Mean Field Methods for a Special Class of Belief Networks

Chiranjib Bhattacharyya, S. Sathiya Keerthi

JAIR 2001 pp. 91-114

doi:10.1613/JAIR.734 /jair/2001/bhattacharyya2001jair-mean/

Abstract

The chief aim of this paper is to propose mean-field approximations for a broad class of Belief networks, of which sigmoid and noisy-or networks can be seen as special cases. The approximations are based on a powerful mean-field theory suggested by Plefka. We show that Saul, Jaakkola, and Jordan's approach is the first order approximation in Plefka's approach, via a variational derivation. The application of Plefka's theory to belief networks is not computationally tractable. To tackle this problem we propose new approximations based on Taylor series. Small scale experiments show that the proposed schemes are attractive.

PDF JAIR Semantic Scholar

Cite

Text

Bhattacharyya and Keerthi. "Mean Field Methods for a Special Class of Belief Networks." Journal of Artificial Intelligence Research, 2001. doi:10.1613/JAIR.734

Markdown

[Bhattacharyya and Keerthi. "Mean Field Methods for a Special Class of Belief Networks." Journal of Artificial Intelligence Research, 2001.](https://mlanthology.org/jair/2001/bhattacharyya2001jair-mean/) doi:10.1613/JAIR.734

BibTeX

@article{bhattacharyya2001jair-mean,
  title     = {{Mean Field Methods for a Special Class of Belief Networks}},
  author    = {Bhattacharyya, Chiranjib and Keerthi, S. Sathiya},
  journal   = {Journal of Artificial Intelligence Research},
  year      = {2001},
  pages     = {91-114},
  doi       = {10.1613/JAIR.734},
  volume    = {15},
  url       = {https://mlanthology.org/jair/2001/bhattacharyya2001jair-mean/}
}