gR2002
Peter Spirtes
Carnegie Mellon University
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Graphs often given causal
interpretation

Graphs can be used to represent both causal
hypotheses and probability distributions
in a directed acyclic graph (DAG) A  B means A
is a direct cause of B
 DAG also represents a set of distributions sharing
conditional independence relations
 e.g.


Causal interpretation is common in social science
applications (structural equation modelling)
Causal representation of genetic regulatory
networks
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TETRAD

Dedicated to search for causal models under a variety of
different assumptions about what is known



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
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Has several different kinds of graphs, depending upon background
assumptions
Has a number of different kinds of search strategies
Allows some explicit representation of background knowledge
Has some modules for calculating equivalence class of given graph
Recently developed graphical interface
Should have module for calculating effects of interventions
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The causal interpretation of
graphical models suggests several
unusual operations
Calculation of effect of manipulation
 Calculation of equivalence class (aid to
calculation of effect of manipulation)

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Kinds of graphical models in
TETRAD
Directed acyclic graphs (discrete, normal)
 Directed cyclic graphs (normal)
 Pattern
 Mixed ancestral graphs (normal)
 Partial ancestral graphs

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Difference between calculation of
manipulation versus conditioning
In conditioning, the result depends only
upon the joint distribution and the event
conditioned on,
 In manipulating, the results depend upon the
joint distribution, the event manipulated,
and the causal relations among the variables

 This
means that locating alternative good
models is essential for correct prediction of
manipulation
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Conditioning
P(Lung Cancer = yes|Smoking = yes) = ¾
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Manipulating Smoking – First Step
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Manipulating Smoking – After waiting
P(Lung Cancer = yes||Smoking = yes) = ¾ =
P(Lung Cancer = yes|Smoking = yes) = ¾
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Calculation of effect of manipulation
When there are no latent variables and
structure is known - simple
 When there are latent variables and the
structure is known (Pearl 2001)
 When the structure is partially known (SGS
2001)

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Calculation of Effect of
Manipulation – Equivalence Class
A
A
A
B
C
B
C
G1
C
D
D
D
B
G2
Pattern
G1 and G2 represent the same distribution, agree on the effect
on D of manipulating B, disagree about the effect on A of
manipulating B
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Calculation of Effect of
Manipulation – Equivalence Classes
B
C
B
C
G1
B
C
G2
o
B
C
o
o
D
D
D
D
A
o
A
A
A
Pattern
PAG
Pattern represents the equivalence class of DAGs if there are
no latent variables. PAG represents the equivalence class of
DAGs if there might be latent variables.
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Edge types in different graphs



 oo
 oo
 combinations of edges subject to varying
constraints

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The Statistical Theory for some
graphical models is only partially
worked out

MAGs and PAGs
 know
how to parameterize in linear cases
 may not be a unique maximum likelihood
estimate
 PAG – not known how to efficiently determine
if arbitrary combination of edges is PAG
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Specific searches

Assuming no latent variables or cycles
 Hill
climbing – BIC, posterior probability
(normal, discrete)
 Constraint based – PC (normal, discrete)
 Combined

Assuming no cycles
 Hill
climbing – BIC (normal)
 Constraint based – FCI (normal, discrete)
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Other features
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Estimate parameters - DAGs (discrete, normal)
Representation of background knowledge
Find equivalence class of given DAG (no latents,
possibly cyclic)
Graphical interface
Should have module to calculate effects of
manipulations
 Known
structure, no latents
 Known structure, latent variables
 Partially known structure
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As a probabilistic model graphical
models require usual operations

As a probabilistic model, it requires the
usual set of procedures
 Search
 Estimation
 Testing
 Scoring
 Conditioning
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Summary

The causal interpretation of graphical
models offers an opportunity to provide
functionality not found in most other kinds
of models (e.g. predicting affects of
manipulations)
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Summary

Added functionality, different domains and
different background knowledge require a
variety of different kinds of graphical
models
 desirability
of flexibility in graphical
representation
 desirability of allowing each type to inherit as
much as possible from more general
representations
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Summary

Because of the need to locate good
alternative models
 Search
plays a very important role (score-based,
constraint-based, and combinations)
 Calculating equivalence classes is essential
 Collection and representation of background
knowledge to guide search is very important
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