Computer generated higher order expansions

Authors:
Martijn A. R. Leisink;Hilbert J. Kappen
Affiliations:
University of Nijmegen, Department of Biophysics, Nijmegen, The Netherlands;University of Nijmegen, Department of Biophysics, Nijmegen, The Netherlands
Venue:
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
Year:
2002

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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 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.