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Unformatted text preview: er to elicit from experts BNs need not actually be causal Sometimes no causal net exists over the domain E.g. consider the variables Traffic and Drips End up with arrows that reflect correlation, not causation What do the arrows really mean? Topology may happen to encode causal structure Topology only guaranteed to encode conditional independence [[If you wanted to learn more about causality, beyond the9
scope of 188: Causility – Judea Pearl]]** Example: Traffic Example: Reverse Traffic Basic traffic net Let s multiply out the joint
r 1/4 ¬r R 3/4 Reverse causality? t
¬t 6/16 1/2 ¬r t X1 6/16 ¬r ¬t 6/16 2/3 r 1/16 t 1/7
6/7 11 The same joint distribution can be
encoded in many different Bayes nets Causal structure tends to be the simplest X2 h 0.5 h 0.5 h 0.5 hh t 0.5 t 0.5 t 0.5 th 0.5 ht 0.5 tt Analysis question: given some edges,
what other edges do you need to add? 0.5 0.5 Adding unneeded arcs isn t
wrong, it s just inefficient 1/3 3/16 ¬t Changing Bayes Net Structure Extra arcs don t prevent representing
independence, just allow nonindependence
X2 r t r ¬r ¬t
10 r ¬r R Example: Coins X1 7/16 ¬r 1/2 ¬t ¬t 9/16 6/16 1/4 t T 1/16 t t
¬t T 3/16 ¬t ¬r 3/4 t r
¬r r r One answer: fully connect the graph Better answer: don t make any false
conditional independence assumptions
12 13 2 An Algorithm for Adding Necessary Edges Choose an ordering consistent with the
partial ordering induced by existing edges,
let’s refer to the ordered variables as X1,
X2, …, Xn For i=1, 2, …, n Example: Alternate Alarm
Burglary Earthquake If we reverse the edges, we
make different conditional
independence assumptions
John calls Mary calls Alarm Find the minimal set parents(Xi) such that Alarm
John calls Mary calls P (xi x1 · · · xi−1 ) = P (xi parents(Xi )) Why does this ensure no spurious
conditional independencies remain? 14 To capture the same joint
distribution, we have to add
more edges to the graph Burglary Earthquake
15 Bayes Nets Status Bayes Nets Representation Summary Bayes nets compactly encode joint distributions Representation Guaranteed independencies of distributions can
be deduced from BN graph structure Inference Dseparation gives precise conditional
independence guarantees from graph alone Lear...
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This note was uploaded on 08/26/2011 for the course CS 188 taught by Professor Staff during the Spring '08 term at University of California, Berkeley.
 Spring '08
 Staff
 Artificial Intelligence

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