1. Cognitive Maps and Bayesian Networks Emel Aktaş

2. Outline Cognitive Maps Influence Diagrams Bayesian Networks

3. Motivation for Graphical Models Systematic construction methods Efficient inference procedures Explicit encoding of independencies Modular representation of probabilities

4. Taxonomy of Network Based Representation Schemes

5. Introduction Person’s thinking about a problem or issue Tolman (1948) Cognition Various fields: Psychology Planning Geography Management

6. Some Definitions Cause-effect networks Srinivas and Shekar (1997) Graphical descriptions Axelrod (1976); Eden (1990)

7. Usage Knowledge / belief representation Capturing causality Network-based formalisms Cognitive Maps (Axelrod, 1976) Belief Networks (Pearl, 1988) Qualitative Probabilistic Networks (Wellman, 1990)

8. Causal Maps

9. Causal map Network representation of beliefs Nodes and arcs Directed graph Harary et al. (1965); Harary (1972) Ideas and actions Visible thinking

10. Mapping Documentary coding Interviews Subjective world of the interviewee Questionnaire survey Groups Personal construct theory Kelly (1955)

11. Representation Short pieces of text Unidirectional arrows cause

12. Merging Decision of a College

13. Heads and tails Incoming or outgoing arrows Negative relationships  minus sign Signed directed graph Head: no outgoing arrows; goals / outcomes Tail: no incoming arrows; options Centrality

14. Structural properties

15. Example (Ulengin, Topcu, Onsel, 2001) Contribution to social improvement Damage on the inhabitants of the surrounding area by crossing Damage to the historical texture of the region Cost of nationalization Possibility of increasing employment through creating jobs - Construction time Facility in constructing (the topographic structure of the crossing area and the surrounding land, etc) Suitability for urban, regional and national progress plans - Suitability for the transportation policy - Financial damage in case of accidents during operation head central

16. Problem/issue complexity Cognitive scientists /organizational scientists Central features total number of nodes total number of arrows cognitive centrality of particular nodes Ratio of arrows to concepts 1.15 to 1.20 for maps elicited from interviews

17. The extent of the map More nodes  more complex Mutual understanding of the issue Number of concepts length of the interview skills of the interviewer

18. Representation Graph See the causal relationships better Matrix Mathematical analysis

19. Example: How can we motivate employees? Variables Motivation Salaries Problems in the work environment Good attitude of the employer Good attitude of the colleagues Carreer possibilities

20. positive (+) salary + motivation Causal relationships between the variables

21. positive (+) salary + motivation negative (-) Problems in the work environment - motivation Causal relationships between the variables

22. positive (+) salary + motivation negative (-) Problems in the work environment - motivation No relationship (0) attitude of colleagues 0 salary Causal relationships between the variables

23. Determination of the causal relationships Square matrix including all concepts Pairwise comparisons mtv.sal.env.emp.col.car. mtv.000000 sal.+00000 env.-00000 emp.+0-00+ col.+00000 car.+00000

24. How can we motivate employees? mtv. sal. env. + emp. + - col. + car. + +

25. Causal Map of a Cement Producer 25 Economic setback Investments on infrastructure, residential and non- residential buildings Development of construction industry Environmental concerns Pressure on environmental issues Application of Kyoto Protocol Compe tition Regulations Demand – supply balance Input costs Capacity usage Profitability Cement demand Restructuring of big players Consolidation and vertical integration + + + + + + - + + - - - + + + + + - - + + Decreasing energy supply +

26. Islands of themes without accounting for hierarchy Nodes in each cluster  tightly linked Bridges with other clusters  minimized Cluster Analysis 26

27. Hierarchical Clusters

28. Potent Options

29. Construction of the Group Cognitive Map Gather related concepts from different persons Prepare a collective list of concepts Persons’ pairwise comparisons Construct of personal cognitive maps Aggregate personal cognitive maps Single number of experts Taking experts’ opinions again about the doubtful relations Size Over 100 nodes on the map

30. 30

31. The most fundamental decisions are Definition of customer service (1) Forecasts of demand (8) Product routing (14) Information to be provided with the product (32) The rest of the decisions cannot be taken unless these 4 decisions are given Hierarchy of decisions 31

