Judea Pearl

1
CAUSAL REASONING FOR DECISION AIDING SYSTEMS

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

2
OUTLINE

• Decision aiding systems and the need for
• flexible query language
• Causal analysis in COA evaluation
• Progress and planned research toward solving
• three basic problems
• Deciding attribution
• Detecting actual causes
• Generating explanations

3
PROBLEM STATEMENT

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

4
NEEDED HIGH-LEVEL QUERY LANGUAGE

• Rigid queries
• Evaluate the probability--of--success of a
  given COA.
• Rank COA's on expected-utility scale
• Problems
• Global evaluation of entire COA
• Advance listing of options and eventualities
• Needed
• Local analysis of impact and tradeoffs of each
• constituent decision-condition-event.

5
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.

6
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.

7
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.

8
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.

9
RESEARCH QUESTIONS

• How the effects of unanticipated actions can be
  predicted from causal models
• How qualitative causal judgments can be
  integrated with statistical data
• How actions interact with observations
• How counterfactuals sentences can be interpreted
  and evaluated
• How explanations and single-event causation can
  be defined in a given causal model

10
QUESTIONS ANSWERED (1994-1998)

• Axiomatic characterization of causal
  dependencies, analogous to the characterization
  of informational dependencies.
• Formal theory and axiomatic characterization of
  actions and observations, using SEM.
• Network-based identification techniques, in the
  presence of unobserved variables, permitting the
  evaluation of actions from passive observations.

11
RESEARCH QUESTIONS REMAINING

• How the effects of unanticipated actions can be
  predicted from causal models
• How qualitative causal judgments can be
  integrated with statistical data
• How actions interact with observations
• How counterfactuals sentences can be interpreted
  and evaluated
• How explanations and single-event causation can
  be defined in a given causal model

12
WHY COUNTERFACTUALS?
Ans.  To formalize 3 basic relations 

• The probability PN that an event is necessary to
  sustain another event and
• The probability PS that an event is sufficient to
  produce another event
• The probability PC that one event was an actual
  cause of another event, in the course of a given
  scenario.
• e.g.,
• Action A in a COA was the actual cause of
  success. It was necessary for sustaining
  condition C, which, in turn, is sufficient for
  producing a desirable effect E.

13
PROGRESS ON LAST TWO QUESTIONS

• Graphical methods and symbolic calculus for
  computing (or bounding) probabilities of
  counterfactuals from partially specified models.
• e.g., Given that action A failed, you would have
  had 30-50 chance  of success had you taken
  action B.
• Applying these methods to questions involving
• Attribution  (e.g., due to)
• Actual causation and explanation (e.g. why?)

14
PROGRESS ON LAST TWO QUESTIONS

• Graphical methods and symbolic calculus for
  computing (or bounding) probabilities of
  counterfactuals from partially specified models.
• e.g., Given that action A failed, you would have
  had 30-50 chance  of success, if that boat had
  not sunk.
• Applying these methods to questions involving
• Attribution  (e.g., due to)
• Actual causation and explanation (e.g. why?)

15
THE PROBLEM OF ATTRIBUTION

• Theoretical Problems
• What is the meaning of PN(x,y) Probability
• that event y would not have occurred if it were
• not for event x, given that x and y did in fact
• occur.
• Under what conditions can PN(x,y) be learned
• from statistical data,
• i.e., observational, experimental, and combined.
• Practical Problems
• Responsibility Was the action responsible
• for the effect?
• Contingent Decisions Will an action succeed,
• given case-specific evidence?

16
THE BASIC PRINCIPLES
Causation encoding of behavior
under interventions Interventions surgeries
on mechanisms Mechanisms
stable functional relationships
equations graphs
17
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
18
3-STEPS TO COMPUTING COUNTERFACTUALS
S5. If the prisoner is dead, he would still be
dead if A were not to have shot. D?D?A
Abduction
Action
Prediction
U
TRUE
C
B
A
D
19
COMPUTING PROBABILITIES OF COUNTERFACTUALS
P(S5). The prisoner is dead. How likely is it
that he would be dead if A were not to have
shot. P(D?AD) ?
Abduction
Action
Prediction
U
C
B
A
D
20
THE SEMANTICS OF NECESSARY AND SUFFICIENT CAUSES
Necessary Cause Event x was a necessary cause of
event y if the probability PNP(y?x?x,y) is
HIGH Read P(Yfalse had Xfalse Xtrue,
Ytrue) Sufficient Cause Event x is a
sufficient cause of event y if the
probability PSP(yxx?,y?) is HIGH Necessary
and Sufficient Cause Event x is a
necessary-and-sufficient cause of event y if the
probability PNSP(yx,y?x?) is HIGH
21
THE ATTRIBUTION PROBLEM (Example)

• Your Honor! My client (Mr. A) died BECAUSE
• of the drug.
• Court to decide if it is MORE PROBABLE THAN
• NOT that A would be alive BUT FOR the drug!
• P(y?x?x,y) gt 0.50?

