Factor Graph & Sum-Product Algorithm

Factor Graph , Sum-Product Algorithm A Mini Demo TonyOuyang, ACM Honored Class 2009 Spring

[object Object],[object Object],02

[object Object],[object Object],[object Object],[object Object],g(x,y)=xy+x g(x,y)=f1(x)f2(y)‏ f1(x)=x f2(y)=y+1.

[object Object],[object Object],[object Object],Why are factor graph useful ? ,[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],A closer look

[object Object],[object Object],[object Object],Msg Passing Algorithm Reference : Information Theory, Inference, and_Learning Algorithms, chp16

[object Object],Msg Passing Algorithm con't

[object Object],Msg Passing Algorithm con't # How many such paths are there from A to B? # If a random path from A to B is selected, what is the probability that it passes through a particular node in the grid?

Reference : Bishop, chp8 Why efficient ? # global -> local # interchange summation & production # reuse ! * fact : dynamic programming

[object Object],[object Object],[object Object],"no pressure" = "pump switched off" OR "pump defect". define the function f1 : f1(np,pso,pd) = 1 if the constraint is satisfied, and f1(np,pso,pd) = 0 otherwise. i.e. f1(np,pso,pd)=1 if [np pso pd] is [F F F], [T F T], [F T T] or [T T T], 0 other four conditions samely, "no pressure" = "pump not working" OR "slide-valve closed" OR "pipe leaks", we get f2 finaly, global function g = f1*f2

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],02 More Online Resources ...

02 Thank you for attention TonyOuyang [email_address]

Factor Graph & Sum-Product Algorithm

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Factor Graph & Sum-Product Algorithm