General Lower Bounds based on Computer Generated Higher Order Expansions
Martijn Leisink, Hilbert Kappen
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 of 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 generated terms can also be used as extra correction terms (beyond TAP) in mean field expansions.
PDF Link: /papers/02/p293-leisink.pdf
AUTHOR = "Martijn Leisink
and Hilbert Kappen",
TITLE = "General Lower Bounds based on Computer Generated Higher Order Expansions",
BOOKTITLE = "Proceedings of the Eighteenth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-02)",
PUBLISHER = "Morgan Kaufmann",
ADDRESS = "San Francisco, CA",
YEAR = "2002",
PAGES = "293--300"