title: A tighter bound for graphical models.
abstract: 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.
authors.affiliation: Department of Biophysics, University of Nijmegen, NL 6525 EZ Nijmegen, The Netherlands.
authors.forename: M A
authors.initials: MA
authors.lastname: Leisink
authors.forename: H J
authors.initials: HJ
authors.lastname: Kappen
mesh_terms: D003198:Computer Simulation; D008959:Models, Neurological; D016571:Neural Networks, Computer; D011336:Probability