ML Anthology

A Tighter Bound for Graphical Models

Martijn A. R. Leisink, Hilbert J. Kappen
NeCo 2001 pp. 2149-2171
doi:10.1162/089976601750399344 /neco/2001/leisink2001neco-tighter/

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.

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Text

Leisink and Kappen. "A Tighter Bound for Graphical Models." Neural Computation, 2001. doi:10.1162/089976601750399344

Markdown

[Leisink and Kappen. "A Tighter Bound for Graphical Models." Neural Computation, 2001.](https://mlanthology.org/neco/2001/leisink2001neco-tighter/) doi:10.1162/089976601750399344

BibTeX

@article{leisink2001neco-tighter,
  title     = {{A Tighter Bound for Graphical Models}},
  author    = {Leisink, Martijn A. R. and Kappen, Hilbert J.},
  journal   = {Neural Computation},
  year      = {2001},
  pages     = {2149-2171},
  doi       = {10.1162/089976601750399344},
  volume    = {13},
  url       = {https://mlanthology.org/neco/2001/leisink2001neco-tighter/}
}