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Connections between the Lines:

Augmenting Social Networks with Text

Jonathan Chang, Jordan Boyd-Graber, David M. Blei

KDD 09

June 29th, 2009

Princeton UniversityIdentity Guidelines Signature or wordmark

WORDMARK

SIGNATURE

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It need not appear in a large or prominent position, but it should be included to signal a publication’s core relationship to Princeton.

The signature should be used in all situations that call for the Princeton “logo,” for instance on promotional materials for public events for which Princeton is the primary sponsor.

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Digital art for the Princeton signature and wordmark is available to the Princeton community for use on publications relating to the University. Please visit our website (www.princeton.edu/identity) or contact Megan Peterson ([email protected] / 609-258-5730) or Laurel Masten Cantor ([email protected] / 609-258-5734) in the Offi ce of Communications for digital fi les.

6

Jonathan Chang, Jordan Boyd-Graber, David M. Blei Connections between the Lines

Motivation

Data that express relationships between ensembles of entities

(people, places, companies, genes, etc.) is pervasive.

Jonathan Chang, Jordan Boyd-Graber, David M. Blei Connections between the Lines

Motivation

Annotating the edges of these networks with rich information is

often a desideratum.

Jonathan Chang

Jordan Boyd-GraberYou and Jordan both went to Princeton.

Jonathan Chang, Jordan Boyd-Graber, David M. Blei Connections between the Lines

Motivation

Unfortunately, much of the rich information about links is encoded

implicitly as free text.

Example

In 1938, Wyman co-starred with Ronald Reagan. Reagan and actressJane Wyman were engaged at the Chicago Theater and married inGlendale, California. Following arguments about Reagan's politicalambitions, Wyman �led for divorce in 1948. Since Reagan is the onlyU.S. president to have been divorced, Wyman is the only ex-wife of anAmerican President.

Jonathan Chang, Jordan Boyd-Graber, David M. Blei Connections between the Lines

Motivation

Using the text as input, our goal is to annotate a network with this

information.

Example

Ronald Reagan

Jane WymanYou and Jane used to be married.

Jonathan Chang, Jordan Boyd-Graber, David M. Blei Connections between the Lines

Main idea

We de�ne a probabilistic model Networks Uncovered By

Bayesian Inference (Nubbi).

Using Nubbi, we can create a social network by discovering

relations over the ensemble of people.

Because Nubbi is a fully Bayesian approach, we can

incorporate information from other data-mining approaches as

priors (Agichtein and Gravano 2003; Diehl et al. 2007; Mei

et al. 2007; Sahay et al. 2008; Banko et al. 2007; Katrenko

and Adriaans 2007; Davidov et al. 2007).

Wikipedia

Joseph Stalin

Winston Churchill

Lyndon B. Johnson

Mao Zedong

Jimmy Carter

Margaret Thatcher

Ronald Reagan

Richard Nixon

Nikita KhrushchevJohn F. KennedyHubert

Humphrey

George H. W. Bush

Ross Perot

Leon Trotsky

Lev Kamenev

Zhou Enlai

Mikhail Gorbachev

labourgovernleaderbritishworld

sovietcommunist

centralunion

full

sovietrussiangovernunion

nuclear

republicanstate

federalistvotevice

Jonathan Chang, Jordan Boyd-Graber, David M. Blei Connections between the Lines

A larger example...

lazio, rick arichter, mikewilder, l douglasforeman, georgemehta, zubinbhutto, benazirwright, jimolmert, ehudpinochet, augustohatch, orrin gberlin, irvingsouter, david htower, john ghusband, rick drisen, jamescharles, eleanorklebold, dylanrather, danmcmellon, edwardsaint laurent, yveshelms, jessespitzer, eliot lpanetta, leon ecolumbus, christopher

jesus christmcveigh, timothy jameso'neill, paulmartinez, pedrobarry, marion s jrels, erniechernomyrdin, viktor s

hynes, charles jewing, patrickmiers, harriet estein, andrew jaung san suu kyi, dawsilver, sheldonspecter, arlencoughlin, tomkennedy, john fitzgerald

