Co-evolution in Epistemic Networks Reconstructing Social Complex - - PowerPoint PPT Presentation

Co-evolution in Epistemic Networks

Reconstructing Social Complex Systems

Camille Roth

CREA – CNRS / Ecole Polytechnique

Presentation of the thesis — Nov 19, 2005

Framework and objectives Epistemic communities Micro-foundations

The Reconstruction Problem

Reconstruction is a reverse problem consisting in successfully reproducing several stylized facts observed in the original empirical system.

Framework and objectives Epistemic communities Micro-foundations

The Reconstruction Problem

Reconstruction is a reverse problem consisting in successfully reproducing several stylized facts observed in the original empirical system. Issues (i) Find P in order to deduce high-level observations H from strictly low-level phenomena L. (ii) Find a low-level dynamics λ that rebuilds high-level evolution ηe.

P? H η

e

λ

e

t+∆t t+∆t t

H L P? L

t

Framework and objectives Epistemic communities Micro-foundations

The Reconstruction Problem

Reconstruction is a reverse problem consisting in successfully reproducing several stylized facts observed in the original empirical system. Issues (i) Find P in order to deduce high-level observations H from strictly low-level phenomena L. (ii) Find a low-level dynamics λ that rebuilds high-level evolution ηe.

H η

e

t+∆t t+∆t t

λ? H L L P

t

P

Framework and objectives Epistemic communities Micro-foundations

Objectives

A socio-semantic complex system

1

Reproduce a hierarchic epistemic hypergraph of a knowledge community that fits a high-level expert-based description

2

Provide a low-level dynamics and a morphogenesis model that rebuilds the empirically observed high-level structure Thesis The structure of a knowledge community, and in particular its epistemic hypergraph, is primarily produced by the co-evolution

• f agents and concepts.

Framework and objectives Epistemic communities Micro-foundations

Objectives

A socio-semantic complex system

1

Reproduce a hierarchic epistemic hypergraph of a knowledge community that fits a high-level expert-based description

2

Provide a low-level dynamics and a morphogenesis model that rebuilds the empirically observed high-level structure Thesis The structure of a knowledge community, and in particular its epistemic hypergraph, is primarily produced by the co-evolution

• f agents and concepts.

Framework and objectives Epistemic communities Micro-foundations

Outline

1

Epistemic communities Rationale & definitions Epistemic community taxonomy and Galois lattices Partial taxonomies: rebuilding history

2

Micro-foundations of epistemic networks Networks Towards a rebuilding model Reconstruction of epistemic communities

Framework and objectives Epistemic communities Micro-foundations

Outline

1

Epistemic communities Rationale & definitions Epistemic community taxonomy and Galois lattices Partial taxonomies: rebuilding history

2

Micro-foundations of epistemic networks Networks Towards a rebuilding model Reconstruction of epistemic communities

Framework and objectives Epistemic communities Micro-foundations Epistemic community taxonomy and Galois lattices

Building taxonomies

Rationale Describe the taxonomy of a knowledge community, in particular scientific communities, that matches high-level descriptions.

P H η

e

λ

e

t+∆t t+∆t t

H L P L

t

Framework and objectives Epistemic communities Micro-foundations Epistemic community taxonomy and Galois lattices

Building taxonomies

Epistemic communities Epistemic Community: group of agents sharing a common set of subjects, concepts, issues; sharing a common goal

• f knowledge creation — Haas (1992), Cowan et al. (2000)

Definition here: “an epistemic community is the largest set

• f agents sharing a given set of concepts” – as such

strongly linked with structural equivalence

Framework and objectives Epistemic communities Micro-foundations Epistemic community taxonomy and Galois lattices

Building taxonomies

Epistemic communities Epistemic Community: group of agents sharing a common set of subjects, concepts, issues; sharing a common goal

• f knowledge creation — Haas (1992), Cowan et al. (2000)

Definition here: “an epistemic community is the largest set

• f agents sharing a given set of concepts” – as such

strongly linked with structural equivalence

Framework and objectives Epistemic communities Micro-foundations Epistemic community taxonomy and Galois lattices

