A tighter bound for graphical models.
We present a method to bound the partition function of a Boltzmann 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 derive a third-order bound for the likelihood of sigmoid belief networks. Numerical experiments indicate that an error reduction of a factor of two is easily reached in the region where expansion-based approximations are useful.
Leisink
M A
MA
Department of Biophysics, University of Nijmegen, NL 6525 EZ Nijmegen, The Netherlands.
Kappen
H J
HJ
D003198:Computer Simulation; D008959:Models, Neurological; D016571:Neural Networks, Computer; D011336:Probability