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Marginal probability

We have the binary-binary marginal probability defined as

pBB(x,h,Θ)=1ZBB(Θ)eMiaixi+Njbjhj+M,Nijxiwijhj=1ZBB(Θ)eaTx+bTh+xTWh

with the partition function

ZBB(Θ)=x,heaTx+bTh+xTWh.