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An Introduction to Bayesian Networks for Multi-Agent Systems

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Title: An Introduction to Bayesian Networks for Multi-Agent Systems


1
An Introduction to Bayesian Networksfor
Multi-Agent Systems
By Vijay Sargunar.M.M
2
A Bayesian Network
Battery
Gas
Radio
Ignition
Starts
Moves
  • Features of a Cars Electrical System and Engine

3
Types of Bayesian Networks Trouble shooting
4
Types of Bayesian Networks Diagnosis
5
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.

6
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.

7
Bayesian Networks for Probabilistic
Reasoning
  • BN is used as a concise graphical repn. of a
    decision makers 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.

8
A Simple Digital Circuit
  • Agent monitoring a digital circuit.

r
a
e
d
t
c
b
g
Agents prior belief P(a,b,c,d,e,g,r,t) P(a0,b0,
c0,d0,e1,gnormal,rnormal,tnormal)
0.2 P(a0,b0,c0,d0,e0,gnormal,rnormal,tabn
ormal) 0.009
9
Local Computation and Message Passing
  • Cavity Example

habit
Posterior distribution P(h/ty) is to be
computed. Node t send message to c. P(ty/c)
0.85,0.05 Node c sends its message to node
h. P(ty/h) ?P(ty,c/h) ?P(ty/c,h)P(c/h)
?P(ty/c)P(c/h) 0.13,0.69 When h receives
P(ty/h) it can compute P(h/ty) const
P(ty/h)P(h) 0.3054,0.6946
cavity
toothache
10
Junction Tree Representation
Q
S
C
c
t,c
c,h
P(t/c)
P(c/h)P(h)
11
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.

12
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.
A digital system.
13
The core representation of each agent is a subnet
(Di, I0,,4).The internal structure and
parameter of each subnet is unknown to other
vendors.
14
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.

15
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.

16
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 vendors
    know-how needs to be protected Multi-agent
    distributed verification.

17
Software Tool
  • Microsofts MSBNX.

18
Research Areas Conclusion.
  • Identification of Trustworthiness (Information
    quality) assessment of other agents
  • If Prior beliefs 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 networks situation assessment.

19
Thank You
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