1 Department of Computer Science and Engineering, University of South Carolina 2005-05-16 Bayesian...

1 Department of Computer Science and Engineering, University of South

Carolina2005-05-16

Bayesian Network Bayesian Network DevelopmentDevelopment

Kevin B. Korb and Ann E. NicholsonBayesian Artificial Intelligence, Chapman and Hall, 2004,

esp. part III Kathryn B. Laskey and Suzanne M. Mahoney

“Knowledge Engineering for Agile Belief Network Models,” IEEE Transactions on Data and Knowledge Engineering, 12, 4 (July/August 2000), 487-498

Paul Sticha, Dennis Buede, and Richard L. Rees“APOLLO: An Analytical Tool for Predicting a Subject’s

Decision Making,” Proceedings of IA-05(https://analysis.mitre.org/proceedings/Final_Papers_Files/143_Camera_Ready_Paper.pdf)


Carolina2005-05-16

APOLLOAPOLLO

Models built to date (May 2005): InvasionNational strikeDomestic threatMissile testingSupport for the Global War on TerrorismDispute over contested territoryPeace/cease-fire negotiationsUse of WMDMonetary devaluationEstablishment of a new caliphateOperational planning in a terror cell


Carolina2005-05-16

Use of the ModelsUse of the Models The analysts want to model the decisions of

foreign leaders Software alerts the analyst when certain

thresholds are met within the model, indicating that evidence suggests a change in what is to be believed

Models are continuously updated Models provide an auditable record of the

assumptions and of the supporting evidence Neutralize various analytic biases such as

Recency, halo, proximity, hindsight, personalization Neutralize various social biases such as

Senior expert, “party line,” published record, “biggest fistful of cables,” personality


Carolina2005-05-16

ProcessProcess Two-day facilitated meetings per model Participants:

Analysts, subject-matter experts, facilitator, and model developer

Analysts provide information about the questions to be addressed by the model

Both analysts and external experts provide the information and assessments

Facilitator keeps the group framing the questions properly, e.g. in terms of conditional probability assessments, and keeps a healthy debate going

Model developer also acts as notetaker Model is projected on screen as it is developed


Carolina2005-05-16

StepsSteps

Defining the question, e.g.: what will a national leader do in case of a national strike

Leave country, make concessions, hold a referendum, let a regional organization arbitrate, wait out, repress violently

Identify situational variables that may affect the leader’s decision, e.g.:

What are the leader’s objectives Add situational variables “subject to the time

constraints for the model development process

“One-and-a-half day of the two-day session are typically completed by this point.”

A personality module is added to each model, linked through “intervening variables.”

What-if analyses Sensitivity


Carolina2005-05-16

General StrikeGeneral Strike

Figures are from Sticha et al.’s paper


Carolina2005-05-16

Conditional Probability Conditional Probability AssessmentAssessment

Table is from Sticha et al.’s paper


Carolina2005-05-16

Monitoring the Situation over Monitoring the Situation over TimeTime

Figure is from Sticha et al.’s paper


Carolina2005-05-16

Linkage Variables for Personality Linkage Variables for Personality ModelModel

Table is from Sticha et al.’s paper


Carolina2005-05-16

A Complete ModelA Complete Model

Figure is from Sticha et al.’s paper


Carolina2005-05-16

Laskey and MahoneyLaskey and Mahoney

Probability elicitation worksheets (figure 6 in paper)

Exploit partitions in the state space of parent variables

Compare distributions Focus on order-of-magnitude differences

in small probabilities


Carolina2005-05-16

Korb and NicholsonKorb and Nicholson

Types of variablesTarget or queryEvidence or observationContext:

Sensing conditions, setting factors, background causal conditions

Controllable May be set, rather than observed

ValuesHow to discretize


Carolina2005-05-16

Graphical StructureGraphical Structure

Causal RelationshipsCause, effect, prevention, interference,

moderation, invalidation, enabling, explanation

Dependence and Independence RelationshipsD-separationRelevanceAssociation relationshipTemporal relationship


Carolina2005-05-16

Parameters (Probabilities)Parameters (Probabilities)

Sources:DataDomain expertsThe literature

ElicitationVerbal mapsOddsPie charts, histogramsLotteriesLocal structure

causal interaction or lack thereof: addition, prevention, XOR, synergy

Partitioning Divorcing

Preference structures (not in Korb and Nicholson)


Carolina2005-05-16

NodesNodes

Nodes in a Bayesian network are in one-to-one correspondence with (random) variables.Variables map states (also known as values) to

subsets of the event spaceThe probability of a variable having a certain

value is the probability of all the events consistent with that variable having that value

Variables represent propositions about which the system reasons; they are therefore sometimes called propositional variables, even though they may take values other than true and false.


