Judea Pearl

1
CAUSAL REASONING FOR DECISION AIDING SYSTEMS

• Judea Pearl
• University of California
• Los Angeles
• http//www.cs.ucla.edu/judea

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.

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COUNTERFACTUALS 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
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TYPES OF QUERIES

• Inference to four types of claims

1. Effects of potential interventions,

1. Claims about attribution (responsibility)

1. Claims about direct and indirect effects

1. Claims about explanations

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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
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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

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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 constraints1. conditional
independencies2. inequalities (for restricted
domains)3. functional
e.g.,
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FROM CORROBORATING MODELS TO CORROBORATING CLAIMS
A corroborated structure can imply identifiable
yet uncorroborated claims.
e.g.,
x
y
x
y
a
11
FROM CORROBORATING MODELS TO CORROBORATING CLAIMS
A corroborated structure can imply identifiable
yet uncorroborated claims.
e.g.,
x
y
x
y
a 0
12
FROM CORROBORATING MODELS TO CORROBORATING CLAIMS
A corroborated structure can imply identifiable
yet uncorroborated claims.
e.g.,
x
y
z
x
y
a
13
FROM CORROBORATING MODELS TO CORROBORATING CLAIMS
A corroborated structure can imply identifiable
yet uncorroborated claims.
e.g.,
x
y
z
x
y
a
14
FROM 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
15
FROM 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
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