Building taxonomies

Formal framework Consider a binary relation R between agents & concepts Intent S∧ of an agent set S: all concepts used by every agent in S Extent C⋆ of a concept set C Epistemic community: the extent of a concept set C “∧⋆” is a closure operation:

1

(idempotent) (S∧⋆)∧⋆ = S∧⋆

2

(extensive) S ⊆ S∧⋆

3

(increasing) S ⊆ S′ ⇒ S∧⋆ ⊆ S′∧⋆

(S, C) is closed iff C = S∧ and S = C⋆

s s s

Prs NS

Concepts (C) Agents (S)

3 2

s

4

Lng

1

Framework and objectives Epistemic communities Micro-foundations Epistemic community taxonomy and Galois lattices

Building taxonomies

Formal framework Consider a binary relation R between agents & concepts Intent S∧ of an agent set S: all concepts used by every agent in S Extent C⋆ of a concept set C Epistemic community: the extent of a concept set C “∧⋆” is a closure operation:

1

(idempotent) (S∧⋆)∧⋆ = S∧⋆

2

(extensive) S ⊆ S∧⋆

3

(increasing) S ⊆ S′ ⇒ S∧⋆ ⊆ S′∧⋆

(S, C) is closed iff C = S∧ and S = C⋆

s s s

Prs NS

Concepts (C) Agents (S)

3 2

s

4

Lng

1

Framework and objectives Epistemic communities Micro-foundations Epistemic community taxonomy and Galois lattices

Building taxonomies

Formal framework Consider a binary relation R between agents & concepts Intent S∧ of an agent set S: all concepts used by every agent in S Extent C⋆ of a concept set C Epistemic community: the extent of a concept set C “∧⋆” is a closure operation:

1

(idempotent) (S∧⋆)∧⋆ = S∧⋆

2

(extensive) S ⊆ S∧⋆

3

(increasing) S ⊆ S′ ⇒ S∧⋆ ⊆ S′∧⋆

(S, C) is closed iff C = S∧ and S = C⋆

s s s

Prs NS

Concepts (C) Agents (S)

3 2

s

4

Lng

1

Framework and objectives Epistemic communities Micro-foundations Epistemic community taxonomy and Galois lattices

Building taxonomies

Representing epistemic communities

1

structured into fields, with common concerns,

2

hierarchically: generalization / specialization,

3

• verlapping.

From trees to lattices

Framework and objectives Epistemic communities Micro-foundations Epistemic community taxonomy and Galois lattices

Building taxonomies

Representing epistemic communities

1

structured into fields, with common concerns,

2

hierarchically: generalization / specialization,

3

• verlapping.

From trees to lattices

platypus mammal bird platypus tree mammal bird platypus lattice lattice Italy Urban Italy Rural Italy Urban Germany Rural Germany Germany Germany Urban Rural Urban Italy Rural Italy Urban Germany Rural Germany Italy Territories Habitat tree

Framework and objectives Epistemic communities Micro-foundations Epistemic community taxonomy and Galois lattices

Building taxonomies

Galois lattices GL={(S∧⋆, S)|S ⊆ S} is the partially-ordered set of all epistemic communities, with the partial order: (X, X ∧) < (X ′, X ′∧) ⇔ X ⊂ X ′

;

s

2

s

2

s

GL

1 2 3 4 1 2 3 2 3 2 3 4

Lng Prs s s s s ; Lng s s s NS ; Lng NS ; s Lng Prs ; s s s s ; ∅ ( ( ( ( ( ( ) ) ) ) ) NS

1

)

Framework and objectives Epistemic communities Micro-foundations Epistemic community taxonomy and Galois lattices

Managing taxonomies

Taxonomy selection & extraction Which ECs should we extract from the lattice? Given the assumptions, a first criterion is agent set size — Small isolated ECs could be interesting too. In order to create a partial taxonomy, with selection heuristics: partially-ordered set overlaying the lattice: “epistemic hypergraph”

;

1 2 3 4 1 2 3 2 3 4

s s s ; Lng s s s NS ; ; s s s s ∅ ( ( ( ) ) )

