Judea Pearl University of California Los Angeles CAUSAL REASONING FOR DECISION AIDING SYSTEMS

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.

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

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.

COUNTERFACTUALS: STRUCTURAL SEMANTICS Notation: Y x (u) = y Abbreviation: y x 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. u Y x (u)=y Z W X=x u Y Z W X Probability of Counterfactuals: Functional Bayes Net

TYPES OF QUERIES Inference to four types of claims: 1.Effects of potential interventions, 2.Claims about attribution (responsibility) 3.Claims about direct and indirect effects 4.Claims about explanations

THE OVERRIDING THEME 1. Define Q(M) as a counterfactual expression 2. Determine conditions for the reduction 3. If reduction is feasible, Q is inferable. Demonstrated on three types of queries: Q 1 : P(y|do(x)) Causal Effect (= P(Y x =y) ) Q 2 : P(Y x = y | x, y) Probability of necessity Q 3 : Direct Effect

OUTLINE Review: Causal analysis in COA evaluation Progress report: 1.Model Correctness – J. Pearl 2.Causal Effects – J. Tian 3.Identifications in Linear Systems – C. Brito 4.Actual Causation and Explanations – M. Hopkins 5.Qualitative Planning Under Uncertainty – B. Bonet

CORRECTNESS and CORROBORATION Data D corroborates structure S if S is (i) falsifiable and (ii) compatible with D. Falsifiability: P*(S)  P* Types of constraints: 1. conditional independencies 2. inequalities (for restricted domains) 3. functional Constraints implied by S P*P* P*(S) D (Data) e.g., wxyz

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

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

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

A corroborated structure can imply identifiable yet uncorroborated claims. e.g., a xyzxyz ab xyz FROM CORROBORATING MODELS TO CORROBORATING CLAIMS 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

OUTLINE Review: Causal analysis in COA evaluation Progress report: 1.Model Correctness – J. Pearl 2.Causal Effects – J. Tian 3.Identifications in Linear Systems – C. Brito 4.Actual Causation and Explanations – M. Hopkins 5.Qualitative Planning Under Uncertainty – B. Bonet