rodman, dennischaney, donjames, caryn

lane, nathanhashimoto, ryutaro

lautenberg, frank r

giambi, jasonde klerk, f wmourning, alonzo

mapplethorpe, robert

glavine, tomwinfrey, oprahvan horn, keithjeter, derek

reagan, ronaldlimbaugh, rush

netanyahu, benjamin

law, bernard fsessions, william s

fujimori, alberto

ward, charliebarron, james

van gundy, jeff

musharraf, pervez

blair, jayson

valentine, bobby

rowland, john g

chass, murray

jacobs, marc

puccini, giacomo

gates, henry louis jr

staples, brent

baker, howard h jr

clark, wesley k

koch, edward i

canseco, jose

major, john

plame, valerie

o'neill, paul h

holyfield, evander

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hard p

abdullahbush, la

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rocker, john

norton, gale

herbert, bob

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lieberman, joseph i

mailer, norm

an

ferguson, colin

kwan, m

ichelle

pavarotti, luciano

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h

mccall, h carl

lott, trent

forrester, douglas r

zemin, jiang

franco, john

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scorsese, martin

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ia

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sather, glen

bowe, riddick

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h

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botha, p w

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zedillo, ernesto

tierney, johnkerrigan, nancy

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jefferson, thomas

chun doo hwan

zuckerman, m

ortimer b

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arfreud, sigm

undchang, m

ichaelhevesi, alan gjohnson, philipcrew

, rudolph fagassi, andrepresley, elvisicahn, carl cbrow

n, ronald hw

ilson, robertchilds, chrislew

is, neil atharp, tw

ylaroosevelt, franklin delanow

eill, sanford ikerkorian, kirkm

uhamm

ad, john allennajibullahw

illiams, jayson

dodd, christopher jtaylor, charlescone, davidpol poto'connor, sandra daygoldm

an, ronald lyleerlanger, stevenking, stephenonassis, jacqueline kennedygoodnough, abbyharris, ericsolom

on, deborahsandom

ir, richardkaye, judith slay, kenneth lrandolph, w

illiecarter, vincestrauss, richardcham

orro, violeta barrios decorzine, jon sholbrooke, richard csinatra, frankbuchanan, patrick jgrasso, richard aahm

