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

1. 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

2. 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.

3. 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

4. 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.

5. 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

6. Classic cluster-based methods • Belief networks: mixture models

7. Classic cluster-based methods • Belief networks: mixture models

8. Classic cluster-based methods • Social networks: block models

9. Classic cluster-based methods • Cultural knowledge (joint social/belief structure): cultural consensus model Not cluster-based. SVD on matrix of people x questions

10. 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….

11. 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

12. Clustering arbitrary relational systems • Alyawarra tribe, central Australia (Denham) • 104 individuals • 27 binary social relations • 3 attributes: kinship class, age, sex (used only for cluster validation, not learning) people people social relation attributes people

13. Clustering arbitrary relational systems Infinite relational model (IRM) discovers 15 clusters

14. 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, ….

16. Hierarchical relational clustering

17. Cross-cutting clustering with nested models • 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.

18. Cross-cutting clustering with nested models Conventional mixture model

19. Cross-cutting clustering with nested models CrossCat model

20. Cross-cutting clustering with nested models Nested relational model: Infinite relational model: people relation people people relation people people relation people

21. 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

22. 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? animal 36 people plant 2 directions

23. Discovering cultural groups with the IRM animal 36 people plant PA+

24. Cultural knowledge across groups animal 24 people (Itza’, Ladino) plant 2 directions

25. “GroundTruth”ecology

26. PA+ AP+ Cultural knowledge across groups Itza’ Ladino

27. 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: L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 I6 I11 Q3 Q6 Q8 Q9 Q10 Q11 Q12 Q1 Q2 Q4 Q5 Q7 I1 I2 I3 I5 I7 I8 I9 I10 I12 I4

28. I1 I2 I3 I5 I7 I8 I9 I10 I12 ciricote ramon chicozapote stranglerfig allspice amapola guano yaxnik broompalm jabin madrial pukte watervine ceiba xate santamaria killervines manchich corozo chapay pacaya herb grasses jaguar paca collaredpeccary whitelippedpeccary margay mountainlion 0.59 chachalaca coatimundi paca collaredpeccary whitelippedpeccary crestedguan ocellatedturkey squirrel greatcurassow tinamou agouti parrot kinkajou toucan boa ferdelance pigeon scarletmacaw bat 0.4 coatimundi paca whitelippedpeccary crestedguan ocellatedturkey greatcurassow tinamou spidermonkey howlermonkey kinkajou pigeon bat 0.63 whitetaileddeer tapir redbrocketdeer boa ferdelance 0.98 chachalaca paca crestedguan ocellatedturkey squirrel greatcurassow tinamou agouti parrot toucan boa ferdelance pigeon scarletmacaw 0.15 agouti armadillo 0.39 … chachalaca squirrel agouti parrot toucan scarletmacaw 0.8 mahogany cedar cordagevine kanlol chaltekok … jaguar boa laughingfalcon … 0.03 … … 0.004 …

29. L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 I6 I11 ciricote ramon chicozapote stranglerfig mahogany guano jabin cedar madrial pukte watervine ceiba allspice santamaria killervines broompalm chapay herb grasses paca collaredpeccary crestedguan ocellatedturkey greatcurassow tinamou armadillo margay mountainlion pigeon 0.25 chachalaca coatimundi paca collaredpeccary whitelippedpeccary crestedguan ocellatedturkey squirrel greatcurassow agouti parrot spidermonkey howlermonkey kinkajou toucan ferdelance pigeon scarletmacaw bat 0.4 coatimundi paca collaredpeccary whitelippedpeccary ocellatedturkey squirrel greatcurassow agouti parrot spidermonkey howlermonkey kinkajou scarletmacaw 0.77 whitetaileddeer tapir redbrocketdeer ferdelance 0.76 greatcurassow pigeon bat 0.22 boa 0.86 chachalaca ocellatedturkey squirrel parrot toucan scarletmacaw 0.27 … toucan 0.8 bat 0.57 … yaxnik cordagevine kanlol chaltekok crestedguan chachalaca whitetaileddeer armadillo jaguar boa laughingfalcon … 0.41 … … 0.028

30. Q3 Q6 Q8 Q9 Q10 Q11 Q12 ciricote ramon chicozapote watervine cordagevine corozo amapola stranglerfig broompalm jabin mahogany cedar guano madrial pukte yaxnik ceiba xate allspice santamaria killervines manchich kanlol chaltekok chapay pacaya herb grasses Redbrocketdeer boa 0.32 jaguar chachalaca whitetaileddeer whitelippedpeccary crestedguan ocellatedturkey greatcurassow tinamou parrot tapir mountainlion spidermonkey howlermonkey kinkajou redbrocketdeer toucan boa ferdelance laughingfalcon scarletmacaw pigeon 0.14 whitetaileddeer collaredpeccary ocellatedturkey greatcurassow armadillo ferdelance pigeon 0.17 spidermonkey howlermonkey 0.4 paca 0.26 … … … 0.01 …

31. Q1 Q2 Q4 Q5 Q7 ciricote pukte watervine killervines amapola mahogany cedar ramon chicozapote madrial stranglerfig yaxnik jabin guano santamaria corozo grasses broompalm collaredpeccary whitelippedpeccary boa ferdelance 0.35 peca collaredpeccary whitelippedpeccaryagouti 0.3 spidermonkey howlermonkey toucan 0.2 … … squirrel 0.1 jaguar chachalaca paca crestedguan ocellatedturkey squirrel greatcurassow tinamou parrot spidermonkey howlermonkey toucan pigeon laughingfalcon scarletmacaw 0.39 … allspice cordagevine manchich kanlol chaltekok chapay herb xate pacaya ceiba whitetaileddeer tinamou parrot armadillo tapir redbrocketdeer pigeon 0.18 jaguar ocellatedturkey squirrel parrot toucan pigeon 0.37 … 0.01 … … …

32. 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).

33. Ongoing and future work people • 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) plants animals directionality

34. The end

36. 3 9 1 13 5 11 7 14 2 10 6 12 4 8 15 3 9 1 13 5 11 7 14 2 10 6 3 9 1 13 5 11 7 14 2 10 6 12 4 8 15 12 4 8 15 Discovering structure in relational data Input Output 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 person 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 person TalksTo(person,person)

37. 3 9 1 13 5 11 7 14 2 10 6 12 4 8 15 3 9 1 13 5 11 7 14 2 10 6 12 4 8 15 Infinite Relational Model (IRM) z 3 9 1 13 5 11 7 14 2 10 6 0.9 0.1 0.1 12 4 8 15 h 0.1 0.1 0.9 0.9 0.1 0.1 O

38. Model fitting

40. 3 9 1 13 5 11 7 14 2 10 6 12 4 8 15 3 9 1 13 5 11 7 14 2 10 6 12 4 8 15 Infinite relational model (IRM) z 3 9 1 13 5 11 7 14 2 10 6 0.9 0.1 0.1 h 0.1 0.1 0.9 12 4 8 15 0.9 0.1 0.1 O

41. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Infinite relational model (IRM) z 3 9 1 13 5 11 7 14 2 10 6 0.9 0.1 0.1 h 0.1 0.1 0.9 12 4 8 15 0.9 0.1 0.1 O

42. Generating h and z • Independent symmetric beta priors on h: • Chinese Restaurant Process over z: • Goal: • Infer • Infer (integrating out hto reduce space of unknowns)

43. Global-local search process

44. animal person plant Joint modeling of belief systems and social systems helps(plant,animal,person judging) Data from Atran and Medin

46. Itza Ladinos