Judea Pearl University of California Los Angeles cs.ucla/~judea

1. Judea Pearl University of California Los Angeles http://www.cs.ucla.edu/~judea CAUSAL REASONING FOR DECISION AIDING SYSTEMS

2. PROBLEM STATEMENT • Coherent fusion of information for situation assessment and COA evaluation under uncertainty. • Friendly language for inputting new information and answering mission-related queries.

3. FLEXIBLE QUERIES AND ANSWERS • What does it (new  evidence) mean? • It means that you  can no longer expect to accomplish task A in two hours, unless you ensure that B does not happen. • How come it took me six hours? • It was probably due to the heavy rains. Thus, it would have been better to use unit-201, instead of unit-200.

4. REQUIREMENTS FOR FLEXIBLE QUERIES • Understanding of causal relationships in the domain. • Causal Interpretation of new evidence. • Interpretation of causal queries. • Automatic generation of explanations, using causal and counterfactual relationships.

5. COUNTERFACTUALS: STRUCTURAL SEMANTICS u u W W Z X X=x Z Y Yx(u)=y Notation: Yx(u) = yAbbreviation:yx Formal:Y has the value y in the solution to a mutilated system of equations, where the equation for X is replaced by a constant X=x. Functional Bayes Net Probability of Counterfactuals:

6. TYPES OF QUERIES • Inference to four types of claims: • Effects of potential interventions, • Claims about attribution (responsibility) • Claims about direct and indirect effects • Claims about explanations

7. THE OVERRIDING THEME • Define Q(M) as a counterfactual expression • Determine conditions for the reduction • If reduction is feasible, Q is inferable. • Demonstrated on three types of queries: Q1: P(y|do(x)) Causal Effect (= P(Yx=y)) Q2: P(Yx = y | x, y) Probability of necessity Q3: Direct Effect

8. OUTLINE • Review: • Causal analysis in COA evaluation • Progress report: • Model Correctness – J. Pearl • Causal Effects – J. Tian • Identifications in Linear Systems – C. Brito • Actual Causation and Explanations – M. Hopkins • Qualitative Planning Under Uncertainty – B. Bonet

9. w x y z CORRECTNESS and CORROBORATION P* P*(S) Falsifiability: P*(S) P* D (Data) Constraints implied by S Data Dcorroborates structure S if S is (i) falsifiable and (ii) compatible with D. Types of constraints:1. conditional independencies2. inequalities (for restricted domains)3. functional e.g.,

10. FROM CORROBORATING MODELS TO CORROBORATING CLAIMS A corroborated structure can imply identifiable yet uncorroborated claims. e.g., x x y y a

11. FROM CORROBORATING MODELS TO CORROBORATING CLAIMS A corroborated structure can imply identifiable yet uncorroborated claims. e.g., x x y y a = 0

12. x y z a b Some claims can be more corroborated than others. FROM CORROBORATING MODELS TO CORROBORATING CLAIMS A corroborated structure can imply identifiable yet uncorroborated claims. e.g., x x y y z a

13. x y z a b Some claims can be more corroborated than others. FROM CORROBORATING MODELS TO CORROBORATING CLAIMS A corroborated structure can imply identifiable yet uncorroborated claims. e.g., x x y y z a

14. x y z a b Some claims can be more corroborated than others. FROM CORROBORATING MODELS TO CORROBORATING CLAIMS A corroborated structure can imply identifiable yet uncorroborated claims. e.g., x x y y z a Definition: An identifiable claim C is corroborated by data if some minimal set of assumptions in S sufficient for identifying C is corroborated by the data. Graphical criterion: minimal substructure = maximal supergraph

15. FROM CORROBORATING MODELS TO CORROBORATING CLAIMS A corroborated structure can imply identifiable yet uncorroborated claims. e.g., x x y y z z x y z a a b Some claims can be more corroborated than others. Definition: An identifiable claim C is corroborated by data if some minimal set of assumptions in S sufficient for identifying C is corroborated by the data. Graphical criterion: minimal substructure = maximal supergraph

16. OUTLINE • Review: • Causal analysis in COA evaluation • Progress report: • Model Correctness – J. Pearl • Causal Effects – J. Tian • Identifications in Linear Systems – C. Brito • Actual Causation and Explanations – M. Hopkins • Qualitative Planning Under Uncertainty – B. Bonet