adinejad, mahm

oudw

ashington, georgebush, georgefox quesada, vicentegram

m, phil

spitzer, eliotfitzw

ater, marlin

sorenstam, annika

edwards, herm

anjackson, m

ichaelvan natta, don jrtrum

an, harry sabbas, m

ahmoud

cooper, michael

diller, barryboss, kennethseles, m

onicam

andela, nelson r

rumsfeld, donald h

weinstein, jack b

gingrich, newt

aspin, lesm

enem, carlos saul

kissinger, henry a

cage, johnbabbitt, bruce

schumer, charles e

assad, bashar al−

boutros−ghali, boutros

simm

s, phillipton, eric

newm

an, paul

mcgw

ire, mark

lee, wen ho

leahy, patrick j

grassley, charles e

libeskind, daniel

gephardt, richard a

brown, lee p

vacco, dennis c

rell, m jodi

tyson, mike

davis, grayo'donnell, rosie

roberts, john g jr

clinton, hillary rodham

goetz, bernhard hugo

stephanopoulos, george

aziz, tariqlew

insky, monica

iacocca, lee a

feiner, paul

smith, w

illiam kennedy

cunningham, m

erce

khomeini, ruhollah

skilling, jeffrey k

showalter, buck

samaranch, juan antonio

abraham, spencer

springsteen, bruce

davenport, lindsay

monroe, m

arilyn

rohde, david

gonzales, alberto r

romney, m

itt

lemieux, m

ario

trump, donald j

pearl, daniel

jackson, bo

kerik, bernard b

mason, c vernon

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gulotta, thomas s

maazel, lorin

lugar, richard g

lincoln, abraham

de la hoya, oscar

lewis, michael

jackson, jesse l

berlusconi, silvio

suhartowachtler, sol

aoun, michel

lendl, ivan

rushdie, salman

mandela, nelson

holden, stephen

chen shui−bian

albright, madeleine k

gotbaum, betsy

hanover, donna

tenet, george j

cardoso, fernando henrique

piniella, lou

sampras, pete

kimmelman, michael

walesa, lech

mozart, wolfgang amadeus

barkley, charles

levy, harold o

byrd, robert c

jones, roy jr

shays, christopher

cohen, william s

mueller, robert s iii

mitterrand, francois

ginsburg, ruth bader

elizabeth ii, queen of great britain

williams, venus

brodeur, martin

el−hage, wadih

aristide, jean−bertrand

feingold, russell d

hawkins, yusuf k

beethoven, ludwig van

carroll, sean

kerrey, bob

giuliani, rudolph w

cruise, tom

stewart, martha

john paul ii

berke, richard l

graf, steffi

mitchell, george j

chawla, kalpana

maxwell, robert

winfield, dave

o'rourke, andrew p

nelson, lemrick jr

rodgers, richard

kohl, helmut

koppel, ted

rubin, robert e

stern, howard

clinton, chelsea

wright, frank lloyd

d'amato, alfonse m

rich, frank

annan, kofi

jackson, phil

putin, vladimir v

irabu, hideki

weiner, anthony d

miller, gifford

sharpton, al

johnson, keyshawn

hubbell, webster l

egan, edward m

libby, i lewis jr

obama, barack

johnson, ben

roddick, andy

bin laden, osama

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boesky, ivan f

connors, jimmy

schwarzenegger, arnold

white, mary jo

ryan, george

mattingly, don

weld, william f

sosa, sammy

silverstein, larry a

wells, david

mccool, william c

traub, james

bratton, william j

sweeney, john j

daschle, tom

milken, michael r

ryan, nolan

blumenthal, richard

moussaoui, zacarias

jordan, michael

vallone, peter f

dylan, bob

christopher, warren m

codey, richard j

pagones, steven a

dershowitz, alan m

hewitt, lleyton

selig, budassad, hafez al−

bach, johann sebastian

altman, lawrence k

gehry, frankzimmer, richard a

daley, richard m

broad, william jbrady, lois smithsimpson, nicole brown

zarqawi, abu musab al−

reeves, dantrump, donaldiverson, allenknoblauch, chuckking, martin luther jrkennedy, anthony mkasparov, garykoresh, davidbenedict xvimarcos, ferdinand eferrer, fernando

Jonathan Chang, Jordan Boyd-Graber, David M. Blei Connections between the Lines

Topic Models

Nubbi leverages the machinery of topic modeling (Blei et al.

2003; Hofmann 1999; Steyvers and Gri�ths 2007), Bayesian

mixture models of discrete data.

Topic models have emerged as powerful tools for unsupervised

analysis of large document collections.

The multinomial parameters of the mixture components are

known as \topics."

Example (NYTimes using LDA)

law art politics sports

lawyer music republican game

justice �lm democrat coach

judge artist senate player

investigate art campaign play

prosecutor ballet mayor match

Jonathan Chang, Jordan Boyd-Graber, David M. Blei Connections between the Lines

Model input

We take as input text whose references to entities have been

identi�ed, and convert this into a collection of documents.

1 When Jesus had spoken these words, he went forth with his disciples over the brook Cedron, where was a garden, into the which he entered, and his disciples.

2 And Judas also, which betrayed him, knew the place: for Jesus ofttimes resorted thither with his disciples.

3 Judas then, having received a band of men and officers from the chief priests and Pharisees, cometh thither with lanterns and torches and weapons.

4 Jesus therefore, knowing all things that should come upon him, went forth, and said unto them, Whom seek ye?

5 They answered him, Jesus of Nazareth. Jesus saith unto them, I am he. And Judas also, which betrayed him, stood with them.

6 As soon then as he had said unto them, I am he, they went backward, and fell to the ground.

7 Then asked he them again, Whom seek ye? And they said, Jesus of Nazareth.

Jonathan Chang, Jordan Boyd-Graber, David M. Blei Connections between the Lines

Model input

4 Jesus therefore, knowing all things that should come upon him, went forth, and said unto them, Whom seek ye?

5 They answered him, Jesus of Nazareth. Jesus saith unto them, I am he. And Judas also, which betrayed him, stood with them.

