Cognitive Maps and Bayesian Networks Emel Aktaş

Outline Cognitive Maps Influence Diagrams Bayesian Networks

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

Taxonomy of Network Based Representation Schemes

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

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

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

Causal Maps

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

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

Representation Short pieces of text Unidirectional arrows cause

Merging Decision of a College

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

Structural properties

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

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

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

Representation Graph See the causal relationships better Matrix Mathematical analysis

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

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

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

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

Determination of the causal relationships Square matrix including all concepts Pairwise comparisons mtv.sal.env.emp.col.car. mtv sal env emp col car

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

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 +

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

Hierarchical Clusters

Potent Options

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

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

Definition of customer service 32

Centrality 33

First Cluster 34

Second Cluster 35

Influence Diagrams

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

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

ID of a Plan for Vacation

Decisions about the Marketing Budget and Product Price

Bayesian Networks

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

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

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

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)

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

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)

Example: Product Development

Bayesian Network Structure

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.

Knowledge Inference Bayesian network is constructed Conditional probabilities are defined. It is possible to infer knowledge now using specific software. Hugin ( Netica (

Knowledge Inference

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.

Framework

Variables of the System

Preliminary Causal Map

Revised Causal Map

Discretization of the Variables

Final Causal Map

Compiled Bayesian Network

Additional Knowledge: Type of Scrutiny Known

The case where type of scrutiny and medicine treatment is known

Target values for the parent variables of time spent for scrutiny

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

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