Carolina2005-05-16

AttributesAttributes

Each variable has a set of identifying attributes

Attributes “play the role of variables in a logic programming language” [Laskey and Mahoney, UAI-97]

Attributes identify a particular instance of a random variable

Attributes are used to combine fragments:Fragments can be combined only if their attributes

unify


Carolina2005-05-16

Fragments As TemplatesFragments As Templates

Fragments are template models:“A template model is appropriate for problem domains

in which the relevant variables, their state spaces, and their probabilistic relationships do not vary from problem instance to problem instance” [L&M, UAI-97]

A scenario is a combination of instantiated template models

The attributes are used to identify and combine fragment instances but the probabilistic relationships do not change from instance to instance:The probability distribution described in the Bayesian

network is a joint distribution on the nodes only, not on the nodes and the attributes


Carolina2005-05-16

Medical IllustrationMedical Illustration

[A] medical diagnosis template network would contain variables representing background information about a patient, possible medical conditions the patient might be experiencing, and clinical findings that might be observed.

The network encodes probabilistic relationships among these variables. To perform diagnosis on a particular patient, background information and findings for the patient are entered as evidence and the posterior probabilities of the possible medical conditions are reported.

Although values of the evidence variables vary from patient to patient, the relevant variables and their probabilistic relationships are assumed to be the same for all patients. It is this assumption that justifies the use of template models.Direct quote from [Laskey and Mahoney, UAI-97]


Carolina2005-05-16

Guidance for Selection of Guidance for Selection of Nodes and AttributesNodes and Attributes

Nodes represent the variables on which the assessment of a situation depends. For example:State and hypothesis variablesObservation and test variables Intermediate and theoretical variablesSetting factors

Attributes identify a particular situation. E.g.:LocationTimeNameCase ID


Carolina2005-05-16

MEBNs As a System Integrating MEBNs As a System Integrating First-Order Logic and First-Order Logic and

ProbabilityProbability Paulo C.G. da Costa and Kathryn B.

Laskey. “Multi-Entity Bayesian Networks without Multi-Tears.” Available at http://ite.gmu.edu/~klaskey/publications.html [Costa, 2005]

Kathryn B. Laskey. “First-order Bayesian Logic.” Available at http://ite.gmu.edu/~klaskey/publications.html [Laskey, 2005]


Carolina2005-05-16

Sample BN FragmentsSample BN Fragments

[Laskey, 2005]


Carolina2005-05-16

Using MEBNsUsing MEBNs

• Bayesian Network Fragment (BNF)It is the basic unit. Each network fragment consists of a set of related variables together with knowledge about the probabilistic relationships among the variables.

• Multi Entity Bayesian Network (MEBN)Collection of BNFs specifying probability distribution over attributes of and relationships among a collection of interrelated entities

• Situation-Specific Network(SSN) Ordinary finite Bayesian Network

constructed from an MEBN knowledge base, to reason about specific target hypothesis, with a particular evidence.

[Laskey, 2005]


Carolina2005-05-16

Formal SpecificationsFormal Specifications

First-Order Bayesian Logic A logical foundation that fully integrates

classical first-order logic with probability theory

Because first-order Bayesian logic contains classical first-order logic as a deterministic subset, it is a natural candidate as a universal representation for integrating domain ontologies expressed in languages based on classical first-order logic or subsets thereof.

[Laskey, 2005]


Carolina2005-05-16

Logic in BN FragmentsLogic in BN Fragments

[Laskey, 2005]


Carolina2005-05-16

A Simple Bayesian NetworkA Simple Bayesian Network

[Laskey, 2005]


Carolina2005-05-16

A Conditional Proabability A Conditional Proabability TableTable

[Laskey, 2005]


Carolina2005-05-16

Multiple InstancesMultiple Instances

[Laskey, 2005]


Carolina2005-05-16

Temporal RepetitionTemporal Repetition

[Laskey, 2005]


Carolina2005-05-16

A Fragment (MFrag)A Fragment (MFrag)

[Laskey, 2005]


Carolina2005-05-16

An Instance of an MFragAn Instance of an MFrag

[Laskey, 2005]


Carolina2005-05-16

A Temporal MFragA Temporal MFrag

[Laskey, 2005]


Carolina2005-05-16

Temporal Situation-Specific BNTemporal Situation-Specific BN

[Laskey, 2005]


Carolina2005-05-16

Other Issues in [Laskey, 2005]Other Issues in [Laskey, 2005] Generative Theories Composition Algorithm Related Research:

