1 / 9

Clique Tree and VE

Inference. Probabilistic Graphical Models. Message Passing. Clique Tree and VE. Variable Elimination & Clique Trees. Variable elimination Each step creates a factor  i through factor product A variable is eliminated in  i to generate new factor  i

shania
Download Presentation

Clique Tree and VE

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. Inference Probabilistic Graphical Models Message Passing Clique Tree and VE

  2. Variable Elimination & Clique Trees • Variable elimination • Each step creates a factor ithrough factor product • A variable is eliminated in ito generate new factor i • i is used in computing other factors j • Clique tree view • Intermediate factors iare cliques • i are “messages” generated by clique iand transmitted to another clique j

  3. Clique Tree from VE • VE defines a graph • Cluster Ci for each factor iused in the computation • Draw edge Ci–Cj if the factor generated from iis used in the computation of j

  4. Example • C: • D: • I: • H: • G: • S: • L: D G,I 3 C,D G,I,D G,S,I 2 1 G,S J,S,L J,L G,J,S,L J,S,L J,L 5 7 6 G,J 4 H,G,J Remove redundant cliques: those whose scope is a subset of adjacent clique’s scope

  5. Properties of Tree • VE process induces a tree • In VE, each intermediate factor is used only once • Hence, each cluster “passes” a factor (message) to exactly one other cluster • Tree is family preserving: • Each of the original factors must be used in some elimination step • And therefore contained in scope of associated i

  6. D G,I C,D G,I,D G,S,I G,S G,J,S,L G,J H,G,J Properties of Tree • Tree obeys running intersection property • If XCi and XCj then X is in each cluster in the (unique) path between Ci and Cj

  7. Running Intersection Property • Theorem: If T is a tree of clusters induced by VE, then T obeys RIP C1 C4 C6 C7 C3 C2 C5

  8. Summary • A run of variable elimination implicitly defines a correct clique tree • We can “simulate” a run of VE to define cliques and connections between them • Cost of variable elimination is ~ the same as passing messages in one direction in tree • Clique trees use dynamic programming (storing messages) to compute marginals over all variables at only twice the cost of VE

  9. END END END

More Related