From Pixels to Propositions: Bridging the Gap from Sensor-Level Data to Cognitive-Level Knowledge Kathryn Blackmond Laskey Department of Systems Engineering & Operations Research George Mason University ©Kathryn Blackmond Laskey February 2005 - UKy Px2Prp 1 This presentation is dedicated to the memory of journalist Danny Pearl, murdered in Pakistan in February 2002, and to the pioneering research of his father Judea Pearl. Danny Pearl’s spirit will live on in the work of those who apply his father’s work to protect the open society for which he gave his life. The Daniel Pearl Foundation (http://www.danielpearl.org) was formed in memory of journalist Daniel Pearl to further the ideals that inspired Daniel's life and work. ©Kathryn Blackmond Laskey February 2005 - UKy Px2Prp 2 Representation: A Key Enabler • Performance of intelligent system depends on good representation of problem space • Good representations for fusion must: – Capture important regularities in the domain – Capture how objects and processes give rise to observable evidence – Rest on a mathematically sound and scientifically principled logical foundation • The best and most efficient algorithm will produce bad results if you are solving the wrong problem – Type III error dwarfs Type I and Type II errors “Everything is easy if you can find the right representation” Herbert A. Simon ©Kathryn Blackmond Laskey February 2005 - UKy Px2Prp 3 Effective multi-source fusion – Depends on good representations – Requires integrating sensor inputs with information from other sources – Depends heavily on background knowledge and context ©Kathryn Blackmond Laskey February 2005 - UKy Px2Prp 4 Models and Representations • Models represent systems and processes – We use models to answer questions about the real world – Goal: Build “good enough” models » “Good enough” depends on purpose for which model is used » Simplifications and inaccuracies don’t matter if they don’t affect results • Representations are approximations – Restricted set of variables – Unrealistic simplifications – Untested assumptions • Models are constructed from: – Past data on system or related systems – Judgment of subject matter experts – Judgment of experienced model builders ©Kathryn Blackmond Laskey February 2005 - UKy Px2Prp 5 Observations Representation Real World Actions ©Kathryn Blackmond Laskey February 2005 - UKy Px2Prp 6 ©Kathryn Blackmond Laskey February 2005 - UKy Px2Prp 7 Representing Representation Observations Real world with real representation created by real conscious subsystem Actions ©Kathryn Blackmond Laskey February 2005 - UKy Artificial world with simulated representation created by simulated conscious subsystem Px2Prp 8 The Fusion Challenge • Fusion is the process of incorporating information from different sources into a single “fused” representation • Why fusion is difficult: – – – – Vast quantities of sensor information Real-time processing requirements Restrictions on weight, communication bandwidth Need to integrate physical and geometrical models with qualitative knowledge – Noisy, unreliable, ambiguous data – Active attempts at deception – Requirement for robustness to new or little-known entities • Why fusion is important: – Features that are meaningless in isolation are definitive in combination Data, data everywhere, and not the time to think… ©Kathryn Blackmond Laskey February 2005 - UKy Px2Prp 9 Paradigm Shift in Computing • Old paradigm: Algorithms running on Turing machines – Deterministic steps transform inputs into outputs – Result is either right or wrong – Semantics based on Boolean logic • New paradigm: Economy of SW agents running on physical symbol system – Agents make decisions (deterministic or stochastic) to achieve objectives – “Program” replaced by dynamic system improving solution quality over time – Semantics based on decision theory / game theory / stochastic processes • Hardware realizations of physical symbol systems – – – – – – Physical systems minimize action Decision theoretic systems maximize utility / minimize loss Hardware realization of physical symbol system maps action to utility Programming languages are replaced by specification / interaction languages Software designer specifies goals, rewards and information flows Unified theory spans sub-symbolic to cognitive levels • Old paradigm is limiting case of new paradigm ©Kathryn Blackmond Laskey February 2005 - UKy Px2Prp 10 “No Computation Without Representation”* • “First figure out what you would do if computation were not an issue, and then figure out how to compute it.”** – Good representation provides theoretical basis for informed choices about computation – Good representation provides statistical basis for evaluating solution quality – Bad representation leads to failures you don’t know are failures and wouldn’t know how to fix if you did * Tod Levitt ** Jay Kadane ©Kathryn Blackmond Laskey February 2005 - UKy Px2Prp 11 Elements of Computational Representation • Vocabulary – Variables, constants, operators, punctuation • Syntax – Rules for composing legal expressions – Organization into higher level structures or patterns » Frames » Objects » Graphs • Proof rules (operational semantics) – Rules for deriving expressions from other expressions – Corresponds to operational semantics of computer language • Semantics - characterizes meaning of expressions – Ontology or theory of reference (denotational semantics) – Theory of truth (axiomatic semantics) ©Kathryn Blackmond Laskey February 2005 - UKy Px2Prp 12 First-Order Logic • Vocabulary: – Constants (stand for particular named objects) – Variables (stand for generic unnamed objects) – Functions (allow objects to be referred to indirectly) » Location(x) » MotherOf(y) – Predicates (represent hypotheses that can be true or false) » Guilty(s) » Near(John,GroceryStore32) – Connectives » Quantification, conjunction, disjunction, implication, negation, equality • Syntax: – Atomic sentences – Composition rules for forming compound sentences from atomic sentences • Semantics – Tarski invented the standard semantics for first-order logic – Compositional: meaning of sentence depends on meaning of parts – Valid sentence is true in all interpretations of a language; unsatisfiable sentence cannot be true in any interpretation • Proof rules – Natural deduction – Resolution with refutation ©Kathryn Blackmond Laskey February 2005 - UKy Px2Prp 13 Privileged Status of FOL • Has been