Bayesian Network Development

1. Bayesian Network Development • Kevin B. Korb and Ann E. Nicholson • Bayesian 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)

2. APOLLO • Models built to date (May 2005): • Invasion • National strike • Domestic threat • Missile testing • Support for the Global War on Terrorism • Dispute over contested territory • Peace/cease-fire negotiations • Use of WMD • Monetary devaluation • Establishment of a new caliphate • Operational planning in a terror cell

3. Use 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

4. Process • 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

5. Steps • 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

6. General Strike Figures are from Sticha et al.’s paper

7. Conditional Probability Assessment Table is from Sticha et al.’s paper

8. Monitoring the Situation over Time Figure is from Sticha et al.’s paper

9. Linkage Variables for Personality Model Table is from Sticha et al.’s paper

10. A Complete Model Figure is from Sticha et al.’s paper

11. Laskey 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

12. Korb and Nicholson • Types of variables • Target or query • Evidence or observation • Context: • Sensing conditions, setting factors, background causal conditions • Controllable • May be set, rather than observed • Values • How to discretize

13. Graphical Structure • Causal Relationships • Cause, effect, prevention, interference, moderation, invalidation, enabling, explanation • Dependence and Independence Relationships • D-separation • Relevance • Association relationship • Temporal relationship

14. Parameters (Probabilities) • Sources: • Data • Domain experts • The literature • Elicitation • Verbal maps • Odds • Pie charts, histograms • Lotteries • Local structure • causal interaction or lack thereof: addition, prevention, XOR, synergy • Partitioning • Divorcing • Preference structures (not in Korb and Nicholson)

15. 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.

16. 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

17. 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

18. 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]

19. 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

20. 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]

21. Sample BN Fragments [Laskey, 2005]

22. 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]

23. 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]

24. Logic in BN Fragments [Laskey, 2005]

25. A Simple Bayesian Network [Laskey, 2005]

26. A Conditional Proabability Table [Laskey, 2005]

27. Multiple Instances [Laskey, 2005]

28. Temporal Repetition [Laskey, 2005]

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

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

31. A Temporal MFrag [Laskey, 2005]

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

33. 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

34. Korb and Nicholson • Types of variables • Target or query • Evidence or observation • Context: • Sensing conditions, setting factors, background causal conditions • Controllable • May be set, rather than observed • Values • How to discretize

35. Graphical Structure • Causal Relationships • Cause, effect, prevention, interference, moderation, invalidation, enabling, explanation • Dependence and Independence Relationships • D-separation • Relevance • Association relationship • Temporal relationship

36. Parameters (Probabilities) • Sources: • Data • Domain experts • The literature • Elicitation • Verbal maps • Odds • Pie charts, histograms • Lotteries • Local structure • causal interaction or lack thereof: addition, prevention, XOR, synergy • Partitioning • Divorcing • Preference structures (not in Korb and Nicholson)

37. Modeling Exercise: Natural Disaster • 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 commodity • Alternate commodity • Alternate supply • Evidence or observation variables: • Projected need for commodity • Import amount • Export amount

38. Motivated Leader Operatives Planners Logistics Funding TerrorAttack Intel Basic Scenario for Terrorism 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)

39. What supply chains are affected? What industries are affected? What countries are involved? Are there alternative suppliers/capabilities? Basic Scenario for Economic Interdependency • 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 Catastrophic Event

40. Economic Disruption Scenario • 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. • The original intelligence message is passed to the Bayesian reasoning system for further analysis. • The message is parsed, marked-up semantically, and matched with prior analytical knowledge in the form of Bayesian network fragments. • 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. • 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. • 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. • 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. • 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. • The analyst is alerted to the risk and is presented with the evidence and the scenario showing the reasoning behind the alert.

41. Basic Scenario for Capabilities to Produce Weapon X • Weapon X Production => • Raw Materials • Personnel • Expertise • Funding • Manufacturing Facilities • Motivation and Intent Motivation and Intent Personnel Expertise Manufacturing Facilities Funding Weapon XProduction Raw Materials