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Probabilistic Reasoning System (II)

Probabilistic Reasoning System (II). 박준식, 신사임 2000.4.19. Outline. Introduction Knowledge Engineering for Uncertain Reasoning Knowledge Engineering The Pathfinder system Other Approaches to Uncertain Reasoning Default reasoning Rule-based methods Dempster-Shafer theory

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Probabilistic Reasoning System (II)

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  1. Probabilistic Reasoning System (II) 박준식, 신사임 2000.4.19

  2. Outline • Introduction • Knowledge Engineering for Uncertain Reasoning • Knowledge Engineering • The Pathfinder system • Other Approaches to Uncertain Reasoning • Default reasoning • Rule-based methods • Dempster-Shafer theory • Fuzzy sets and fuzzy logic Probabilistic Reasoning System (II)

  3. Introduction • Probabilistic Reasoning • reach rational decisions even with not enough information • Handling Uncertain Knowledge • uncertainty : ‘probable’, ‘possible’, ‘incomplete’ are attached to domain knowledge and data • Belief nets : subjective probabilities to determine the value of random variables • In this presentation … • knowledge engineering techniques for building probabilistic reasoning system • a survey of alternate approaches Probabilistic Reasoning System (II)

  4. Knowledge Engineering for Uncertain Reasoning

  5. Knowledge Engineering • Knowledge Engineering • process of buliding a KB • Knowledge Engineer • investigate domain : interview the domain expert • determine what concepts are important • create formal representation of objects and relations Probabilistic Reasoning System (II)

  6. Knowledge Engineering (Cont’d) • 5-step methodology • Decide what to talk about • Decide on a vocabulary of predicates, functions,and constants • Encode general knowledge about the domain • Encode a description of the specific problem instance • Pose queries to the inference procedure and get answers Probabilistic Reasoning System (II)

  7. Circuit Verification C1 1 X1 X2 • Q: Is the Circuit an adder ? 1 2 A2 3 A1 O1 2 Probabilistic Reasoning System (II)

  8. 1. Decide what to talk about • Analyze the design of circuits • if circuits match their spec. • Talk about • circuits, terminals, signals, gates and gate types Probabilistic Reasoning System (II)

  9. 2. Decide on a vocabulary • Choose functions, predicates and constants to name “objects” • Ontology of the domain Probabilistic Reasoning System (II)

  10. 3. Encode general rules • few general rules  good ontology 1.If two terminals are connected, then they have the same signal : 2.The signal at every terminal is either on or off (but not both) : 3.Connected is a commutative predicate : … Probabilistic Reasoning System (II)

  11. 4. Encode the specific instance • circuit -> C1 • Type(X1)=XOR Type(X2)=XORType(A1)=AND Type(A2)=ANDType(O1)=OR • Connected(Out(1,X1),In(1,X2))Connected(In(1,C1),In(1,X1))Connected(Out(1,X1),In(2,A2))Connected(Out(1,C1),In(1,A1))… Probabilistic Reasoning System (II)

  12. 5. Pose queries to the inference procedure • I/O table  check if it adds input correctly Query : What are the possible sets of values of all the terminals ? Probabilistic Reasoning System (II)

  13. Knowledge Engineering for Uncertain Reasoning Successful real-world Implementation Theoretical understandingof Belief Network • Primary challenges for belief network to represent a real-world system • Approach to analyze the problem domain • Model-based approaches : guide to problem-solving process and underlying domain knowledge • Tools and approaches to Implementations Probabilistic Reasoning System (II)

  14. Primary Challenges Unknown bug incompiler First use of Programming Language Unexpectedcompiler error Error in Code Probabilistic Reasoning System (II)

  15. Primary Challenges (1) • Deciding what to talk about • Which factors should be modeled ? • Which factors should be summarized by prob. statements ? • Look at inter-relationships between factors • ex) decide to model the factors • bug in compiler, errors in code Probabilistic Reasoning System (II)

  16. Primary Challenges (2) • Deciding on a vocabulary of random variables • how to represent those factors from a notational point of view • ex) use of ‘unknown bug in compiler’, ‘unexpected compiler error’each of modeled component : Boolean Probabilistic Reasoning System (II)

