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Graphical Models

Graphical Models. Chain Graphs. Other Graphical Semantics Models. DGMs. UGMs. A. B. Examples: bd({C,D}) = {A,B} bd({A}) = {B} and so on…. C. D. A. B. Examples: bd({A}) = Ø bd({C,D}) = {A,B} cl({A}) = {A} cl({D}) = {C,B,D} and so on…. C. D. A. B. C. D. E. F. G. A.

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Graphical Models

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  1. Graphical Models Chain Graphs Other Graphical Semantics Models DGMs UGMs

  2. A B • Examples: • bd({C,D}) = {A,B} • bd({A}) = {B} • and so on… C D

  3. A B • Examples: • bd({A}) = Ø • bd({C,D}) = {A,B} • cl({A}) = {A} • cl({D}) = {C,B,D} • and so on… C D

  4. A B C D E

  5. F G A E B D C

  6. 1 2 3 4 5

  7. C A B E D F G H

  8. {A,B,C,D} is an ancestral set. {A,B,C,D} is not an ancestral set. B E A C B D A C E D

  9. Nodes in A are separated from C by B A B C

  10. A B C

  11. Amoral graphs Moral graphs

  12. Triangulated Graphs Not Triangulated Graphs

  13. A,B,C B,C,D D,E,F

  14. Moral Triangulated A DAG A A A B D B D B D C C C E F G E F G E F G H I H I H I

  15. A,B,C,D B,C,D,F B,E,F D,F,G E,F,H F,G,I

  16. A C B

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