Talk:Markov network

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Needs much more work - discussion of inference, the Hammersley-Clifford Theorem, links, etc. Will add more. Revise away. -- Soultaco, 22:50 24 Dec 2004 (UTC)

[edit] Potential functions

From the current version of the article:

  • What's the relationship between the potential function and the Gibbs function?


  • a set of potential functions \Phi = \phi_{c_i} : A_{c_i} \rightarrow R^+, where each c_i = \lbrace i_1, i_2, ... i_{|c_i|} \rbrace represents a clique in G, and A_{c_i} is the set of all possible assignments to the random variables represented by v_{i_1}, v_{i_2}, ... v_{i_{|c_i|}}. In other words, each clique has associated with it a function from possible assignments to all nodes to the nonnegative real numbers.

I find this needlessly complex and somewhat confusing. Here is how I would word it:

  • a set Φ of potential functions \phi_{c_i} : A_{c_i} \rightarrow R^+, where each ci is a clique in G, and A_{c_i} is the set of all possible assignments to the elements of ci. In other words, each clique has associated with it a function from assignments (to each element of the clique) to nonnegative real numbers.

It's not clear to me why the definition needs to mention both i's and v's, or why such schematic letters are even necessary for the definition at all. (Can't we just identify the vertices of the graph with random variables rather than invoking some "representation" relation between them?) However, I'm hesitant to just unilaterally edit the article, as I'm not very knowledgeable about these things. Thoughts? Dbtfz (talk - contribs) 02:21, 4 February 2006 (UTC)

I went ahead and revised the passage mentioned above as well as much of the rest of the article. Anyone who is interested, please review and revise as needed. Dbtfz (talk - contribs) 06:02, 10 February 2006 (UTC)
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