群体智慧--复杂网络上的最佳共识形成

Xiaofan Wang

xfwang@

SOCIAL LEARNING IN COMPLEX NETWORKS

What is social learning?

(Consensus on the true state)

Our recent researches

(Pinning, Similarity ‐based, Chaos)

Social learning algorithms

(Bayesian +

Consensus)

我的在线历程20002005200620102011

汪小帆老师

90

关注4761粉丝

¾极度不均匀：

¾并非很社会：¾高度同质化：¾两步信息流：

¾不同生命期：

人肉搜索为何百发百中？

教育医疗等却为何如此难以形成最佳共识？

围脖上的意见领袖对粉丝的影响力有多大？

热门话题、名人堂。。。

群体智慧：大众比精英更聪明！Galton, Nature, 1907

¾Private signals

¾Network structure

¾Update rules Observing

Communicating

Updating Beliefs

Social Learning Process

1

2

3

一致性：能否形成共识？

最优性：是否最佳共识？

可控性：能否引导共识？

Case study: Who is singing?

State space True state Private signal

Likelihood function

Network structure ,,0()1,()1

i t k i t k k

μθμθ≤≤=∑,(*)1

i t μθ→Belief

{}

12,,,n θθθΘ=L *θ∈Θ

i t

s

(|)1

i s

l s θ=∑(,)

G V E =

Bayesian Learning ：A Single Agent Case

()

t →∞*

()1P

t μθ→

11

111(

|)()

()(|)()

t t t t t t l s s m s θμθμθμθ+++++=

Observationally equivalent states

Agent i is called an indiscriminative agent

*:,(|)(|)for all i i i

i i i

l s l s s S θθθθθ∗∃∈Θ≠=∈

¾Each agent should know the global structure of the network ¾Each agent tries to deduce the information of every other agent

Bayesian Social Learning: Network Case

Computation burden + high complexity (|)()

(|)()

l s s m s θμθμθ=

人肉搜索有效克服了这两个困难！

Consensus

,1,,()()i

i t ii i t ij j t j N a a μθμθμθ+∈=+∑（）,,()i t j t μθμθ−→（）

0,()i t μθ→0,(*)1

i t μθ→θ∀∈Θ

θ∀∈Θ*

θθ∀≠Social Learning = Best Consensus

Consensus Algorithm

Consensus

,,01

()i t j j

N μθμθ→∑（）

Consensus

,1,,()()i

i t ii i t ij j t j N a a μθμθμθ+∈=+∑（）,,()i t j t μθμθ−→（）

0,()i t μθ→0,(*)1

i t μθ→θ∀∈Θ

θ∀∈Θ*

θθ∀≠Social Learning = Best Consensus

Consensus Algorithm

Consensus

,,01

()i t j j

N μθμθ→∑（）

Consensus

,1,,()()i

i t ii i t ij j t j N a a μθμθμθ+∈=+∑（）,,()i t j t μθμθ−→（）

0,()i t μθ→0,(*)1

i t μθ→θ∀∈Θ

θ∀∈Θ*

θθ∀≠Social Learning = Best Consensus

Consensus Algorithm

Consensus

,,01

()i t j j

N μθμθ→∑（）

Consensus

,1,,()()i

i t ii i t ij j t j N a a μθμθμθ+∈=+∑（）,,()i t j t μθμθ−→（）

0,()i t μθ→0,(*)1

i t μθ→θ∀∈Θ

θ∀∈Θ*

θθ∀≠Social Learning = Best Consensus

Consensus Algorithm

Consensus

,,01

()i t j j

N μθμθ→∑（）θ∀∈Θ