22
SOLUTION TO THE ATTRIBUTION PROBLEM
Find PNP(drug x was the cause of Mr. As
death) Defendant Plaintiff Mr. A is
not a typical subject, he chose the Drug
(x), and died (y). Jury
Experimental Nonexperimental
do(x) do(x?) x x? Deaths (y)
16 14 2 28 Survival (y?)
984 986 998 972 1000 1000 1000
1000
23
SOLUTION TO THE ATTRIBUTION PROBLEM (Cont)

• WITH PROBABILITY ONE P(y?x?x,y) 1
• From population data to individual case
• Combined data tell more that each study alone

24
SUMMARY (ATTRIBUTION)

• Formal semantics for the probability of necessary
  causation (PN) and sufficient causation (PS)
• Conditions for learning (and bounding) PN and PS
  from data
• Method of combining experimental and
  nonexperimental data to yield inferences that
  neigher one alone would support

25
ACTUAL CAUSATION AND THE COUNTERFACTUAL TEST
"We may define a cause to be an object followed
by another,..., where, if the first object had
not been, the second never had existed."
Hume, Enquiry, 1748 Lewis (1973) "x
CAUSED y " if x and y are true, and
y is false in the closest non-x-world. Structural
interpretation (i) X(u)x (ii) Y(u)y (iii)
Yx ?(u) ? y for x ? ? x
26
PROBLEMS WITH THE COUNTERFACTUAL TEST
1. NECESSITY Ignores aspects of sufficiency
(Production) Fails in presence of other causes
(Overdetermination) 2. COARSENESS Ignores
structure of intervening mechanisms. Fails when
other causes are preempted (Preemption) SOLUTION
Supplement counterfactual test with Sustenance
27
NUANCES IN CAUSAL TALK
y depends on x (in u) X(u)x, Y(u)y, Yx?
(u)y? x can produce y (in u) X(u)x?, Y(u)y?,
Yx (u)y x sustains y relative to W X(u)x,
Y(u)y, Yx w (u)y, Yx? w? (u)y?
28
NUANCES IN CAUSAL TALK
x caused y, necessary for, responsible for, y
due to x, y attributed to x.
y depends on x (in u) X(u)x, Y(u)y, Yx?
(u)y? x can produce y (in u) X(u)x?, Y(u)y?,
Yx (u)y x sustains y relative to W X(u)x,
Y(u)y, Yxw (u)y, Yx?w? (u)y?
29
NUANCES IN CAUSAL TALK
y depends on x (in u) X(u)x, Y(u)y, Yx?
(u)y? x can produce y (in u) X(u)x?, Y(u)y?,
Yx (u)y x sustains y relative to W X(u)x,
Y(u)y, Yxw (u)y, Yx?w? (u)y?
x causes y, sufficient for, enables, triggers,
brings about, activates, responds
to, susceptible to.
30
NUANCES IN CAUSAL TALK
maintain, protect, uphold, keep up, back
up, prolong, support, rests on.
y depends on x (in u) X(u)x, Y(u)y, Yx?
(u)y? x can produce y (in u) X(u)x?, Y(u)y?,
Yx (u)y x sustains y relative to W X(u)x,
Y(u)y, Yxw (u)y, Yx? w? (u)y?
31
CAUSAL BEAM Locally sustaining sub-process
ACTUAL CAUSATION x is an actual cause of y in
scenario u, if x passes the following test
1. Construct a new model Beam(u, w ?) 1.1 In
each family, retain a subset of parents that
minimally sustains the child 1.2 Set the
other parents to some value w ? 2. Test if x
is necessary for y in Beam(u, w ?) for some w ?
32
THE DESERT TRAVELER (After Pat Suppes)
X
P
Enemy-2 Shoots canteen
Enemy -1 Poisons water
dehydration D
C cyanide intake
Y death
33
THE DESERT TRAVELER (The actual scenario)
Enemy-2 Shoots canteen
Enemy -1 Poisons water
dehydration D
C cyanide intake
Y death
34
THE DESERT TRAVELER (Constructing a causal beam)
Enemy-2 Shoots canteen
Enemy -1 Poisons water
? X ? P
dehydration D
C cyanide intake
Y death
35
THE DESERT TRAVELER (Constructing a causal beam)
Enemy-2 Shoots canteen
Enemy -1 Poisons water
C ? X
dehydration D
C cyanide intake
y death
36
THE DESERT TRAVELER (Constructing a causal beam)
Enemy-2 Shoots canteen
Enemy -1 Poisons water
C ? X
dehydration D
C cyanide intake
D ? C
y death
37
THE DESERT TRAVELER (The final beam)
Enemy-2 Shoots canteen
Enemy -1 Poisons water
C ? X
dehydration D
C cyanide intake
YD
YX
y death
38
FUTURE WORK
Attribution Actual Cause Explanation