1

s

2

s

2

s

GL poset

1 2 3 4 1 2 3 2 3 2 3 4

Lng Prs s s s s ; Lng s s s NS ; Lng NS ; s Lng Prs ; s s s s ; ∅ ( ( ( ( ( ( ) ) ) ) ) NS )

Framework and objectives Epistemic communities Micro-foundations Epistemic community taxonomy and Galois lattices

Managing taxonomies

Taxonomy selection & extraction Which ECs should we extract from the lattice? Given the assumptions, a first criterion is agent set size — Small isolated ECs could be interesting too. In order to create a partial taxonomy, with selection heuristics: partially-ordered set overlaying the lattice: “epistemic hypergraph”

;

1 2 3 4 1 2 3 2 3 4

s s s ; Lng s s s NS ; ; s s s s ∅ ( ( ( ) ) )

1

s

2

s

2

s

GL poset

1 2 3 4 1 2 3 2 3 2 3 4

Lng Prs s s s s ; Lng s s s NS ; Lng NS ; s Lng Prs ; s s s s ; ∅ ( ( ( ( ( ( ) ) ) ) ) NS )

Framework and objectives Epistemic communities Micro-foundations Epistemic community taxonomy and Galois lattices

Managing taxonomies

Taxonomy selection & extraction Which ECs should we extract from the lattice? Given the assumptions, a first criterion is agent set size — Small isolated ECs could be interesting too. In order to create a partial taxonomy, with selection heuristics: partially-ordered set overlaying the lattice: “epistemic hypergraph”

;

1 2 3 4 1 2 3 2 3 4

s s s ; Lng s s s NS ; ; s s s s ∅ ( ( ( ) ) )

1

s

2

s

2

s

GL poset

1 2 3 4 1 2 3 2 3 2 3 4

Lng Prs s s s s ; Lng s s s NS ; Lng NS ; s Lng Prs ; s s s s ; ∅ ( ( ( ( ( ( ) ) ) ) ) NS )

Framework and objectives Epistemic communities Micro-foundations Epistemic community taxonomy and Galois lattices

Managing taxonomies

Taxonomy evolution

1

Progress or decline of a field

decrease (S ,C)

1

(S ,C)

2

(S ,C)

2

growth

2

Merging or scission of a field

scission ∪ ∩ (S,C) (S’,C’) merge (S S’,C C’)

Framework and objectives Epistemic communities Micro-foundations Partial taxonomies: rebuilding history

Empirical results

Hierarchical epistemic hypergraph 1990-1995

All (255) Hom (67) Mou (92) Hum (34) Ver (75) Dev (168) Pat (99) Brn (102) Spi (30) Ven (50) Dor (49) Gro (44) Sig (53) Pwy (38) Hom Mou (40) Hom Hum (11) Mou Hum (18) Mou Ver (30) Mou Dev (72) Ver Dev (68) Ver Pat (42) Dev Pat (77) Dev Brn (81) Brn Spi Crd (29) Brn Ven (43) Brn Dor (38) Ven Dor (34) Brn Spi Crd Ven (15) Brn Ven Dor (30) Brn Pat (62)

Framework and objectives Epistemic communities Micro-foundations Partial taxonomies: rebuilding history

Empirical results

Hierarchical epistemic hypergraph 1998-2003

All (255) Hom (57) Mou (100) Hum (100) Ver (86) Dev (150) Pat (90) Brn (82) Spi Crd (18) Ven (40) Dor (40) Gro (67) Sig (133) Pwy (93) Hom Mou (35) Hom Hum (38) Mou Hum (58) Mou Ver (48) Mou Dev (71) Ver Dev (70) Ver Pat (58) Dev Pat (78) Dev Brn (62) Pat Brn (47) Gro Sig (51) Rec (67) Ven Dor (24) Gro Pwy (42) Sig Pwy (84) Hum Ver (44) Sig Rec (48) Pwy Rec (34) Gro Sig Pwy (39) Sig Pwy Rec (31)

Framework and objectives Epistemic communities Micro-foundations Partial taxonomies: rebuilding history

Empirical results

Historical description

1

Research on brain and spinal cord depreciated,

2

The community started to enquire relationships between signal, pathway, and receptors,

3

Mouse-related research is stable, yet significant stress on human-related topics & new relationship to homologous genes and vertebrates: growing focus on differential studies.