6 As soon then as he had said unto them, I am he, they went backward, and fell to the ground.

7 Then asked he them again, Whom seek ye? And they said, Jesus of Nazareth.

1 When Jesus had spoken these words, he went forth with his disciples over the brook Cedron, where was a garden, into the which he entered, and his disciples.

2 And Judas also, which betrayed him, knew the place: for Jesus ofttimes resorted thither with his disciples.

3 Judas then, having received a band of men and officers from the chief priests and Pharisees, cometh thither with lanterns and torches and weapons.

received band officers chief priests Pharisees lanterns

torches weapons

spoken words disciples brook Cedron garden enter disciples knowing things

seek asked seek NazarethJesus

Judas

Jonathan Chang, Jordan Boyd-Graber, David M. Blei Connections between the Lines

Model input

1 When Jesus had spoken these words, he went forth with his disciples over the brook Cedron, where was a garden, into the which he entered, and his disciples.

2 And Judas also, which betrayed him, knew the place: for Jesus ofttimes resorted thither with his disciples.

3 Judas then, having received a band of men and officers from the chief priests and Pharisees, cometh thither with lanterns and torches and weapons.

4 Jesus therefore, knowing all things that should come upon him, went forth, and said unto them, Whom seek ye?

5 They answered him, Jesus of Nazareth. Jesus saith unto them, I am he. And Judas also, which betrayed him, stood with them.

6 As soon then as he had said unto them, I am he, they went backward, and fell to the ground.

7 Then asked he them again, Whom seek ye? And they said, Jesus of Nazareth.

betrayed knew place disciples answered Nazareth saith betrayed

Jesusand

Judas

Jonathan Chang, Jordan Boyd-Graber, David M. Blei Connections between the Lines

Intuition

Both individuals and pairs of people can be described by

topics.

Nubbi hypothesizes that each word in a pair context describes

either one of the entities or their relationship.

In 1938, Wyman co-starred with Ronald Reagan. Reagan and

actress Jane Wyman were engaged at the Chicago Theater and

married in Glendale, California. Following arguments about

Reagan's political ambitions, Wyman �led for divorce in 1948.

Since Reagan is the only U.S. president to have been divorced,

Wyman is the only ex-wife of an American President.

Jonathan Chang, Jordan Boyd-Graber, David M. Blei Connections between the Lines

Intuition

Red words can be explained by a politics topic.

Blue words can be explained by an acting topic.

politics words can be attributed to Ronald Reagan.

acting words can be attributed to either

Ronald Reagan or Jane Wyman.

The remaining words characterize their relationship.

In 1938, Wyman co-starred with Ronald Reagan. Reagan and

actress Jane Wyman were engaged at the Chicago Theater and

married in Glendale, California. Following arguments about

Reagan's political ambitions, Wyman �led for divorce in 1948.

Since Reagan is the only U.S. president to have been divorced,

Wyman is the only ex-wife of an American President.

Jonathan Chang, Jordan Boyd-Graber, David M. Blei Connections between the Lines

Graphical Model

MNe Ne,e'Kθ

βθ

ψe,e'

αθ

w

z

θe

αψ

c

πe,e'

ηθz

w

απ

βψ

ηψ

Ne'

z

w

θe'

...Ne''

z

w

θe''

N entity contexts M pair contexts Kψ relationship topicsKθ entity topics

These intuitions are encoded in this graphical model.

Jonathan Chang, Jordan Boyd-Graber, David M. Blei Connections between the Lines

Graphical Model

MNe Ne,e'Kθ

βθ

ψe,e'

αθ

w

z

θe

αψ

c

πe,e'

ηθz

w

απ

βψ

ηψ

Ne'

z

w

θe'

...Ne''

z

w

θe''

N entity contexts M pair contexts Kψ relationship topicsKθ entity topics

We must then infer the posterior probability over the hidden

variables (e.g., the hidden topics and the assignments of

topics to people and relationships) given the data.

