Issues for Discussion and Work Jan 2007

1. Issues for Discussion and Work Jan 2007 • Choose meeting time for Sp07 • Tuesday 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. Nodes • 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 space • The 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. Attributes • 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. Fragments 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. Medical 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. Guidance for Selection of Nodes and Attributes • Nodes represent the variables on which the assessment of a situation depends. For example: • State and hypothesis variables • Observation and test variables • Intermediate and theoretical variables • Setting factors • Attributes identify a particular situation. E.g.: • Location • Time • Name • Case ID

7. Use of MEBNs in Magellan and Evolution of MEBNs • In Magellan, • No provision is made for the combination of multiple instances of the same fragment • This 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. MEBNs As a System Integrating First-Order Logic and Probability • 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. Sample BN Fragments [Laskey, 2005]

10. Using 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. Formal 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. Logic in BN Fragments [Laskey, 2005]

13. A Simple Bayesian Network [Laskey, 2005]

14. A Conditional Proabability Table [Laskey, 2005]

15. Multiple Instances [Laskey, 2005]

16. Temporal Repetition [Laskey, 2005]

17. A Fragment (MFrag) [Laskey, 2005]

18. An Instance of an MFrag [Laskey, 2005]

19. A Temporal MFrag [Laskey, 2005]

20. Temporal Situation-Specific BN [Laskey, 2005]

21. Other Issues in [Laskey, 2005] • Generative Theories • Composition Algorithm • Related Research: • HMMs • DBNs • Plates • Object-Oriented BNs • Probabilistic Relational Models • Learning • Decision Making • Multiple-entity decision graphs (MEDGs) are to influence diagrams what MEBNs are to Bayesian networks • OWL-P • A planned MEBN-based extension to OWL