Matches expert-based descriptions

Framework and objectives Epistemic communities Micro-foundations Partial taxonomies: rebuilding history

Empirical results

Historical description

1

Research on brain and spinal cord depreciated,

2

The community started to enquire relationships between signal, pathway, and receptors,

3

Mouse-related research is stable, yet significant stress on human-related topics & new relationship to homologous genes and vertebrates: growing focus on differential studies.

Matches expert-based descriptions

Framework and objectives Epistemic communities Micro-foundations

Outline

1

Epistemic communities Rationale & definitions Epistemic community taxonomy and Galois lattices Partial taxonomies: rebuilding history

2

Micro-foundations of epistemic networks Networks Towards a rebuilding model Reconstruction of epistemic communities

Framework and objectives Epistemic communities Micro-foundations Networks

Overview

P H η

e

λ

e

t+∆t t+∆t t

H L P L

t

Framework and objectives Epistemic communities Micro-foundations Networks

Overview

P H η

e

λ

e

t+∆t t+∆t t

H L P L

t

Micro-foundation Reconstructing high-level structure from low-level dynamics: — reverse problem: find λ such that P ◦ λ = ηe ◦ P.

Framework and objectives Epistemic communities Micro-foundations Networks

Overview

P H η

e

t+∆t t+∆t t

λ H L P L

t

Micro-foundation Reconstructing high-level structure from low-level dynamics: — reverse problem: find λ such that P ◦ λ = ηe ◦ P.

Framework and objectives Epistemic communities Micro-foundations Networks

Epistemic networks

Definitions What is an epistemic network? A network of agents: S=(S, ES), evolving with time: S(t) Semantic network: network of concepts, C=(C, EC) Agents are linked to concepts they use, through R. Three kinds of relations: RS, RC and R:

s s’ s" c’ c c" S C

Framework and objectives Epistemic communities Micro-foundations Networks

Epistemic networks

Definitions What is an epistemic network? A network of agents: S=(S, ES), evolving with time: S(t) Semantic network: network of concepts, C=(C, EC) Agents are linked to concepts they use, through R. Three kinds of relations: RS, RC and R:

s s’ s" c’ c c" S C

Framework and objectives Epistemic communities Micro-foundations Networks

Epistemic networks

Definitions What is an epistemic network? A network of agents: S=(S, ES), evolving with time: S(t) Semantic network: network of concepts, C=(C, EC) Agents are linked to concepts they use, through R. Three kinds of relations: RS, RC and R:

s s’ s" c’ c c" S C

Framework and objectives Epistemic communities Micro-foundations Networks

Network morphogenesis

A brief survey

1

Early times: Erdos-Renyi, until unsatisfying power-law degree distribution and other statistical parameters

2

Pioneering models rebuild clustering, and degree distribution (preferential attachment (PA), network growth)

3

Since then and until now: models introducing various kinds

• f PA to rebuild diverse statistical parameters

4

But even with credible hypotheses, rare empirical validations, yet needed for realistic morphogenesis models

Framework and objectives Epistemic communities Micro-foundations Networks

Network morphogenesis

A brief survey

1

Early times: Erdos-Renyi, until unsatisfying power-law degree distribution and other statistical parameters

2

Pioneering models rebuild clustering, and degree distribution (preferential attachment (PA), network growth)

3

Since then and until now: models introducing various kinds

• f PA to rebuild diverse statistical parameters

4

But even with credible hypotheses, rare empirical validations, yet needed for realistic morphogenesis models

Framework and objectives Epistemic communities Micro-foundations Towards a rebuilding model

High-level features

Degree distributions Four degree distributions: social, semantic, socio-semantic (from agents, from concepts) Power-law tail, log-normal fit Clustering structure High clustering both for monopartite coefficients and bipartite coefficients Epistemic community structure Many large ECs, particular distribution of EC sizes.

