Martijn Leisink, Hilbert Kappen
We present a method to bound the partition function of a Boltz(cid:173) mann machine neural network with any odd order polynomial. This is a direct extension of the mean field bound, which is first order. We show that the third order bound is strictly better than mean field. Additionally we show the rough outline how this bound is applicable to sigmoid belief networks. Numerical experiments in(cid:173) dicate that an error reduction of a factor two is easily reached in the region where expansion based approximations are useful.