CAUSAL REASONING FOR DECISION AIDING SYSTEMS Judea Pearl University of California Los Angeles http://www.cs.ucla.edu/~judea The subject of my lecture this evening is CAUSALITY. It is not an easy topic to speak about, but it is a fun topic to speak about. It is not easy because, like religion, sex and intelligence, causality was meant to be practiced, not analyzed. And it is fun, because, like religion, sex and intelligence, emotions run high, examples are plenty, there are plenty of interesting people to talk to, and above all, an exhilarating experience of watching our private thoughts magnified under the microscope of formal analysis.

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 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.

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

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

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

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

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

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

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

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

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

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

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

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