Framework and objectives Epistemic communities Micro-foundations Towards a rebuilding model

Suggest empirically credible low-level dynamics

Measuring interaction behavior Measure the interaction behavior of agents Have an essential preference f for nodes of kind m: P(L|m) → we may estimate f through ˆ f(m) = ν(m)

P(m)

Check correlations between parameters: ˆ cm′(m) = P(m|m′)

P(m)

Event-based modeling Distinguish activity from attractivity: rich-get-richer or rich-work-harder? Activity and interactivity: f(m) = a(m)ι(m)

Framework and objectives Epistemic communities Micro-foundations Towards a rebuilding model

Suggest empirically credible low-level dynamics

Measuring interaction behavior Measure the interaction behavior of agents Have an essential preference f for nodes of kind m: P(L|m) → we may estimate f through ˆ f(m) = ν(m)

P(m)

Check correlations between parameters: ˆ cm′(m) = P(m|m′)

P(m)

Event-based modeling Distinguish activity from attractivity: rich-get-richer or rich-work-harder? Activity and interactivity: f(m) = a(m)ι(m)

Framework and objectives Epistemic communities Micro-foundations Towards a rebuilding model

Measuring low-level dynamics

Network growth Event-based low-level dynamics Choice of agents Geometric distribution of agents, tri-modal distribution for newbies Choice of concepts Geometric distribution of concepts, uni-modal distribution of novel concepts

Framework and objectives Epistemic communities Micro-foundations Reconstruction of epistemic communities

Model design

selection ~P(k )

t ν

S (i)

t

S (i)

t

S (i)

t

C (i)

t

S (i)

t

S (i)

t ν

\

A (i)

t

4 3 1 2 C (i)

t ν

C (i)

t

C (i)

t ν

S (i)

t

S (i)

t ν

new agents concept set of old agents recruitment of initiator (~P(k))

• ther agents ~P(k,d)

concepts−>agents

S (i)

Framework and objectives Epistemic communities Micro-foundations Reconstruction of epistemic communities

Reconstruction

Epistemic communities are produced by the co-evolution

• f agents and concepts

Degree distributions, clustering structure, epistemic structure are reconstructed.

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 EC size 0.1 1 10 100 1000 number

• f ECs

Reconstruct high-level statistical parameters meaningful for epistemic networks Respecting low-level dynamics: descriptive rather than normative

Framework and objectives Epistemic communities Micro-foundations Reconstruction of epistemic communities

Reconstruction

Epistemic communities are produced by the co-evolution

• f agents and concepts

Degree distributions, clustering structure, epistemic structure are reconstructed.

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 EC size 0.1 1 10 100 1000 number

• f ECs

Reconstruct high-level statistical parameters meaningful for epistemic networks Respecting low-level dynamics: descriptive rather than normative

Framework and objectives Epistemic communities Micro-foundations

Conclusion

H η

e

t+∆t t+∆t t

λ H L L P

t

P

Integrated example of reconstruction in social science preliminary to studying knowledge diffusion and, eventually, naturalizing cultural anthropology

Framework and objectives Epistemic communities Micro-foundations

Conclusion

H η

e

t+∆t t+∆t t

λ H L L P

t

P

Integrated example of reconstruction in social science preliminary to studying knowledge diffusion and, eventually, naturalizing cultural anthropology

Framework and objectives Epistemic communities Micro-foundations

Conclusion

H η

e

t+∆t t+∆t t

λ H L L P

t

P

Integrated example of reconstruction in social science preliminary to studying knowledge diffusion and, eventually, naturalizing cultural anthropology

Framework and objectives Epistemic communities Micro-foundations

Framework and objectives Epistemic communities Micro-foundations

Appraising levels

Relationships between different levels Dualism, reductionism ? Emergentism: low-level phenomena cause high-level phenomena, yet in turn not necessarily reduceable to low-level phenomena. Is it ok that a lower level creates a higher level, then the higher level in turn influences the lower level? Rather, different modes of access to a same process: dual-mode of operational access.

