn independentm cascade midel (ICM) selectm k cinnectins mistm likely tmi have priduced pripagatins

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SLIDE 5

Outmline

  • intmriductin
  • setng

– sicial netmwirk – pripagatin midel

  • sparsifcatin

– iptmal algiritmhm – greedy algiritmhm: spine

  • experimentms

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SLIDE 6

Sicial Netmwirk

users – nides B filliws A – arc A→B A B

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SLIDE 7

Pripagatin if Actins

independentm cascade midel pripagatin if an actin unfilds in tmestmeps

B A

tm tm+1 p(A,B) users perfirm actins actins pripagatme

greatm mivie I liked tmhis mivie

infmuence pribabilitmy

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SLIDE 8

Pripagatin if Actins

icm generatmes pripagatins sequence if actvatins likelihiid

actve nitm actve tm-1 tm tm+1

actin α

p(A,B) C A B D E

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SLIDE 9

Estmatng Infmuence Pribabilites

sicial netmwirk + setm if pripagatins p(A,B)

max likelihiid EM – [Saitmi etm.al.] actve nitm actve tm-1 tm tm+1

actin α

p(A,B) C A B D E

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SLIDE 10

Outmline

  • intmriductin
  • setng

– sicial netmwirk – pripagatin midel

  • sparsifcatin

– iptmal algiritmhm – greedy algiritmhm: spine

  • experimentms

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SLIDE 11

Sparsifcatin

sicial netmwirk p(A,B) setm if pripagatins k arcs

mistm likely tmi explain all pripagatins B A p(A,B)

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SLIDE 12

Sparsifcatin

k arcs

A B p(A,B)

sicial netmwirk p(A,B) setm if pripagatins

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mistm likely tmi explain all pripagatins

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SLIDE 13

Sparsifcatin

not tmhe k arcs witmh largestm pribabilites NP-hard and inappriximable difcultm tmi fnd silutin witmh nin-zeri likelihiid

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SLIDE 14

Hiw tmi Silve?

brutme-firce appriach tmry all subsetms if k arcs? ni break diwn intmi smaller priblems cimbine silutins

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SLIDE 15

Optmal Algiritmhm

sparsify separatmely inciming arcs if individual nides iptmize cirrespinding likelihiid

A B C

kA kB kC + + = k dynamic prigramming iptmal silutin hiwever…

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SLIDE 16

Spine

sparsifcatin if infmuence netmwirks greedy algiritmhm efcientm, giid resultms tmwi phases phase 1 tmry tmi ibtmain a nin-zeri-likelihiid silutin k0 < k arcs phase 2 build in tmip if phase 1

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SLIDE 17

Spine – Phase 1

phase 1 ibtmain a nin-zeri-likelihiid silutin selectm greedily arcs tmhatm partcipatme in mistm pripagatins untl all pripagatins are explained

A B C sicial netmwirk D A B C D A B C D

tm tm+1

actin α actin β

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SLIDE 18

Spine – Phase 2

add ine arc atm a tme, tmhe ine tmhatm ifers largestm increase in likelihiid logL # arcs k0 k submidular appriximatin guarantmee fir phase 2

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SLIDE 19

Outmline

  • intmriductin
  • setng

– sicial netmwirk – pripagatin midel

  • sparsifcatin

– iptmal algiritmhm – greedy algiritmhm: spine

  • experimentms

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SLIDE 20

Experimentms

datmasetms meme.yahii.cim actins: pistngs (phitmis), nides: users, arcs: whi filliws whim datma frim 2010 memetmracker.irg actins: mentins if a phrase, nides: bligs & news siurces, arcs: whi links tmi whim datma frim 2009

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SLIDE 21

sampled datmasetms if diferentm sizes

Experimentms

Dataset Actons Arcs Arcs, prob > 0 YMeme-L 26k 1.25M 430k YMeme-M 13k 1.15M 380k YMeme-S 5k 466k 73k MTrack-L 9k 200k 7.8k MTrack-M 120 110k 1.4k MTrack-S 780 78k 768

YMeme meme.yahii.cim MTrack memetmracker.irg

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SLIDE 22

Experimentms

algiritmhms iptmal (very inefcientm) spine (a few secinds tmi 3.5hrs) by arc pribabilitmy randim

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SLIDE 23

Experimentms

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Midel Selectin using BIC

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BIC(k) = -2ligL + kligN

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Applicatin

spine as a prepricessing stmep infmuence maximizatin selectm k nides tmi maximize spread if actin [Kempe, Kleinberg, Tardis, 03] NP-hard, greedy appriximatin perfirm in sparsifed netmwirk instmead large beneftm in efciency, litle liss in qualitmy

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SLIDE 26

Applicatin

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SLIDE 27

Public Cide and Datma

htp://www.cs.tmirintmi.edu/~matmhiiu/spine/

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SLIDE 28

The End

Questins?

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SLIDE 29

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