An Introduction to Bayesian Networks

for Multi-Agent Systems

By Vijay Sargunar.M.M

A Bayesian Network

Battery

Radio Ignition

Starts

Moves

Gas

• 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

b gc

r

dt

e

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

cavity

toothache

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

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

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

cc,h t,c

Q S C

P(t/c)P(c/h)P(h)

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 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.

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