Presentation on theme: "Javier Turek and Eyal Regev. Several causes sharing a common effect. Y Z UiUi e+e+ e-e- X Polytrees U1U1 UnUn … … Like a tree, but with multiple parents."— Presentation transcript:
Javier Turek and Eyal Regev
Several causes sharing a common effect. Y Z UiUi e+e+ e-e- X Polytrees U1U1 UnUn … … Like a tree, but with multiple parents.
Link matrix T x|u T x|u contains the conditional probabilities: P(X=x | U 1 =u 1,…,U n =u n ) 1. The table is huge (contains 2 n entries). 2. Who can know such information anyway? You cannot expect to find the P(X | U 1,…,U n ) table. However, you may know how every U i influences X separately.
The OR-gate Havent done homework Caught cheating Failed an exam More likely! OR
Inhibitors Failed an exam Caught cheating OR AND Paid the TA Havent done homework AND Re-doing the course
Inhibitors U1U1 X U2U2 UnUn I1I1 I2I2 InIn OR AND Inhibitors are independent Associate probability to an inhibitor.
Noisy OR-Gate U1U1 X U2U2 UnUn I1I1 I2I2 InIn OR AND
Noisy OR-Gate U1U1 X U2U2 UnUn I1I1 I2I2 InIn OR AND TuTu
Message Passing – updating X Y Z U e+e+ e-e- X
Y Z U e+e+ W e-e- X
Message Passing – updating U,Y,Z Y Z U e+e+ e-e- X
Y Z U e+e+ W e-e- X Message Passing – updating W,U,Y,Z
Y Z UiUi e+e+ e-e- X Message Passing – many parents Link matrix U1U1 UnUn … …
Belief Update – Noisy OR-Gate
Update messages Where The message to the child is the same:
Example Windows Vista No electricity Virus2K bug Does not start Wrong date Stolen Password Lost data D1D1 D2D2 D3D3 D4D4 M1M1 M2M2 M3M3 M4M4