Title: Judea Pearl
1CAUSAL REASONING FOR DECISION AIDING SYSTEMS
- Judea Pearl
- University of California
- Los Angeles
- http//www.cs.ucla.edu/judea
2PROBLEM STATEMENT
- Coherent fusion of information for situation
assessment and COA evaluation under uncertainty. - Friendly language for inputting new information
and answering mission-related queries.
3FLEXIBLE 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.
4REQUIREMENTS 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.
5COUNTERFACTUALS STRUCTURAL SEMANTICS
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 Xx.
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(ydo(x)) Causal Effect ( P(Yxy)) Q2
P(Yx? y x, y) Probability of necessity Q3
Direct Effect
8OUTLINE
- 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
9CORRECTNESS 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 constraints1. conditional
independencies2. inequalities (for restricted
domains)3. functional
e.g.,
10FROM CORROBORATING MODELS TO CORROBORATING CLAIMS
A corroborated structure can imply identifiable
yet uncorroborated claims.
e.g.,
x
y
x
y
a
11FROM CORROBORATING MODELS TO CORROBORATING CLAIMS
A corroborated structure can imply identifiable
yet uncorroborated claims.
e.g.,
x
y
x
y
a 0
12FROM CORROBORATING MODELS TO CORROBORATING CLAIMS
A corroborated structure can imply identifiable
yet uncorroborated claims.
e.g.,
x
y
z
x
y
a
13FROM CORROBORATING MODELS TO CORROBORATING CLAIMS
A corroborated structure can imply identifiable
yet uncorroborated claims.
e.g.,
x
y
z
x
y
a
14FROM CORROBORATING MODELS TO CORROBORATING CLAIMS
A corroborated structure can imply identifiable
yet uncorroborated claims.
e.g.,
x
y
z
x
y
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
15FROM CORROBORATING MODELS TO CORROBORATING CLAIMS
A corroborated structure can imply identifiable
yet uncorroborated claims.
e.g.,
x
y
z
x
y
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
16OUTLINE
- 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