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I'm reading this paper http://image.diku.dk/igel/paper/AItRBM-proof.pdf and I got stuck in page 4 with equation (1) that's based on Hammersley–Clifford theorem. I'm not good in reading set theory notation and also I wasn't able to understand the point from the equation.

I couldn't understand what are $x_c$ and $\hat{x}_c$

Here's the section, I'm stuck just at equation (1):

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  • $\begingroup$ That $\widehat{x}$ denotes a different random variable in the set. This says that if $x_c$ and $\widehat{x}_c$ are two observations in the same clique, the potential function evaluated at $x_c$ and $\widehat{x}_c$ is equivalent. $\endgroup$
    – Donnie
    Apr 18, 2014 at 12:00

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