HMMsDBNsPlatesObject-Oriented BNsProbabilistic Relational Models

Learning Decision Making

Multiple-entity decision graphs (MEDGs) are to influence diagrams what MEBNs are to Bayesian networks

OWL-PA planned MEBN-based extension to OWL


Carolina2005-05-16

Korb and NicholsonKorb and Nicholson

Types of variablesTarget or queryEvidence or observationContext:

Sensing conditions, setting factors, background causal conditions

Controllable May be set, rather than observed

ValuesHow to discretize


Carolina2005-05-16

Graphical StructureGraphical Structure

Causal RelationshipsCause, effect, prevention, interference,

moderation, invalidation, enabling, explanation

Dependence and Independence RelationshipsD-separationRelevanceAssociation relationshipTemporal relationship


Carolina2005-05-16

Parameters (Probabilities)Parameters (Probabilities)

Sources:DataDomain expertsThe literature

ElicitationVerbal mapsOddsPie charts, histogramsLotteriesLocal structure

causal interaction or lack thereof: addition, prevention, XOR, synergy

Partitioning Divorcing

Preference structures (not in Korb and Nicholson)


Carolina2005-05-16

Modeling Exercise: Natural Modeling Exercise: Natural DisasterDisaster

What will be the economic effect on a country due to a natural disaster disrupting the availability of a commodity?Answers: Uprising, War to acquire by force, Recession,

None Situational variables:

Extent of disaster Importance of commodityAlternate commodityAlternate supply

Evidence or observation variables:Projected need for commodity Import amountExport amount


Carolina2005-05-16

Basic Scenario for Basic Scenario for Terrorism NetworkTerrorism Network

Leader – communicates goals and ideology to planners and operatives

Planners – arrange funds; choose target; specify logistics

Logistics – types are weapons, transportation resources

Funds – support operatives; pay for logistics

Operatives – acquire logistics; use Intel; use logistics; perform terrorist act

Intel – identify logistics; identify target; support planners

Targets – types are facilities, resources, people, relationships

Terrorist act – requires operatives; requires logistics

(Not all relationships are shown)

Operatives Planners

Motivated Leader

Logistics

Intel

FundingTerrorAttack


Carolina2005-05-16

Basic Scenario for Basic Scenario for Economic Economic

InterdependencyInterdependency Catastrophic Event – either a

natural disaster, such as an earthquake, or a terrorist action, such as an oil pipeline disrupted

Supply Chains – the key resources and industries, from raw materials to finished goods

Industries – types Countries – locations of

resources and factories Consequences –the possibilities

for political or military actions, and the ramifications

CatastrophicEvent

What supply chainsare affected?

What industriesare affected?

What countriesare involved?

Are there alternativesuppliers/capabilities?


Carolina2005-05-16

Economic Disruption ScenarioEconomic Disruption Scenario1. An analyst receives the following message:

Intelligence Report 11/11/04: A conversation recorded by a wiretap on a suspected terrorist cell in Beirut had a discussion about crippling the Iranian economy by destroying oil production facilities.

2. The original intelligence message is passed to the Bayesian reasoning system for further analysis.

3. The message is parsed, marked-up semantically, and matched with prior analytical knowledge in the form of Bayesian network fragments.

4. The fragments are assembled into a number of plausible scenarios that explain the input information. The most plausible and complete scenario is shown to the analyst.

5. The scenario shows that the most likely and highest value target would be a pipeline, if it were known that the pipeline crossed an international border and that the nations on each side of the border had a history of distrust.

6. The analyst is interested in pipelines as a means of oil transportation for all known refineries and fields in Iran and asks for that information from the CBR for KD system.

7. The CBR for KD system locates a URL concerning the locations of cross border pipelines in the region: http://www.eia.doe.gov/emeu/cabs/iran.html The URL is passed to the Bayesian reasoning system.

8. The Bayesian reasoning system augments the scenario it constructed earlier with the additional information and determines that there is a pipeline that would be at risk.

9. The analyst is alerted to the risk and is presented with the evidence and the scenario showing the reasoning behind the alert.


Carolina2005-05-16

Basic Scenario for Capabilities Basic Scenario for Capabilities to Produce Weapon Xto Produce Weapon X

Weapon X Production => Raw Materials Personnel Expertise Funding Manufacturing Facilities Motivation and Intent

Personnel Expertise

Motivation andIntent

ManufacturingFacilities

RawMaterials

Funding

Weapon XProduction

1 Department of Computer Science and Engineering, University of South Carolina 2005-05-16 Bayesian...

Documents

Transcript of 1 Department of Computer Science and Engineering, University of South Carolina 2005-05-16 Bayesian...