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We are working a bit with Inference in Graphs, and in Bishop's book (page 403) He mentions that Belief Propagation is an special case of the Sum-Product Algorithm. The thing is, I seem unable to infer that special case, most papers I read (and even the Wikipedia page) treat the Sum-Product as a tool for Belief Propagation. I understand how you update the messages, I just don't get very well when do we call it belief propagation. Thanks |
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I think the paper by Aji/McEliece, "The Generalized Distributive Law" provides a nice overall picture. |
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Afaik the sum-product algorithm is a general algorithm to calculate functions that can be expressed using factor graphs. I believe it is called belief propagation when this factor graph represents a probabilistic graphical model. Maybe this paper helps: Factor graphs and the sum-product algorithm That's y point, I've understand that paper and I get a hold of what they are doing, I just wanted to know when is it called belief propagation. In there they don't mention belief prop at all.
(Sep 30 '11 at 07:23)
Leon Palafox
As I said, I think it's just called belief propagation if the function is a probability density function.
(Sep 30 '11 at 07:25)
Andreas Mueller
I think as far as graphical models go BP is always a special-case of sum-product (although sometimes vitberbi is referred to as max-product belief propagation). Maybe he means that sum-product generalizes to semirings and turns out to be the same algorithm for all sort of dynamic programming problems?
(Sep 30 '11 at 07:26)
Alexandre Passos ♦
Indeed, I get confused from time to time in Graph Models, since they change some of the terminology for the same tasks if they change the kind of graph (even though the inference process is very similar).
(Sep 30 '11 at 07:33)
Leon Palafox
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