Jonathan Chang, Jordan Boyd-Graber, David M. Blei Connections between the Lines

Graphical Model

MNe Ne,e'Kθ

βθ

ψe,e'

αθ

w

z

θe

αψ

c

πe,e'

ηθz

w

απ

βψ

ηψ

Ne'

z

w

θe'

...Ne''

z

w

θe''

N entity contexts M pair contexts Kψ relationship topicsKθ entity topics

The posterior lacks the structure for e�cient computation, so

exact posterior inference is intractable. We appeal instead to

mean-�eld variational inference (Jordan et al. 1999).

Jonathan Chang, Jordan Boyd-Graber, David M. Blei Connections between the Lines

Bible Topics

Relationships are described by relationship topics

(c.f. Bhattacharya et al. 2008; Newman et al. 2006; Rosen-Zvi

et al. 2004; Culotta et al. 2005; Rabbat et al. 2006).

Topics cluster words which are used to describe similar

relationships and pairs who participate in similar relationships.

People in the Bible

Topic 1 Topic 2

Jacob-Laban Adonizedek-Piram

Top pairs Miriam-Moses Abraham-Birsha

Ishmael-Sarah Birsha-Lot

wife king

abraham cave

Top words daughter lord

child smote

call great

Jonathan Chang, Jordan Boyd-Graber, David M. Blei Connections between the Lines

Describing relationships

Nubbi can predict words in each entity pair's text pro�le.

This describes the relationship between the entities.

6 8 10 12 14 16 18

−5.

9−

5.8

−5.

7−

5.6

−5.

5−

5.4

biological

Number of topics

Wor

d P

redi

ctio

n Lo

g Li

kelih

ood

6 8 10 12 14 16 18

−6.

5−

6.4

−6.

3−

6.2

−6.

1−

6.0

−5.

9

bible

Number of topics

6 8 10 12 14 16 18

−7.

5−

7.0

−6.

5

wikipedia

Number of topics

● Nubbi Author−Topic LDA Unigram Mutual

Jonathan Chang, Jordan Boyd-Graber, David M. Blei Connections between the Lines

Predicting entities

Nubbi can also predict which entities are best described by a text

pro�le.

6 8 10 12 14 16 18

−6.

0−

5.5

−5.

0−

4.5

−4.

0

biological

Number of topics

Ent

ity P

redi

ctio

n Lo

g Li

kelih

ood

●●

6 8 10 12 14 16 18

−6.

5−

6.0

−5.

5

bible

Number of topics

●●

6 8 10 12 14 16 18

−7.

0−

6.5

−6.

0−

5.5

−5.

0−

4.5

−4.

0

wikipedia

Number of topics

● Nubbi Author−Topic LDA Unigram Mutual

Jonathan Chang, Jordan Boyd-Graber, David M. Blei Connections between the Lines

NY Times social network

lazio, rick arichter, mikewilder, l douglasforeman, georgemehta, zubinbhutto, benazirwright, jimolmert, ehudpinochet, augustohatch, orrin gberlin, irvingsouter, david htower, john ghusband, rick drisen, jamescharles, eleanorklebold, dylanrather, danmcmellon, edwardsaint laurent, yveshelms, jessespitzer, eliot lpanetta, leon ecolumbus, christopher

jesus christmcveigh, timothy jameso'neill, paulmartinez, pedrobarry, marion s jrels, erniechernomyrdin, viktor s

hynes, charles jewing, patrickmiers, harriet estein, andrew jaung san suu kyi, dawsilver, sheldonspecter, arlencoughlin, tomkennedy, john fitzgerald