32. Definition of customer service 32

33. Centrality 33

34. First Cluster 34

35. Second Cluster 35

36. Influence Diagrams

37. Compact graphical /mathematical representation of a decision situation It is a generalization of a Bayesian network, probabilistic inference problems decision making problems Influence Diagrams 37

38. Nodes Decision node [rectangle] Uncertainty node [oval] Deterministic node [double oval] Value node [diamond] Arcs Functional arcs (ending in value node) Conditional arcs (ending in uncertainty / deterministic node) Informational arcs (ending in decision node) Influence Diagrams 38

39. ID of a Plan for Vacation http://en.wikipedia.org/wiki/Influence_diagram

40. Decisions about the Marketing Budget and Product Price http://www.lumina.com/software/influencediagrams.html

41. Bayesian Networks

42. Probabilistic graphical model Variables Probabilistic dependencies Uncertain, ambiguous, and/or incomplete domains Directed acyclic graphs

43. Bayesian Network Structure A Bayesian Network has 3 components: X, S and P; X= {X1; X2;…; Xn} variables S: causal structure P: conditional probabilities

44. Bayesian Network Structure Rearrangement of the causal map Acyclic (no loops allowed) Direct and indirect relationships

45. Bayesian Network Structure F is dependent on C and D A and B: root nodes F and G: leaves P(A,B,C,D,E,F,G)=P(G/D) P(F/C,D) P(E/B) P(D/A,B) P(C/A) P(A) P(B)

46. Bayesian Network Steps 1. Specification of the variables 2. Specification of the network structure 3. Determination of the conditional probabilities 4. Acquisition of additional knowledge 5. Inference based on knowledge 6. Interpretation of the results

47. Example: Product Development 4 variables Market Dynamics Product Life Cycle Market Leadership Rate of Product Launch Dependence relations should be defined as conditional probabilities. Nadkarni and Shenoy (2001)

48. Example: Product Development

49. Bayesian Network Structure

50. P(D,C,L,R)=P(D)*P(C/D)*P(L)*P(R/C,L) Two variables are conditionally independent if there is no arrow relating them No arrow between D and L  L is independent on D.

51. Knowledge Inference Bayesian network is constructed Conditional probabilities are defined. It is possible to infer knowledge now using specific software. Hugin (www.hugin.com)www.hugin.com Netica (www.norsys.com)www.norsys.com

52. Knowledge Inference

54. A cognitive map – bayesian network application Domain: tomography section within the radiology department of a private hospital in Turkey, Objective: improve management system performance The hospital operates 42 branches, including clinical research, diagnostics, and outpatient and inpatient care, with 279 expert physicians and 1038 healthcare and support staff. A total of 36,000 radiological tests are conducted per annum.

55. Framework

56. Variables of the System

57. Preliminary Causal Map

58. Revised Causal Map

59. Discretization of the Variables

60. Final Causal Map

61. Compiled Bayesian Network

62. Additional Knowledge: Type of Scrutiny Known

63. The case where type of scrutiny and medicine treatment is known

64. Target values for the parent variables of time spent for scrutiny

65. Sensitivity of ‘‘time spent for scrutiny’’ based on findings at another node

66. References Axelrod, R., 1976. Structure of Decision. University of Princeton Press, Princeton. Eden, C., 1988. Cognitive mapping: A review. European Journal of Operational Research 36, 1-13. Harary, F., Norman, R., Cartwright, D., 1965. Structural Models: An Introduction to the Theory of Directed Graphs. Wiley, New York. Harary, F., 1972. Graph Theory. Addison-Wesley, Reading. Pearl, J., 1988. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Mateo, CA. Nadkarni S., Shenoy, P., 2001. A Bayesian network approach to making inferences in causal maps, European Journal of Operational Research 128(3),479-498. Srinivas V., Shekar B., 1997. Applications of uncertainty-based mental models in organizational learning: A case study in the Indian automobile industry. Accounting, Management and Information Technologies, 7(2), 87-112. Tolman E. C., 1948. Cognitive Maps in Rats and Man. Psychological Review 55: 189-208. Wellman M.P., 1990. Fundamental Concepts of Qualitative Probabilistic Networks. Artificial Intelligence, 44(3):257–303.