SP11 cs188 lecture 16 -- bayes nets IV 6PP

G consider the variables traffic and drips end up

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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 h|h t 0.5 t 0.5 t 0.5 t|h 0.5 h|t 0.5 t|t   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 non-independence 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   D-separation 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.

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