General Lower Bounds Based on Computer Generated Higher Order Expansions
Abstract
In this article we show the rough outline of a computer algorithm to generate lower bounds on the exponential function of (in principle) arbitrary precision. We implemented this to generate all necessary analytic terms for the Boltzmann machine partition function thus leading to lower bounds any order. It turns out that the extra variational parameters can be optimized analytically. We show that bounds upto nineth order are still reasonably calculable in practical situations. The gen erated terms can also be used as extra cor rection terms (beyond TAP) in mean field ex pansions.
Cite
Text
Leisink and Kappen. "General Lower Bounds Based on Computer Generated Higher Order Expansions." Conference on Uncertainty in Artificial Intelligence, 2002.Markdown
[Leisink and Kappen. "General Lower Bounds Based on Computer Generated Higher Order Expansions." Conference on Uncertainty in Artificial Intelligence, 2002.](https://mlanthology.org/uai/2002/leisink2002uai-general/)BibTeX
@inproceedings{leisink2002uai-general,
title = {{General Lower Bounds Based on Computer Generated Higher Order Expansions}},
author = {Leisink, Martijn A. R. and Kappen, Hilbert J.},
booktitle = {Conference on Uncertainty in Artificial Intelligence},
year = {2002},
pages = {293-300},
url = {https://mlanthology.org/uai/2002/leisink2002uai-general/}
}