## Neural Computation

September 1, 2001, Vol. 13, No. 9, Pages 2149-2171
(doi: 10.1162/089976601750399344)
© 2001 Massachusetts Institute of Technology
A Tighter Bound for Graphical Models
Article PDF (787.13 KB)
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.