rodman, dennischaney, donjames, caryn

lane, nathanhashimoto, ryutaro

lautenberg, frank r

giambi, jasonde klerk, f wmourning, alonzo

mapplethorpe, robert

glavine, tomwinfrey, oprahvan horn, keithjeter, derek

reagan, ronaldlimbaugh, rush

netanyahu, benjamin

law, bernard fsessions, william s

fujimori, alberto

ward, charliebarron, james

van gundy, jeff

musharraf, pervez

blair, jayson

valentine, bobby

rowland, john g

chass, murray

jacobs, marc

puccini, giacomo

gates, henry louis jr

staples, brent

baker, howard h jr

clark, wesley k

koch, edward i

canseco, jose

major, john

plame, valerie

o'neill, paul h

holyfield, evander

mills, ric

hard p

abdullahbush, la

ura

odeh, mohammed saddiq

kozlowski, l dennis

karadzic, radovan

salinas de gortari,

carlos

federer, roger

jospin, lio

nel

bennett, willia

m j

nader, ralph

jackson, m

ark

steinbrenner, g

eorge m 3d

steinberg, li

sa

velella

, guy j

moynihan, d

aniel patric

k

kahane, m

eir

khamenei, a

li

darman, ri

chard g

barber, tiki

friedman, th

omas l

bradley, bill

minaya, o

mar

goldin, harris

on j

hernandez,

orlando

brown, d

ave

reich, ro

bert b

smith

, willi

am k

scoppetta

, nich

olas

james

, sha

rpe

gore

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mitterrand, francois

ginsburg, ruth bader

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king, martin luther jr

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fightmatch

trial

Jonathan Chang, Jordan Boyd-Graber, David M. Blei Connections between the Lines

Examining predictions on solicited descriptions

1 2 3 4 5 6 7 8

12

34

56

78

Lower is betterLog Rank (Author−Topic Model)

Log

Ran

k (N

ubbi

)

time

president

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countriesbush

prime

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figureolympic

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2004

opponents

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previously

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1996

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spot

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track stars

olympic

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president

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2000

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israelieast middle

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house

clinton

speaker

american

political

figures

case

accused

sexual

president

court

failed

supreme

reagan

time

countries

worldleaders

powers

worldleaders

person

president

general

attorney

president

stategeneral

attorney

washington

area

baseball

players

baseball

atlanta

president

republican

politicians

york

city

party

mayor

democratic

candidates

players

baseball

politicians

american

political

administration

figures

politicians

president

administration

defense

secretary

leaders

countries

republican

running

politicians

person

senators

president

state

leaders

palestinian

time

political

leaders

countries

court

candidates

supreme

americanpolitical

figures

party

democratic

electionpresidential

primary

president

ranpoliticians

leaders

countriesmiddle

eastern

politicians

yorkmayor

politicians

york

politicians

police

commissioner

jersey

baseball

owner

chief

staff

person

senators

part

east

process

middle

peacehusband

won

governor

ran

convicted

york

city

mayor

candidates

2001

state

politicians

president

state

secretary

york

city

politicians

executives disney

players

subject

iranpoliticians

president

vice

1988

candidates

president

political

south

africa

worldleaders

victim

leaders

countries

convicted

prime

israeli

Jonathan Chang, Jordan Boyd-Graber, David M. Blei Connections between the Lines

Examining predictions on solicited descriptions

1 2 3 4 5 6 7

12

34

56

7

Lower is betterLog Rank (Author−Topic Model)

Log

Ran

k (N

ubbi

)

baseball

africa

baseball

south

presidential

israeli

owner

chairman

terrorist

palestinianisraeli

ministerminister

olympic

palestinian

primeprimeprime

fed

israeliisraeli

democratic

peacepeace

trackiran

peaceparty

candidates

democraticiraq

primaryrussian

russia

candidates

presidentialpresidentialpresidential

stars

candidates

supreme

presidential

senatedemocratic

presidential

politicianspoliticians2001

case

running

administrationcourt

time

worldworld

presidentstatestate

governor

figure

nations

president

tennis

wife

opponents

disney

baseball

nations

york

brothers

president

brothers

married

tennistennis

wife

fatherfather

husband

wifewife

sex

husband

wifehusbandhusbandwifewife

sonson

sexual

husbandhusband

sex

husbandhusband

relationship

brother

husband

sexualsexual

Jonathan Chang, Jordan Boyd-Graber, David M. Blei Connections between the Lines

Conclusion

Networks of entities are a pervasive form of data.

There are deep meanings associated with the links in these

networks.

These meanings are often not encoded in the network itself,

but rather as free text elsewhere.

The Nubbi model allows us to take this text and infer

characterizations of the relationships between the ensemble of

entities.

This is an important step towards mining complete social

networks from free text.

Thanks!

Jonathan Chang, Jordan Boyd-Graber, David M. Blei Connections between the Lines

Wikipedia Topics

Nubbi learns topics associated with individual entities.

