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					                An
Introduction to Bayesian Networks
                for
       Multi-Agent Systems


                  By Vijay Sargunar.M.M
        A Bayesian Network


        Battery


                                      Gas
Radio             Ignition


                             Starts



                             Moves


 • Features of a Car’s Electrical System and Engine
Types of Bayesian Networks –
      Trouble shooting
Types of Bayesian Networks –
          Diagnosis
Guessing the state of the problem
            domain
• The agent makes observations on the domain,
  guesses the state of the problem domain based on
  the observations and its prior knowledge about the
  domain, and determines the most appropriate
  action based on its belief and goal.
• Agents constructed from a rule-based system uses
  a symbolic knowledge representation.
• We consider agents using symbolic knowledge
  representations and reasoning explicitly about the
  state of the domain.
          Reasons for guessing
• Agent does not observe some aspects of the
  domain – estimated indirectly through observable
• Relations between domain events are often
  uncertain
• Observations themselves may be imprecise,
  ambiguous, vague, noisy, and unreliable
• Lack of resources to observe all – incomplete
  information
• Event relations are certain – Impractical to analyze
  all of them explicitly.
     Bayesian Networks for
   Probabilistic Reasoning
• BN is used as a concise graphical repn. of a
  decision maker’s probabilistic knowledge of
  an uncertain domain.
• BN is primarily used to update the belief of
  an agent from that of a prior belief to a
  posterior belief when evidence is received.
• Probabilistic reasoning using Bayesian
  networks is called belief updating.
           A Simple Digital Circuit
 • Agent monitoring a digital circuit.

   a                                      r
                                                      e

                                              d
                          c                       t
       b        g
Agent’s prior belief P(a,b,c,d,e,g,r,t)
P(a=0,b=0,c=0,d=0,e=1,g=normal,r=normal,t=normal) =0.2
P(a=0,b=0,c=0,d=0,e=0,g=normal,r=normal,t=abnormal) =0.009
            Local Computation and
              Message Passing
• Cavity Example                               habit


 Posterior distribution P(h/t=y) is to be
computed.                                       cavity

Node t send message to c. P(t=y/c) =
[0.85,0.05]                                     toothache

Node c sends its message to node h.
P(t=y/h) = P(t=y,c/h) = P(t=y/c,h)P(c/h) =
P(t=y/c)P(c/h) = [0.13,0.69]
When h receives P(t=y/h) it can compute
P(h/t=y) = const P(t=y/h)P(h) =
[0.3054,0.6946]
    Junction Tree Representation


Q                S             C


      c,h            c   t,c


    P(c/h)P(h)           P(t/c)
     Multi-Agent Uncertain
    Reasoning with Multiply
  Sectioned Bayesian Networks
• MSBN is knowledge representation formalism for
  multi-agent uncertain reasoning.
• Areas used
  Aircraft (Intricate Machines)
  Monitoring & Trouble shooting in Chemical
  processes.
  Problem domain spread over a large geographical
  area.
A digital system.
• A digital system consists of five components (U0,..,U4) from different
vendors.
 Each vendor has built an agent capable of monitoring the component.
 Here, we assume identical faulty behavior of gates only for convenience.
The core representation of each agent is a subnet (Di, I=0,…,4).
The internal structure and parameter of each subnet is unknown to other
vendors.
 Multiply Sectioned Bayesian
    Networks (MSBNs)
A set of Bayesian subnets that collectively define a BN.
Interface subnets renders them conditionally
 independent.
Compiled into a linked junction forest (LJF) for
 inference.
In a single-agent MSBN, evidence is entered one
 subnet at a time.
In a multi-agent MSBN, evidence are entered
 asynchronously at multiple subnets in parallel.
Distributed Multi-agent Inference
• Pass messages among agents effectively so
  that each agent can update its belief
  correctly with respect to the observations
  made by all agents in the system.
       Model Construction &
          Verification
• Integrate an MSBN-based Multi-agent
  system from agents developed by
  independent vendors.
• Verification Process becomes subtle when
  agents are built by independent vendors and
  vendor’s know-how needs to be protected –
  Multi-agent distributed verification.
           Software Tool

• Microsoft’s MSBNX.
  Research Areas & Conclusion.
• Identification of Trustworthiness (Information
  quality) assessment of other agents
• If Prior belief’s quality of Information is less or
  excessively high the entire network gets distorted
  towards underestimation or overestimation of
  other agents.
• Generation of Plans by an agent based on a
  Bayesian network’s situation assessment.
Thank You

				
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posted:8/11/2012
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