1 / 28

Noisy Or Gate

Javier Turek and Eyal Regev. Noisy Or Gate. Polytrees. …. U i. …. Like a tree, but with multiple parents. U 1. U n. e +. X. Y. Z. e -. Several causes sharing a common effect. Link matrix T x| u. T x| u contains the conditional probabilities: P(X=x | U 1 =u 1 ,…,U n =u n )

walda
Download Presentation

Noisy Or Gate

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Javier Turek and Eyal Regev Noisy Or Gate

  2. Polytrees … Ui … • Like a tree, but with multiple parents. U1 Un e+ X Y Z e- • Several causes sharing a common effect.

  3. Link matrix Tx|u • Tx|u contains the conditional probabilities: • P(X=x | U1=u1,…,Un=un) • The table is huge (contains 2n entries). • Who can know such information anyway? • You cannot expect to find the P(X | U1,…,Un) table. • However, you may know how every Ui influences X separately.

  4. The OR-gate Caught cheating Haven’t done homework OR Failed an exam More likely!

  5. Inhibitors Haven’t done homework Re-doing the course Caught cheating Paid the TA AND AND OR Failed an exam

  6. Inhibitors In I2 Un U2 I1 • Inhibitors are independent • Associate probability to an inhibitor. U1 AND AND AND OR X

  7. Noisy OR-Gate In I2 Un U2 I1 U1 AND AND AND OR X

  8. Noisy OR-Gate In I2 Un U2 I1 U1 Tu AND AND AND OR X

  9. Message Passing – updating X U e+ X Y Z e-

  10. Message Passing – updating X U W e+ X Y Z e-

  11. Message Passing – updating U,Y,Z U e+ X Y Z e-

  12. Message Passing – updating W,U,Y,Z U W e+ X Y Z e-

  13. Message Passing – many parents … Ui … U1 Un e+ X Link matrix Y Z e-

  14. Belief Update – Noisy OR-Gate

  15. Belief Update – Noisy OR-Gate

  16. Update messages Where • The message to the child is the same:

  17. Example D1 Windows Vista D2 No electricity D3 Virus D4 2K bug M1 Does not start Wrong date M2 M3 Stolen Password M4 Lost data

  18. Example 0.01\0.99 0.1\0.9 0.2\0.8 0.2\0.8 D1 D2 D3 D4 0.8 0.2 0.5 0.2 0.8 0.1 0.1 0.9 0.7 M1 M2 M3 M4

  19. Conjunction query • Conjunction query q: find the belief that several events happen simultaneously. • Applying the chain rule: • Product of m belief updates

  20. Answering a query • In our example: • Computing P(q):

  21. Example • Update the belief on M1 • Update likelihoods and priors: D1 D2 D3 D4 M1 M2 M3 M4

  22. Example • Update the belief on M2 • Update likelihoods and priors: D1 D2 D3 D4 M1 M2 M3 M4

  23. Example • Update the belief on M3 • Update likelihoods and priors: D1 D2 D3 D4 M1 M2 M3 M4

  24. Example • Update the belief on M4 D1 D2 D3 D4 M1 M2 M3 M4

  25. Example • And the final solution is…

  26. Example • And the final solution is…

  27. Thank You!

More Related