Multi-Entity Decision Graphs: A Graphical Modeling Language

1. Multi-Entity Decision Graphs:A Graphical Modeling Language Kathryn Blackmond Laskey George Mason University klaskey@gmu.edu February, 2002

2. [Security experts] pointed out that the linchpin of the system is not Jersey barriers and metal detectors, but intelligence that a threat may be coming.Washington Post, September 12, 2001 This presentation is dedicated to the memory of journalist Danny Pearl, brutally murdered in Pakistan in February 2002, and to the pioneering research of his father Judea Pearl, which will enable unprecedented leaps in decision support technology that could anticipate and prevent future terrorist incidents.

3. Requirements for Inference and Decision Support • Support not replace the human • Extract relevant conclusions from huge volumes of data • Detect anomalous configurations of indicators that appear minor when taken individually • Respond rapidly to unanticipated situations • Cope with uncertainty and ambiguity • Support top-down control of • Allocation of computational resources • Choice of information to display and format of display • Management of collection resources

4. Plausible inference The evidence for cat allergy “explains away” your sneezing and cold is no longer needed as an explanation 1 3 2 Example: An Evolving Situation • Maria is visiting a friend when she suddenly begins sneezing. • "Oh dear, I'm getting a cold," she thinks. “I had better not visit Grandma.” • Then she notices scratches on the furniture. She sighs in relief. "I'm not getting a cold! It's only my cat allergy acting up!”

5. Decision Graphs • Both a knowledge representation and a computational architecture • Represents knowledge about variables and their interactions • Modular elements with defined interconnections • Computation can exploit loosely coupled structure for efficiency • Standard software & theory limited to “template models” • All problem instances involve: • Same set of variables • Same states for variables • Same relationships between variables • Same decision graph can be used for all problem instances • Only “evidence” (instantiated variables) varies from instance to instance • All potentially relevant explanations are explicitly represented

6. Technology Gap • In complex, open-world problems: • Number of actors and relationships to each other not fixed in advance • Attribution of evidence to actors may not be known in advance • Situation evolves in time • Need to represent only the most important explanations • Why there is hope • Actors of given type have similar features & behavior • Relevant variables & relationships depend on type of actor • Can we capture the regularities and retain open-world flexibility?

7. Maria’s Continuing Saga… • Variation 1: • Tran is sneezing and saw scratches • Tran was recently exposed to a cold and probably is not allergy prone • Variation 2: • Tran saw scratches • Maria did not see scratches • Tran is in room with Maria • Variation 3: • Tran and Maria both are sneezing, are allergy prone, and saw scratches • Tran and Maria are a continent apart

8. Variation 1 • Add background variables to specialize model to different individuals • Still a “template model” with limited expressive power

9. Variation 2 • Decision graph has replicated sub-parts • Different kinds of entities (cats and people)

10. Variation 3 Done Wrong • Version 2 model gets wrong answer if Maria and Tran are not near each other and both are near cats! • We need to be able to hypothesize additional cats if and when necessary

11. Variation 3 Done Right(…but what a mess!) • This model gets the right answer on all the variations

12. The Solution • Specify model in pieces and let the computer compose them Spatial Fragment Hypothesis Management Fragment Cats & Allergies Fragment Value Fragment Colds&Time Fragment Sneezing Fragment

13. Multi-Entity Decision Graphs • Represent knowledge as model fragments • Implicitly represents complete and consistent model of domain and anticipated situations • No a priori bound on #entities, #relevant relationships, #observations • Compose fragments dynamically into situation specific network (SSN) • A situation is a snapshot of the world at an instant of time • A situation-specific network is an ordinary, finite Bayesian network or decision graph constructed from the MEDG knowledge base using network construction operators • Use SSN to compute response to query • Approximates the “correct answer” encoded by the knowledge base • Use expert-guided Bayesian learning to update knowledge patterns over time

14. Model Construction • Simpler models give same results as more complex model on problems for which they are adequate • We want to construct “good enough” model for our situation • Model constructor builds situation-specific DG from knowledge base implicitly encoding infinite-dimensional DG

15. Models • Our real goal is to find the action that maximizes E[Utility(Consequence)|Action)] • We don't know E[Utility(Consequence)|Action)] • We construct a model M (decision theoretic or not) which is a recipe for selecting an action • We hope M is a good representation of the problem and will get us close to our optimal expected utility • For a decision theoretic model this means: • E[Utility(Consequence)|Action,M)] ≈ E[Utility(Consequence)|Action)] All models are wrong but some are useful

16. Savage and the “Problem of Small Worlds” • L. J. Savage on the problem of small worlds • "A person has only one decision to make in his life. He must … decide how to live." • "[There is a] practical necessity of confining attention … to relatively simple situations…" • "I find it difficult to say with any completeness how such isolated situations are actually arrived at and justified." • What happens when you make your small world too small? • Capturing that inviting rook gives your opponent the opportunity for checkmate • Actions intended to increase standard of living lead to pollution and global warming • Actions intended to improve world health (large-scale use of antibiotics) lead to disease-resistant bacteria and overpopulation • MEDGs solve the problem of small worlds • “Grand world” model is specified implicitly via “small world” models plus conditional exchangeability assumptions • SSN construction can be formulated as a decision problem • Model tradeoff between tractability and problem utility • Theoretical optimum SSN construction and evidence propagation algorithm exists for any class of problems • Practical engineering problem: approximate theoretical optimum

17. Physical Object Physical Object Physical Object Near Mammal Location Time Physical Object Cat Human MEDGs andObject-Oriented Representation • Entities of MEDG can be modeled as objects • Organized in type/subtype hierarchy • Similar behavior and structure across types • Can be composed of other entities • Can be related to other entities • Inheritance, composition, association • Probability part of MEDG expresses uncertainty about attributes of entities, composition of entities, and their associations • Value and action part of MEDG represents objectives and plans of software agent Composition Association Inheritance

18. Speculations on the Future • 20th century physics replaced traditional deterministic dynamics with explicitly probabilistic dynamics • Uncertainty is an intrinsic, irreducible element of present-day physics • Most non-physical scientists were trained in classical deterministic physics and are not fully aware of the implications of quantum mechanics • This has influenced the way in which researchers have attempted to model the natural world • This has also influenced our approach to computing and the development of intelligent systems • Speculation: 21st century computing will replace deterministic computing dynamics with probabilistic “physical symbol system” dynamics • Old paradigm: • Deterministic steps transform inputs into outputs • Result is either right or wrong • Semantics based on Boolean logic • New paradigm • Stochastic steps transform inputs into sequence of trial solutions • “Program” is replaced by dynamic system in which solution quality improves over time • Semantics based on decision theory • Old paradigm model is limiting case of new paradigm

19. Physical Symbol Systemsand 21st Century Computing • Physical symbol system (Newell and Simon) • Contains physical entities that serve as symbols • Symbols can designate entities in the world • System can interpret symbol structures to alter its behavior in a way that depends on designated entities • Recent trend in optimization and learning: • Construct fictitious physical system in which measure of solution quality maps onto action (or free energy or energy) • Apply solution methods imported from computational physics • This works because physical systems minimize action • Suggested 21st century computing paradigm • Implement MEDG (or similar) logic in quantum hardware • Replace “programming” with “goal setting” and let system find the best way to evolve to high-quality solution

20. Summary • MEDGs move Bayesian Network and influence diagram technology from hand-crafted special purpose models to genuine open-world reasoning capability • Knowledge base of modular elements is combined at run time to construct problem-specific model • MEDGs provide an answer to Savage’s “problem of small worlds” • MEDGs may lead to a new logic for computing