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Why “potential”?
Why not use something more “probability-friendly” like marginal?
Why “potential”?
Why not use something more “probability-friendly” like marginal?
Answer: Marginal of a small subset of variablesdepends on the entire graph!
A
B
C
𝑃 𝐴,𝐵,𝐶 =  1 𝑍 𝑃 𝐴,𝐵 𝑃(𝐵,𝐶)
Say
Why “potential”?
Why not use something more “probability-friendly” like marginal?
Answer: Marginal of a small subset of variablesdepends on the entire graph!
A
B
C
𝑃 𝐴,𝐵,𝐶 =  1 𝑍 𝑃 𝐴,𝐵 𝑃(𝐵,𝐶)
Say
To calculate the marginal 𝑃 𝐴,𝐵 :
𝑃 𝐴,𝐵 =  𝐶   1 𝑍 𝑃 𝐴,𝐵 𝑃 𝐵,𝐶  =𝑃 𝐴,𝐵  1 𝑍 𝑃 𝐵 
⇒𝑃 𝐵 =𝑍 regardless of what B is!
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𝜙(𝑐,𝑑)
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𝜙(𝑐,𝑑)
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