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Unformatted text preview: NonBayesian Social Learning Presented by Arastoo Fazeli November 30, 2009 1 Learning in Complex Networks: Model and Abstractions I Each vertex represents an agent I Each edge represents information flow between two agents I Agents have access to their neighbors’ information 2 Learning in Complex Networks: Model and Abstractions I Each vertex represents an agent I Each edge represents information flow between two agents I Agents have access to their neighbors’ information Θ parameter space θ * ∈ Θ the unobservable true state of the world s t = ( s 1 t ,...,s n t ) random signals observed by the agents 2 Bayesian Learning over Networks μ i,t ( θ ) = P [ θ = θ * F i,t ] where F i,t = σ ( s i 1 ,...,s i t , { μ j,k : j ∈ N i ,k ≤ t } ) is the information available to agent i up to time t . 3 Bayesian Learning over Networks μ i,t ( θ ) = P [ θ = θ * F i,t ] where F i,t = σ ( s i 1 ,...,s i t , { μ j,k : j ∈ N i ,k ≤ t } ) is the information available to agent i up to time t . Agents need to make rational deductions about everybody’s beliefs based on only observing neighbors’ beliefs: 3 Bayesian Learning over Networks μ i,t ( θ ) = P [ θ = θ * F i,t ] where F i,t = σ ( s i 1 ,...,s i t , { μ j,k : j ∈ N i ,k ≤ t } ) is the information available to agent i up to time t . Agents need to make rational deductions about everybody’s beliefs based on only observing neighbors’ beliefs: Computationally hard! 3 The Problem with Bayesian Learning 1. Incomplete network information 4 The Problem with Bayesian Learning 1. Incomplete network information 2. Incomplete information about other agents’ signal structures 4 The Problem with Bayesian Learning 1. Incomplete network information 2. Incomplete information about other agents’ signal structures 3. Higher order beliefs matter 4 The Problem with Bayesian Learning 1. Incomplete network information 2. Incomplete information about other agents’ signal structures 3. Higher order beliefs matter 4. The source of each piece of information is not immediately clear Intractable and not local . 4 NonBayesian Social Learning Need a local and computationally tractable update, which hopefully delivers asymptotic social learning. 5 NonBayesian Social Learning Need a local and computationally tractable update, which hopefully delivers asymptotic social learning. Agent i is I Bayesian when it comes to her observation I nonBayesian when incorporating others information 5 Model N = { 1 , 2 ,...,n } individuals in the society 6 Model N = { 1 , 2 ,...,n } individuals in the society G = ( N , E ) social network 6 Model N = { 1 , 2 ,...,n } individuals in the society G = ( N , E ) social network Θ finite parameter space 6 Model...
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This note was uploaded on 12/08/2011 for the course CIS 677 taught by Professor Michaelkearns during the Fall '09 term at Penn State.
 Fall '09
 MichaelKearns

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