  17. Primary Challenges (3) • Encoding general knowledge about the dependence between variables • quality and quantity perspective • ex) ‘error in code’ is dependent on ‘first use of programming language’conditional probability table Probabilistic Reasoning System (II)

  18. Primary Challenges (4) • Encoding a description of the specific problem instance • ex) set the state values of ‘beta release of compiler’ • Posing queries to the inference procedure and getting answers • ex) queried on the prob. that ‘unexpected compiler error’ is T, and return the correct value Probabilistic Reasoning System (II)

  19. Tools and approaches to Implementations • Tools • IDEAL • Influence Diagram and Evaluation in Lisp • Microsoft Belief Net • GUI network builder • Netica • Belief Networks and Influence Diagrams • Belief • Graphical Belief Function Models in Lisp Probabilistic Reasoning System (II)

  20. Tools and approaches to Implementations (Cont’d) • Approaches • problem domain is analyzed and the belief network is implemented • expert assistant • belief network’s performance is tested • against specific problem instance • ensure modeling is reliable • refine the belief network implementation and start again • after use and the identification of obvious shortfalls in design Probabilistic Reasoning System (II)

  21. The Pathfinder system • Diagnostic ES for lymph-node diseases (Stanford Medical Computer Science) Probabilistic Reasoning System (II)

  22. Other approaches to Uncertain Reasoning

  23. Other approaches to Uncertain Reasoning • Default Reasoning : • numerical nature of probability theory vs. qualitative nature of human reasoning • Rule Based : • success of logical rule-based system, but with an added “fudge factor” • Dempster-Shafer Theory : • the question of ignorance as opposed to uncertainty • Fuzzy logic : • probability and logic make the same ontological commitment to truth and falsity Probabilistic Reasoning System (II)

  24. Default Reasoning • Qualitative Reasoning • default conclusion is assumed unless evidence is found to believe something else • likened to “jumping to conclusions” • Default Reasoning • simulate the qualitative nature of human reasoning • ex) You conclude by default that your blood is red, unless you cut yourself and it turns out to be green. • nonmonotonicity • previous beliefs can be doubted • retraction of beliefs • if evidence is found to believe something other than the default conclusion Probabilistic Reasoning System (II)

  25. Default Reasoning Issues • semantic status of default rules • evidence matching default premises with conflicting conclusions • keeping track of retractions • dependencies between conclusions and beliefs • truth maintenance systems • the strength of beliefs based on default premises in various contexts Probabilistic Reasoning System (II)

  26. Logical systems vs. Probability system Probabilistic Reasoning System (II)

  27. Rule-Based Methods • Rule-Based Methods • Tradition rule-based systems + Fudge factor • Fudge factor • Assigning a degree of belief to proposition Probabilistic Reasoning System (II)

  28. Restrictions • Inappropriate for uncertain reasoning Ex) Wet-grass situation (Section 15.4) Sprinkler Wet Grass Unavoidable!! Rain Probabilistic Reasoning System (II)

  29. To build a useful System.. • Controlling types of tasks • Careful engineering • Undesirable interactions between rules • Ex) Certainty factor models Probabilistic Reasoning System (II)

  30. Certainty factors model • Truth-functional system for uncertain reasoning • Certainty factor • Numbers ranging from -1.00 to +1.00 • Quantative impression of the probability of correctness • -1 : false +1 : true Probabilistic Reasoning System (II)

  31. MYCIN • Most famous certainty factor model • Ted Shortliffe (1970s) • Function • Identifying bacterial infections • Advises on the course of treatment • Performance • As well as faculty Probabilistic Reasoning System (II)

  32. Dempster-Shafer theory • Addresses the distinction between uncertainty and ignorance • Uncertainty • Expression in incomplete and incorrectness • Ignorance = Belief + Disbelief • Belief : Sum of probability of assignment for all sets • Disbelief : Complement of belief set • Probability of interval : Dealing with both • Bel (X) • Belief function • Computing supporting probability in proposition Probabilistic Reasoning System (II)

