1 Department of Computer Science and Engineering, University of South

Carolina2007-01-05

Issues for Discussion and Work Jan Issues for Discussion and Work Jan 20072007

Choose meeting time for Sp07Tuesday 1500-1600 (or earlier, if compatible with Dr. Huhns).

“MEBN logic includes FOL as a subset” [Laskey 2006, section 5 (p.36)]. Explain and prove this claim

Continue work on technical report Upgrade Magellan with ACHv2.0.3

[Marco] Contact PARC for Source Code of ACH version 2.0.3[Jingshan] Prepare Magellan for the update[JH] Show JW and SL how Magellan works and how it is

organized

2 Department of Computer Science and Engineering, University of South

Carolina2007-01-05

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.

3 Department of Computer Science and Engineering, University of South

Carolina2007-01-05

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

4 Department of Computer Science and Engineering, University of South

Carolina2007-01-05

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

5 Department of Computer Science and Engineering, University of South

Carolina2007-01-05

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]

6 Department of Computer Science and Engineering, University of South

Carolina2007-01-05

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

7 Department of Computer Science and Engineering, University of South

Carolina2007-01-05

Use of MEBNs in Magellan and Use of MEBNs in Magellan and Evolution of MEBNsEvolution of MEBNs

In Magellan, No provision is made for the combination of

multiple instances of the same fragmentThis simplifies the specification of local

probability distributions In later versions of MEBNs:

A language is provided for the description of local probability distributions

Multiple instances of the same fragments can be used

Local probability distributions depend on the values of attributes

8 Department of Computer Science and Engineering, University of South

Carolina2007-01-05

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]

Kathryn B. Laskey. “MEBN: A Logic for Open-World Probabilistic Reasoning.” Available at http://ite.gmu.edu/~klaskey/publications.html [Laskey, 2006]

9 Department of Computer Science and Engineering, University of South

Carolina2007-01-05

Sample BN FragmentsSample BN Fragments

[Laskey, 2005]

10 Department of Computer Science and Engineering, University of South

Carolina2007-01-05

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]

11 Department of Computer Science and Engineering, University of South

Carolina2007-01-05

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]

12 Department of Computer Science and Engineering, University of South

Carolina2007-01-05

Logic in BN FragmentsLogic in BN Fragments

[Laskey, 2005]

13 Department of Computer Science and Engineering, University of South

Carolina2007-01-05

A Simple Bayesian NetworkA Simple Bayesian Network

[Laskey, 2005]

14 Department of Computer Science and Engineering, University of South

Carolina2007-01-05

A Conditional Proabability A Conditional Proabability TableTable

[Laskey, 2005]

15 Department of Computer Science and Engineering, University of South

Carolina2007-01-05

Multiple InstancesMultiple Instances

[Laskey, 2005]

16 Department of Computer Science and Engineering, University of South

Carolina2007-01-05

Temporal RepetitionTemporal Repetition

[Laskey, 2005]

17 Department of Computer Science and Engineering, University of South

Carolina2007-01-05

A Fragment (MFrag)A Fragment (MFrag)

[Laskey, 2005]

18 Department of Computer Science and Engineering, University of South

Carolina2007-01-05

An Instance of an MFragAn Instance of an MFrag

[Laskey, 2005]

19 Department of Computer Science and Engineering, University of South

Carolina2007-01-05

A Temporal MFragA Temporal MFrag

[Laskey, 2005]

20 Department of Computer Science and Engineering, University of South

Carolina2007-01-05

Temporal Situation-Specific BNTemporal Situation-Specific BN

[Laskey, 2005]

21 Department of Computer Science and Engineering, University of South

Carolina2007-01-05

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