causal reasoning for decision aiding systems cognitive systems laboratory ucla
DESCRIPTION
CAUSAL REASONING FOR DECISION AIDING SYSTEMS COGNITIVE SYSTEMS LABORATORY UCLA Judea Pearl, Mark Hopkins, Blai Bonet, Chen Avin, Ilya Shpitser. PRESENTATIONS. Judea Pearl Robustness of Causal Claims Ilya Shpitser and Chen Avin Experimental Testability of Counterfactuals Blai Bonet - PowerPoint PPT PresentationTRANSCRIPT
CAUSAL REASONING FOR DECISION AIDING SYSTEMS
COGNITIVE SYSTEMS LABORATORYUCLA
Judea Pearl, Mark Hopkins, Blai Bonet,Chen Avin, Ilya Shpitser
Judea Pearl Robustness of Causal Claims
Ilya Shpitser and Chen AvinExperimental Testability of Counterfactuals
Blai BonetLogic-based Inference on Bayes Networks
Mark HopkinsInference using Instantiations
Chen AvinInference in Sensor Networks
Blai BonetReport from Probabilistic Planning Competition
PRESENTATIONS
FROM STATISTICAL TO CAUSAL ANALYSIS:1. THE DIFFERENCES
Datajoint
distribution
inferencesfrom passiveobservations
Probability and statistics deal with static relations
ProbabilityStatistics
CausalModel
Data
Causalassumptions
1. Effects of interventions
2. Causes of effects
3. Explanations
Causal analysis deals with changes (dynamics)
Experiments
Z
YX
INPUT OUTPUT
TYPICAL CAUSAL MODEL
TYPICAL CLAIMS
1. Effects of potential interventions,
2. Claims about attribution (responsibility)
3. Claims about direct and indirect effects
4. Claims about explanations
ROBUSTNESS:MOTIVATION
The effect of smoking on cancer is, in general, non-identifiable (from observational studies).
Smoking
x y
Genetic Factors (unobserved)
Cancer
u
In linear systems: y = x + is non-identifiable.
ROBUSTNESS:MOTIVATION
Z – Instrumental variable; cov(z,u) = 0
Smoking
y
Genetic Factors (unobserved)
Cancer
u
x
ZPrice ofCigarettes
xz
yz
xz
yzR
R
R
R
is identifiable
ROBUSTNESS:MOTIVATION
Problem with Instrumental Variables:The model may be wrong!
xz
yzyz R
RR
Smoking
ZPrice ofCigarettes
x y
Genetic Factors (unobserved)
Cancer
u
Smoking
ROBUSTNESS:MOTIVATION
Z1
Price ofCigarettes
Solution: Invoke several instruments
Surprise: 1 = 2 model is likely correct
2
22
1
11
xz
yz
xz
yz
R
R
R
R
x y
Genetic Factors (unobserved)
Cancer
u
PeerPressure
Z2
ROBUSTNESS:MOTIVATION
Z1
Price ofCigarettes
x y
Genetic Factors (unobserved)
Cancer
u
PeerPressure
Z2
Smoking
Greater surprise: 1 = 2 = 3….= n = qClaim = q is highly likely to be correct
Z3
Zn
Anti-smoking Legislation
ROBUSTNESS:MOTIVATION
x y
Genetic Factors (unobserved)
Cancer
u
Smoking
Symptoms do not act as instruments
remains non-identifiable
s
Symptom
Why? Taking a noisy measurement (s) of an observed variable (y) cannot add new information
ROBUSTNESS:MOTIVATION
x
Genetic Factors (unobserved)
Cancer
u
Smoking
Adding many symptoms does not help.
remains non-identifiable
ySymptom
S1
S2
Sn
ROBUSTNESS:MOTIVATION
Find if can evoke an equality surprise1 = 2 = …n
associated with several independent estimands of
x y
Given a parameter in a general graph
Formulate: Surprise, over-identification, independenceRobustness: The degree to which is robust to violations
of model assumptions
ROBUSTNESS:FORMULATION
Bad attempt: Parameter is robust (over identifies)
f1, f2: Two distinct functions
)()( 21 ff
distinct. are
then constraint induces model if
)]([
)]([)()]([)(
,0)(
21
gt
gtfgtf
g
i
if:
ROBUSTNESS:FORMULATION
ex ey ez
x y zb c
x = ex
y = bx + ey
z = cy + ez
Ryx = bRzx = bcRzy = c
zyyxzx
yxzxzy
zyzxyx
RRR
RRcRc
RRbRb
/
/
constraint:
(b)
(c)
y → z irrelvant to derivation of b
RELEVANCE:FORMULATION
Definition 8 Let A be an assumption embodied in model M, and p a parameter in M. A is said to be relevant to p if and only if there exists a set of assumptions S in M such that S and A sustain the identification of p but S alone does not sustain such identification.
Theorem 2 An assumption A is relevant to p if and only if A is a member of a minimal set of assumptions sufficient for identifying p.
ROBUSTNESS:FORMULATION
Definition 5 (Degree of over-identification)A parameter p (of model M) is identified to degree k (read: k-identified) if there are k minimal sets of assumptions each yielding a distinct estimand of p.
ROBUSTNESS:FORMULATION
x y
b
z
c
Minimal assumption sets for c.
xy z
c xy z
c
G3G2
xy z
c
G1
Minimal assumption sets for b. xy
bz
FROM MINIMAL ASSUMPTION SETS TO MAXIMAL EDGE SUPERGRAPHS
FROM PARAMETERS TO CLAIMS
DefinitionA claim C is identified to degree k in model M (graph G), if there are k edge supergraphs of G that permit the identification of C, each yielding a distinct estimand.
TE(x,z) = Rzx TE(x,z) = Rzx Rzy ·x
xy zx
y z
e.g., Claim: (Total effect) TE(x,z) = q x y z
FROM MINIMAL ASSUMPTION SETS TO MAXIMAL EDGE SUPERGRAPHS
FROM PARAMETERS TO CLAIMS
DefinitionA claim C is identified to degree k in model M (graph G), if there are k edge supergraphs of G that permit the identification of C, each yielding a distinct estimand.
xy zx
y z
e.g., Claim: (Total effect) TE(x,z) = q x y z
Nonparametric y x
xPyxzPxyPxzTExzPzxTE'
)'(),'|()|(),()|(),(
CONCLUSIONS
1. Formal definition to ROBUSTNESS of causal claims.
2. Graphical criteria and algorithms for computing the degree of robustness of a given causal claim.