Cluster-based models of belief networks, social networks, and cultural knowledge Josh Tenenbaum, MIT 2007 MURI Annual Meeting Work of Charles Kemp, Chris.

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 Peoples beliefs about properties of objects Relations between people Peoples 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 environments 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 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.

people 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) people attributes Clustering arbitrary relational systems

Infinite relational model (IRM) discovers 15 clusters 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, .

concept predicate Learning a medical ontology Data from UMLS (McCrae et al.): 134 concepts: enzyme, hormone, organ, disease, cell function... 49 predicates: affects(hormone, organ), complicates(enzyme, cell function), treats(drug, disease), diagnoses(procedure, disease)

Learning a medical ontology e.g., Diseases affect Organisms Chemicals interact with Chemicals Chemicals cause Diseases

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 individuals 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

Experimental tests of CrossCat = Stimuli: Task: Repeated free sorting

Experimental tests of CrossCat Results: Conventional mixture model CrossCat model Human frequency

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

Culture and cognition in Guatamela (Atran & Medin) Subjects 12 native Itza maya 12 immigrant Ladino 12 immigrant Qeqchi maya Questions Does plant i help animal j? Does animal j help plant i? animal plant 36 people 2 directions

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

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

Ground Truth ecology

Cultural knowledge across groups Itza Ladino PA+AP+

I1 I2 I3 I5 I7 I8 I9 I10 I12 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 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:

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

L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 I6 I11 ciricote ramon chicozapote stranglerfig coatimundi paca collaredpeccary whitelippedpeccary ocellatedturkey squirrel greatcurassow agouti parrot spidermonkey howlermonkey kinkajou scarletmacaw 0.77 toucan 0.8 mahogany guano chachalaca coatimundi paca collaredpeccary whitelippedpeccary crestedguan ocellatedturkey squirrel greatcurassow agouti parrot spidermonkey howlermonkey kinkajou toucan ferdelance pigeon scarletmacaw bat 0.4 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 greatcurassow pigeon bat 0.22 whitetaileddeer tapir redbrocketdeer ferdelance 0.76 boa 0.86 yaxnik cordagevine kanlol chaltekok 0.028 chachalaca ocellatedturkey squirrel parrot toucan scarletmacaw 0.27 bat 0.57 crestedguan chachalaca whitetaileddeer armadillo jaguar boa laughingfalcon 0.41

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

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

Discovering cultural groups with the nested IRM Data: AP+ Nesting structure Cluster people Cluster plants within people Cluster animals within plants and people Clusters of people found: L2 L3 L6 L7 L10 L11 L12 I1 I2 I3 I4 I5 I6 I7 I8 I9 I11 I12 L4 L5 L8 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 L1 L9 I10

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 plantsanimals directionality

The end

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

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

Model fitting

a(3). a(9). a(1). a(13). a(5). a(11). b(7). b(14). b(2). b(10). b(6). c(12). c(4). c(8). c(15). r(X,Y) a(X),a(Y). (0.0) r(X,Y) a(X),b(Y). (0.9) r(X,Y) c(X),a(Y). (0.95)... r(3,7). r(1,10). r(2,4)... The concepts discovered by the IRM can serve as primitives in complex logical theories (cf. clustering approaches to predicate invention, e.g., Craven and Slattery (2001) or Popescul and Ungar (2004)) 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

Related Work Relational models Sociology: Wang and Wong (1987); Nowicki and Snijders (2001) Machine learning: Taskar, Segal and Koller (2001) Wolfe and Jensen (2004) Wang, Mohanty and McCallum (2005) Nonparametric Bayesian models Ferguson (1973); Neal (1991) Nonparametric Bayesian relational models Carbonetto, Kisynski, de Freitas and Poole (2005) Xu, Tresp, Yu, Kriegel (2006)

Optimization (or inference) Global proposals Split and merge clusters Local proposals Re-assign one entity to best cluster based on current assignments of all other entities (i.e., Gibbs sampling) Both cognitively plausible and computationally reasonable.

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

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

Independent symmetric beta priors on : Chinese Restaurant Process over z: Goal: Infer Infer (integrating out to reduce space of unknowns) Generating and z

Global-local search process

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

ItzaLadinos

Cluster-based models of belief networks, social networks, and cultural knowledge Josh Tenenbaum, MIT 2007 MURI Annual Meeting Work of Charles Kemp, Chris.

Documents

data relational models

classic methods

mixture models

joint socialbelief structure

nested models cross

block models

different belief networks

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