“There may be emergence without emergent properties. Not asymmetric emergence of high-level properties out of basic properties, but symmetrical co-emergence of microscopic low-level features and high level behavior” (Bitbol, 2005)

Framework and objectives Epistemic communities Micro-foundations

Appraising levels

Relationships between different levels Dualism, reductionism ? Emergentism: low-level phenomena cause high-level phenomena, yet in turn not necessarily reduceable to low-level phenomena. Is it ok that a lower level creates a higher level, then the higher level in turn influences the lower level? Rather, different modes of access to a same process: dual-mode of operational access.

“There may be emergence without emergent properties. Not asymmetric emergence of high-level properties out of basic properties, but symmetrical co-emergence of microscopic low-level features and high level behavior” (Bitbol, 2005)

Framework and objectives Epistemic communities Micro-foundations

Appraising levels

Relationships between different levels Dualism, reductionism ? Emergentism: low-level phenomena cause high-level phenomena, yet in turn not necessarily reduceable to low-level phenomena. Is it ok that a lower level creates a higher level, then the higher level in turn influences the lower level? Rather, different modes of access to a same process: dual-mode of operational access.

“There may be emergence without emergent properties. Not asymmetric emergence of high-level properties out of basic properties, but symmetrical co-emergence of microscopic low-level features and high level behavior” (Bitbol, 2005)

Framework and objectives Epistemic communities Micro-foundations

Appraising levels

Relationships between different levels Dualism, reductionism ? Emergentism: low-level phenomena cause high-level phenomena, yet in turn not necessarily reduceable to low-level phenomena. Is it ok that a lower level creates a higher level, then the higher level in turn influences the lower level? Rather, different modes of access to a same process: dual-mode of operational access.

“There may be emergence without emergent properties. Not asymmetric emergence of high-level properties out of basic properties, but symmetrical co-emergence of microscopic low-level features and high level behavior” (Bitbol, 2005)

Framework and objectives Epistemic communities Micro-foundations

Levels as observations

Each level is an observation instrument (a phenomenon), and may provide information about some other observation gained through other instruments.

Framework and objectives Epistemic communities Micro-foundations

Levels as observations

Each level is an observation instrument (a phenomenon), and may provide information about some other observation gained through other instruments. “Observationism”

1

no substantial reality of levels

2

no reciprocal causation, but informational links

3

some phenomena cannot be rebuild from some given lower-level decriptions

Framework and objectives Epistemic communities Micro-foundations

Modeling links between levels

Reconstruction “Observationism” induces simply informational dependence between both levels: λ(L|H), η(L|H) Thus, reconstruction failure may also come from ill-defined levels: not yielding enough information about the given phenomenon (e.g. learning & glial cells; concepts in addition to simple social interactions between agents) Reductionism only works when H is fully deduceable, not reduceable, from L.

Framework and objectives Epistemic communities Micro-foundations

Modeling links between levels

Reconstruction “Observationism” induces simply informational dependence between both levels: λ(L|H), η(L|H) Thus, reconstruction failure may also come from ill-defined levels: not yielding enough information about the given phenomenon (e.g. learning & glial cells; concepts in addition to simple social interactions between agents) Reductionism only works when H is fully deduceable, not reduceable, from L.

Framework and objectives Epistemic communities Micro-foundations

Stigmergence

Co-evolutionary framework Additionally, this viewpoint is not contradictory with some sort of causal retroaction: action of a group of neurons

• nto another group of neurons, agents creating &

modifying their environment which in turn “acts upon them”: stigmergence. No downward causation either, simply influence of already existing environmental artifacts In our case, there is a co-evolution between semantic and social networks.

Framework and objectives Epistemic communities Micro-foundations

Stigmergence

Co-evolutionary framework Additionally, this viewpoint is not contradictory with some sort of causal retroaction: action of a group of neurons

• nto another group of neurons, agents creating &

modifying their environment which in turn “acts upon them”: stigmergence. No downward causation either, simply influence of already existing environmental artifacts In our case, there is a co-evolution between semantic and social networks.