This clusters entities according to the words used to describe

them.

People in Wikipedia

Topic 1 Topic 2

Frederick Sanger Kate Winslet

Top Entities Svante Arrhenius Ringo Starr

William Ramsay Al Pacino

work �lm

universe music

Top Terms year album

develop award

society song

Jonathan Chang, Jordan Boyd-Graber, David M. Blei Connections between the Lines

Wikipedia Topics

Nubbi also learns topics associated with pairs of entities.

These topics cluster together pairs with similar relationships.

People in Wikipedia

Topic 1 Topic 2

Tyler-Roosevelt Perot-Bush

Top Pairs McKinley-Roosevelt J.Q. Adams-Monroe

Taft-Roosevelt J.Q. Adams-Clay

president republican

vice march

Top Terms roosevelt reagan

calvin vote

johnson state

Jonathan Chang, Jordan Boyd-Graber, David M. Blei Connections between the Lines

Graphical Model

MNe Ne,e'Kθ

βθ

ψe,e'

αθ

w

z

θe

αψ

c

πe,e'

ηθz

w

απ

βψ

ηψ

Ne'

z

w

θe'

...Ne''

z

w

θe''

N entity contexts M pair contexts Kψ relationship topicsKθ entity topics

1 For each entity e,1 Draw entity topic proportions �e � Dir(��);2 For each word associated with this entity's context,

1 Draw topic assignment ze;n � Mult(�e);2 Draw word we;n � Mult(��

ze;n).

Jonathan Chang, Jordan Boyd-Graber, David M. Blei Connections between the Lines

Graphical Model

MNe Ne,e'Kθ

βθ

ψe,e'

αθ

w

z

θe

αψ

c

πe,e'

ηθz

w

απ

βψ

ηψ

Ne'

z

w

θe'

...Ne''

z

w

θe''

N entity contexts M pair contexts Kψ relationship topicsKθ entity topics

1 For each pair of entities e; e 0,1 Draw relationship topic proportions e;e0 � Dir(� );2 Draw selector proportions �e;e0 � Dir(��);3 For each word associated with this entity pair's context,

1 Draw selector ce;e0;n � Mult(�e;e0);

Jonathan Chang, Jordan Boyd-Graber, David M. Blei Connections between the Lines

Graphical Model

MNe Ne,e'Kθ

βθ

ψe,e'

αθ

w

z

θe

αψ

c

πe,e'

ηθz

w

απ

βψ

ηψ

Ne'

z

w

θe'

...Ne''

z

w

θe''

N entity contexts M pair contexts Kψ relationship topicsKθ entity topics

1 If ce;e0;n = 1,

1 Draw topic assignment ze;e0;n � Mult(�e);2 Draw word we;e0;n � Mult(��

ze;e

0;n

):

Jonathan Chang, Jordan Boyd-Graber, David M. Blei Connections between the Lines

Graphical Model

MNe Ne,e'Kθ

βθ

ψe,e'

αθ

w

z

θe

αψ

c

πe,e'

ηθz

w

απ

βψ

ηψ

Ne'

z

w

θe'

...Ne''

z

w

θe''

N entity contexts M pair contexts Kψ relationship topicsKθ entity topics

1 If ce;e0;n = 2,

1 Draw topic assignment ze;e0;n � Mult(�e0);2 Draw word we;e0;n � Mult(��

ze;e

0;n

):

Jonathan Chang, Jordan Boyd-Graber, David M. Blei Connections between the Lines

Graphical Model

MNe Ne,e'Kθ

βθ

ψe,e'

αθ

w

z

θe

αψ

c

πe,e'

ηθz

w

απ

βψ

ηψ

Ne'

z

w

θe'

...Ne''

z

w

θe''

N entity contexts M pair contexts Kψ relationship topicsKθ entity topics

1 If ce;e0;n = 3,

1 Draw topic assignment ze;e0;n � Mult( e;e0);2 Draw word we;e0;n � Mult(�

ze;e

0;n

):

Jonathan Chang, Jordan Boyd-Graber, David M. Blei Connections between the Lines

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Jonathan Chang, Jordan Boyd-Graber, David M. Blei Connections between the Lines