# Vijay

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```					                An
Introduction to Bayesian Networks
for
Multi-Agent Systems

By Vijay Sargunar.M.M
A Bayesian Network

Battery

Gas

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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