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Graphical Models

This overview explores various types of graphical models, including Directed Graphical Models (DGMs) and Undirected Graphical Models (UGMs). We delve into the semantics of these models with practical examples, illustrating concepts such as boundary (bd) and closure (cl) of sets. Key topics include ancestral sets, moral and triangulated graphs, along with their implications in separating nodes. This resource serves as a foundational guide for students and professionals looking to deepen their understanding of graphical semantics in data representation.

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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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