  33. Belief function : Example • Tossing a coin • Case of ignorance • No evidence of fairness of coin Bel (Heads) = 0 Bel (Tail) = 0 • Case of uncertainty • Assurance of fairness : 90% Bel (Heads) = 0.9 * 0.5 = 0.45 Bel (Tails) = 0.9 * 0.5 = 0.45 Probabilistic Reasoning System (II)

  34. Probability interval • Difference between belief and disbelief • Larger interval  More evidences • Coin Toss With Probability Interval • Case of ignorance : [0,1] • Assurance of fairness : 90% : [0.45, 0.55] Probabilistic Reasoning System (II)

  35. An illustration of probability interval Plausibitity Doubt 0 1 Belief Uncertainty Disbelief Probabilistic Reasoning System (II)

  36. Restrictions • Badly defined semantics of Bel(X) • Ex) Coin Toss with no evidence • No evidence results inBel (Heads) = 0Bel (Tails) = 0 • No way to decide : Heads or Tails Probabilistic Reasoning System (II)

  37. Fuzzy theory • Fuzzy : Vague expressions • Ex) Jane is old. • Fuzzy theory • 불확실한 상태를 그대로 표현하는 방법 • 인간이 사용하는 애매한 표현을 처리하는 이론적 바탕 제공 • Ex) 내일 비가 올 확률이 매우 많다. • cf) 내일 비가 올 확률이 70%이다. Probabilistic Reasoning System (II)

  38. Fuzzy Set • Mathematic expression of vague expression • Ex) “두어” = {(2,1.0),(3,0.5)} “2 또는 3” = {(2,1.0),(3,1.0)} Probabilistic Reasoning System (II)

  39. Fuzzy logic • 복잡한 문장의 진리값을 구성원소들의 진리값을 이용하여 결정 • rule을 이용 • Truth –functional system • Rules for evaluating • T(A∧B) = MIN(T(A),T(B)) • T(A∨B) = MAX(T(A),T(B)) • T(!A) = 1 – T(A) Probabilistic Reasoning System (II)

  40. Addition with fuzzy set 포함가능성 1.0 1.0 0.5 0.5 숫자 2 3 2 3 {(2,1.0),(3,0.5)} {(2,1.0),(3,0.5)} 1.0 0.5 4 5 6 {(4,1.0),(5,0.5),(6,0.5)} ‘두어’+’두어’ Probabilistic Reasoning System (II)

  41. Fuzzy expert system • Small rule base • No chaining of inferences is allowed (Rule sets singly connected) • Tunable parameters are included to improve performance for a particular application Probabilistic Reasoning System (II)

  42. 응용 제어 방법론 로봇 클러스터링 지식공학 확장원리 퍼지명제 진리값의 언어항 (소속정도) (진리값) 영상처리 퍼지관계 퍼지 집합 이론 퍼지 이론 퍼지알고리즘 패턴인식 퍼지컴퓨터 추론 퍼지숫자 언어변수 퍼지 척도론 전문가 시스템 통계학 퍼지최적화 퍼지적분 퍼지척도 가능성척도 의사결정 데이터 처리 확률척도 예측 평가 퍼지이론의 응용 Probabilistic Reasoning System (II)

  43. Web References • Hybrid Logic Paper Abstracts http://iridia.ulb.ac.be/saffiotti/abstracts.html • Bayesian Belief Nets - general interest http://www.cs.ualberta.ca/~greiner/bn.html • Belief - development tool http://www.cs.cmu.edu/afs/cs/project/ai-repository/ai/areas/reasonng/probabl/belief/0.html • IDEAL - development tool http://www.rpal.rockwell.com/ideal.html • MS Research Decision Theory and Adaptive Systems Group http://research.microsoft.com/dtas/ • Norsys’ Netica - development tool http://www.norsys.com/networklibrary.html • The KADS-II Project Description http://swi.psy.uva.nl/projects/CommonKADS/description/root.html • Fuzzy shower demo http://ai.iit.nrc.ca/fuzzy/shower/title.html Probabilistic Reasoning System (II)

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