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A Bayesian Approach to Learning Causal networks

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Title: A Bayesian Approach to Learning Causal networks


1
A Bayesian Approach to Learning Causal
networks
  • David Heckerman

2
Objectives
  • Showing that causal networks are different from a
    causal ones
  • Identification of circumstances in which methods
    for learning acausal networks
  • are applicable to learning causal networks

3
A Causal Network is
  • A directed acyclic graph where
  • Nodes correspond to chance variables in U
  • Non root node is a direct causal effect of its
    parents.

4
Causal Bayesian Networks and Influence
diagrams
  • A Causal Network

s
5
Some new terms
  • Unresponsiveness.
  • Set decision
  • Mapping variable

6
What is an Influence Diagram ?
  • A model for the domain U U D having a
  • structural component
  • probabilistic component

7
An Example
f(?)
b(?)
f
b
b
f
s
s
s(b,f)
m
m(s)
m
8
Building an Influence diagram
  • Steps involved
  • Add a node to the diagram corresponding to each
    variable in U U D
  • Order the variables so that the unresponsiveness
    to D comes first.
  • For each Xi do
  • Add a causal mechanism node
  • Make Xi a deterministic function of Ci U
    Xi(Ci)where Ci is a causal mechanism node.
  • Finally Assess the dependencies among the
    variables that are unresponsive D.

9
Influence diagrams in canonical forms
  • Conditions
  • Chance nodes descendents of D are decision nodes
  • Descendents of decision nodes are deterministic
    nodes

10
Learning Influence diagrams
  • Observations
  • Information arcs and predecessors of a utility
    node are not learned
  • We learn only the relevance arc structure and the
    physical probability
  • We also know the states of all the decision
    variables and thus have a complete data for D in
    every case of the data base.

11
Hence
  • The problem of learning influence diagrams for
    the domain U U D
  • reduces to
  • Learning acausal bayesian networks for
  • U UD where decision variables are interpreted as
    chance variables

12
Learning Causal Networks
  • An example
  • Decision to quit smoking
  • do we get lung cancer before
    sixty?

x
y
13
The problem
  • We cannot fully observe the mapping
    variable y(x)

14
Mechanism Components
  • What are they?

15
Decomposition of the mapping variable y(x)
y(x0)
y(x1)
x
y
y
16
Component Independence
  • Assumption that the mechanism components are
    independent.

Y(x1)
y(x0)
x
y
y
17
Another Problem
  • The problem Dependent Mechanisms
  • A solution Introduce additional domain
    variables in order to render mechanisms
    independent
  • But.
  • We may not be able to observe the variables we
    introduce.

18
  • Learning in a causal network reduces to learning
    of acausal network when
  • Mechanism Independence
  • Component Independence and
  • Parameter Independence

19
Learning Causal Network structure
  • We can use prior network methodology to establish
    priors for causal network learning provided the
    following holds
  • Mechanism independence
  • Component independence
  • Parameter independence
  • Parameter modularity

20
Conclusion
  • Some important points of focus
  • Mechanism Independence
  • Component Independence
  • Parameter Independence
  • Parameter Modularity
  • We use the above to learn causal networks from
    acausal networks
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