Cluster-based models of belief networks, social networks, and

cultural knowledge

Josh Tenenbaum, MIT

2007 MURI Annual Meeting

Work of Charles Kemp, Chris Baker, Tom Griffiths, Pat Shafto, Vikash

Mansinghka, Dan Roy

Goal

• Algorithmic tools for uncovering structure in belief networks, social networks, and joint structure (social-belief networks).

• Why?– Joint social-belief structure ~ culture – Algorithms let us map cultural knowledge quickly

and semi-automatically, detect changes and track dynamics.

Approach

• Data– People’s beliefs about properties of objects – Relations between people– People’s beliefs about relations between objects (or people).

• Representation: cluster-based models– Clusters of things: categories– Clusters of people: social groups– Clusters of people who share similar beliefs about clusters of

things (or people): cultural groups

Approach• Learning: Bayesian inference from data

– Relational models: analyze arbitrary relational databases of beliefs, not just a single matrix

– Nonparametric models: automatically determine complexity of representations

– Hierarchical models: multiple levels of structure– Nested models: structures with structure

Result: a flexible toolkit that goes qualitatively beyond standard algorithms. – e.g., ability to discover cultural groups characterized by a shared understanding of the

environment’s relational structure.

Talk outline

• Classic cluster-based methods

• New methods– Clustering with arbitrary relational systems– Hierarchical relational clustering– Cross-cutting clustering with nested models– Cross-cutting relational clustering

• Application to Guatemala data from Atran & Medin

Classic cluster-based methods

• Belief networks: mixture models

Classic cluster-based methods

• Belief networks: mixture models

Classic cluster-based methods

• Social networks: block models

Classic cluster-based methods

• Cultural knowledge (joint social/belief structure): cultural consensus model

Not cluster-based.

SVD on matrix of people x questions

Problems with classic methods

• No principled tools for discovering different cultural groups characterized by different belief networks. – CCM not intended to find cultural groups, but rather to

uncover (and test for) shared knowledge and authoritativeness in a single cultural group. “Test theory without an answer key”

• Can only represent simple forms of knowledge that fit into a single two-mode matrix.– Cultural knowledge is often much richer….

Talk outline

• Classic cluster-based methods

• New methods– Clustering with arbitrary relational systems– Hierarchical relational clustering– Cross-cutting clustering with nested models– Cross-cutting relational clustering

• Application to Guatemala data from Atran & Medin

peop

lepeople

social relation

• Alyawarra tribe, central Australia (Denham)– 104 individuals– 27 binary social relations– 3 attributes: kinship class, age, sex

(used only for cluster validation, not learning)

peop

le

attributes

Clustering arbitrary relational systems

Infinite relational model (IRM) discovers 15 clusters

Clustering arbitrary relational systems

Clustering arbitrary relational systems

International relations circa 1965 (Rummel)– 14 countries: UK, USA, USSR, China, ….– 54 binary relations representing interactions between countries:

exports to( USA, UK ), protests( USA, USSR ), …. – 90 (dynamic) country features: purges, protests, unemployment,

communists, # languages, assassinations, ….

Hierarchical relational clustering

• Models so far all learn a single system of clusters.

• We would like to be able to discover multiple cross-cutting systems of clusters.– Within an individual’s mind: multiple mental

models of a single complex domain. – Across individuals in a population: multiple

cultural groups with different characteristic mental models.

Cross-cutting clustering with nested models

Conventional mixture model

Cross-cutting clustering with nested models

CrossCat model

Cross-cutting clustering with nested models

Nested relational model:

Cross-cutting clustering with nested modelspe

ople

people

relation

Infinite relational model:

peop

le

peoplerelation

peop

le

peoplerelation

Talk outline

• Classic cluster-based methods

• New methods– Clustering with arbitrary relational systems– Hierarchical relational clustering– Cross-cutting clustering with nested models– Cross-cutting relational clustering

• Application to Guatemala data from Atran & Medin

Culture and cognition in Guatamela(Atran & Medin)

• Subjects– 12 native Itza’ maya

– 12 immigrant Ladino

– 12 immigrant Q’eqchi’ maya

• Questions– Does plant i help animal j?

– Does animal j help plant i?

anim

alplant

36 people

2 directions

Discovering cultural groups with the IRM

anim

alplant

36 people

PA+

Cultural knowledge across groups

anim

al

plant

24 people(Itza’, Ladino)

2 directions

“GroundTruth”ecology

Cultural knowledge across groups

Itza’

Ladino

PA+ AP+

I1I2I3I5I7I8I9I10I12

L1L2L3L4L5L6L7L8L9L10L11L12I6I11

Q3Q6Q8Q9Q10Q11Q12

Q1Q2Q4Q5Q7

I4

Discovering cultural groups with the nested IRM

• Data: PA+

• Nesting structure– Cluster people– Cluster plants

within people– Cluster animals

within plants and people

• Clusters of people found:

I1I2I3I5I7I8I9I10I12

ciricoteramonchicozapotestranglerfigallspice

coatimundipacawhitelippedpeccarycrestedguanocellatedturkeygreatcurassowtinamouspidermonkeyhowlermonkeykinkajoupigeonbat 0.63

chachalacasquirrelagoutiparrottoucanscarletmacaw 0.8

…

amapolaguanoyaxnikbroompalm

chachalacacoatimundipacacollaredpeccarywhitelippedpeccarycrestedguanocellatedturkeysquirrelgreatcurassowtinamouagoutiparrotkinkajoutoucanboaferdelancepigeonscarletmacawbat 0.4

…

jabinmadrialpuktewatervineceibaxatesantamariakillervinesmanchichcorozochapaypacaya