proposed as unifying language for – Defining extended logics – Interchanging knowledge • FOL “has enough expressive power to define all of mathematics, every digital computer that has ever been built, and the semantics of every version of logic, including itself.” (Sowa,2000) • Issues: – Cannot express generalizations about sets, predicates, functions – Cannot represent gradations of plausibility – No built-in approaches to » » » » » » Categories Time and space Causality Action Events Value ©Kathryn Blackmond Laskey February 2005 - UKy Px2Prp 14 Ontology • Categories of things that can exist in a domain – Organized hierarchically into types / subtypes – Objects of a given type have: » Similar structure (part-whole composition) » Similar behavior (processes) » Similar associations – Subtypes can inherit structure, behavior, association from supertype • Ontology describes – Types of entities in the domain – Attributes of entities – Relationships they can participate in • Ways to specify ontology – Formal - types defined by logical rules (usually FOL) – Informal - types specified via prototypical instances ©Kathryn Blackmond Laskey February 2005 - UKy Px2Prp 15 Requirements for New Paradigm Computational Representation • • • • Embrace uncertainty Perform plausible reasoning Learn from experience Incorporate observation, historical data, expert knowledge • Explore multiple alternatives • Replace rote procedure with focus on attaining objectives • Trade off multiple objectives ©Kathryn Blackmond Laskey February 2005 - UKy Px2Prp 16 Complementary Technologies • Traditional Logic-Based Artificial Intelligence + Structured representations for symbolic knowledge + Efficient methods for searching complex problem spaces - Rudimentary and atheoretical methods for reasoning under uncertainty • Traditional Probability - Rudimentary and unstructured knowledge representation - Assumes all hypotheses are known in advance + Theoretical justified and practically proven method for reasoning under uncertainty ©Kathryn Blackmond Laskey February 2005 - UKy Px2Prp 17 Bayesian Networks • Language for representing knowledge about uncertain phenomena – Multiple hypotheses – Cause and effect relationships between evidence & hypotheses – Time evolution (dynamic Bayesian networks) • Architecture for efficient computation – Apply Bayes rule to incorporate evidence ©Kathryn Blackmond Laskey February 2005 - UKy Px2Prp 18 Probabilistic Knowledge Representation • Bayesian networks are insufficiently expressive for general knowledge representation • Requirements for a probabilistic representation – – – – Represent classes having multiple similar but non-identical instances Represent hierarchical structure of classes Represent relationships between classes Represent different types of uncertainty » » » » » Attribute-value uncertainty Type uncertainty Association uncertainty Existence uncertainty Model uncertainty (structure and parameters) – Learn better representations (structure and parameters) as observations accrue ©Kathryn Blackmond Laskey February 2005 - UKy Px2Prp 19 Emerging Directions in Knowledge Representation • Increasingly expressive languages for encoding probabilistic domain theories • Probabilistic versions of historically successful representation frameworks – Decision theoretic justification for why they work – Extend to incorporate uncertainty – Integrate with legacy systems • Graphical model semantics provides principled theoretical foundation to address key issues – Multi-resolution modeling: High-level summary is (approximate) sufficient statistic for relevant data from low-level sensor data – Distributed M&S: elements pass (approximate) sufficient statistics across communication pathways – Learning uses (approximate) Bayesian inference to refine structure & parameters as data accrue – Probabilistic semantics for model interoperability – Efficient exact and approximate computation ©Kathryn Blackmond Laskey February 2005 - UKy Px2Prp 20 Multi-Entity Bayesian Network (MEBN) Logic • Represent knowledge as collection of partial Bayesian networks – Instantiate & compose into problem-specific models – MEBN is to BN as algebra is to arithmetic • Consistency constraints ensure existence of global probability distribution • Integrates classical first-order logic with probability – Predicates Boolean random variables – Functions Non-Boolean random variables – Existence results » MTheory implicitly represents coherent joint distribution on interpretations of associated first-order theory » Universal MTheory specifies joint distribution on satisfiable first-order sentences & conditional distribution given any consistent finite set of axioms • Provides logical basis for probabilistic databases (Probabilistic Relational Models research @ Stanford) ©Kathryn Blackmond Laskey February 2005 - UKy Px2Prp 21 On the Fly BN Constrution Example ©Kathryn Blackmond Laskey February 2005 - UKy Px2Prp 22 Illustrative Applications • Identify & type groups of vehicles from individual reports – BN construction module takes inputs from (simulated) tracker – Ability to identify and type platoons is robust to » » » » Missed tracks Mis-association between closely spaced vehicles Incorrect vehicle types or inability to type many vehicles Spurious tracks • Information architecture for missile defense – Distributed Bayesian inference, value of information, optimal interceptor allocation – Slated for insertion into ‘06 build • Translation of user requirements into SRS – Proof of concept evaluated on HLA requirements document – Found requirements humans had missed ©Kathryn Blackmond Laskey February 2005 - UKy Px2Prp 23 Summary: Advantages of MEBN Logic • Modular, object-oriented representation – – – – Compose complex probability models from manageable sub-units Implicitly represent consistent domain theory over unbounded number of entities Constructed SSN approximates implicit model MEBN theory provides metrics for estimating quality of approximation • Can balance fidelity to domain against – – – – Knowledge engineering burden Model construction resources Inference resources Learning ability • Probability and decision theory provides unified modeling approach and semantics spanning JDL Levels 0 through 4 • Combines logic & probability • Application experience to date is promising ©Kathryn Blackmond Laskey February 2005 - 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# SYST 201 Systems Modeling I