A tighter bound for graphical models.

M A Leisink; H J Kappen

doi:10.1162/089976601750399344

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PubMed · 11516361

A tighter bound for graphical models.

M A Leisink·H J Kappen

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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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Computer Simulation Models, Neurological Neural Networks, Computer Probability Journal Article Research Support, Non-U.S. Gov't

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M A Leisink, H J Kappen. 2001. A tighter bound for graphical models.. https://doi.org/10.1162/089976601750399344

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