…

herbgrasses

jaguarpacacollaredpeccarywhitelippedpeccarymargaymountainlion 0.59

…

chachalacapacacrestedguanocellatedturkeysquirrelgreatcurassowtinamouagoutiparrottoucanboaferdelancepigeonscarletmacaw 0.15

whitetaileddeertapirredbrocketdeerboaferdelance 0.98

agoutiarmadillo 0.39

mahoganycedarcordagevinekanlolchaltekok

… 0.004

jaguarboalaughingfalcon… 0.03

L1L2L3L4L5L6L7L8L9L10L11L12I6I11

ciricoteramonchicozapotestranglerfig

coatimundipacacollaredpeccarywhitelippedpeccaryocellatedturkeysquirrelgreatcurassowagoutiparrotspidermonkeyhowlermonkeykinkajouscarletmacaw 0.77

toucan 0.8

mahoganyguano

chachalacacoatimundipacacollaredpeccarywhitelippedpeccarycrestedguanocellatedturkeysquirrelgreatcurassowagoutiparrotspidermonkeyhowlermonkeykinkajoutoucanferdelancepigeonscarletmacawbat 0.4

…

jabincedarmadrialpuktewatervineceibaallspicesantamariakillervinesbroompalmchapay

…

herbgrasses

pacacollaredpeccarycrestedguanocellatedturkeygreatcurassowtinamouarmadillomargaymountainlionpigeon 0.25

…

greatcurassowpigeonbat 0.22

whitetaileddeertapirredbrocketdeerferdelance 0.76

boa 0.86

yaxnikcordagevinekanlolchaltekok

… 0.028

chachalacaocellatedturkeysquirrelparrottoucanscarletmacaw 0.27

bat 0.57

crestedguan chachalacawhitetaileddeerarmadillojaguarboalaughingfalcon… 0.41

Q3Q6Q8Q9Q10Q11Q12

ciricoteramonchicozapotewatervinecordagevinecorozo

spidermonkeyhowlermonkey 0.4

…

amapolastranglerfigbroompalm

jaguarchachalacawhitetaileddeerwhitelippedpeccarycrestedguanocellatedturkeygreatcurassowtinamouparrottapirmountainlionspidermonkeyhowlermonkeykinkajouredbrocketdeertoucanboaferdelancelaughingfalconscarletmacaw pigeon 0.14

…

herbgrasses

whitetaileddeercollaredpeccaryocellatedturkeygreatcurassowarmadilloferdelancepigeon 0.17

…

paca 0.26

jabinmahoganycedarguanomadrialpukteyaxnikceibaxateallspicesantamariakillervinesmanchichkanlolchaltekokchapaypacaya

… 0.01

Redbrocketdeerboa 0.32

Q1Q2Q4Q5Q7

ciricotepuktewatervinekillervines

spidermonkeyhowlermonkeytoucan 0.2

…

amapolamahoganycedarramonchicozapotemadrialstranglerfigyaxnik

jaguarchachalacapacacrestedguanocellatedturkeysquirrelgreatcurassowtinamouparrotspidermonkeyhowlermonkeytoucanpigeonlaughingfalconscarletmacaw 0.39

…

grassesbroompalm

collaredpeccarywhitelippedpeccaryboaferdelance 0.35

…

allspicecordagevinemanchichkanlolchaltekokchapay

… 0.01

squirrel 0.1

ceiba

jaguarocellatedturkeysquirrelparrottoucanpigeon 0.37

…

jabinguanosantamariacorozo

pecacollaredpeccarywhitelippedpeccaryagouti 0.3

…

herbxatepacaya

whitetaileddeertinamouparrotarmadillotapirredbrocketdeerpigeon 0.18

…

Conclusions

• A flexible toolkit for statistical learning about cultural knowledge and cultural groups. – Relational models: analyze arbitrary relational databases of beliefs, not

just a single matrix

– Nonparametric models: automatically determine complexity of representations

– Hierarchical models: multiple levels of structure

– Nested models: structures with structure

• Can automatically discover important qualitative structure in real-world data (Atran & Medin).

Ongoing and future work

• More flexible nested structures

• More dynamic data and analyses– Second-generation Guatemala data– Political data sets: voting records, international relations

• More structured representations necessary to capture “cultural stories”: grammars, logical schemas (c.f. Forbus, Richards, Atran)

people

plants animals

directionality

The end

Discovering structure in relational data

391

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Input Output

pers

on

TalksTo(person,person)

person

O

z

Infinite Relational Model (IRM)

3 9 113 511

7 14 2

10 6

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0.90.1 0.1

0.1 0.1 0.9

0.9 0.1 0.1

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Model fitting

O

z

Infinite relational model (IRM)

3 9 113 511

7 14 2

10 6

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0.90.1 0.1

0.1 0.1 0.9

0.9 0.1 0.1

391

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117

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1248

15

3 9 1 13 5 11 7 14 2 10 6 12 4 8 15

O

z

Infinite relational model (IRM)

3 9 113 511

7 14 2

10 6

12 4

8 15

0.90.1 0.1

0.1 0.1 0.9

0.9 0.1 0.1

123456789

101112131415

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

• Independent symmetric beta priors on :

• Chinese Restaurant Process over z:

• Goal: – Infer

– Infer (integrating out to reduce space of unknowns)

Generating and z

)(Beta~ ββ,ηij

)|,( Oηzp)|( Ozp

class new a is

0

),,|( 11C

αn

α

nαn

n

zzCzPC

C

nn

Global-local search process

Joint modeling of belief systems and social systems

anim

al

plant

person

helps(plant,animal,person judging)

Data from Atran and Medin

Itza Ladinos