Means, Correlations and Bounds

Part of Advances in Neural Information Processing Systems 14 (NIPS 2001)

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Martijn Leisink, Bert Kappen


The partition function for a Boltzmann machine can be bounded from above and below. We can use this to bound the means and the correlations. For networks with small weights, the values of these statistics can be restricted to non-trivial regions (i.e. a subset of [-1 , 1]). Experimental results show that reasonable bounding occurs for weight sizes where mean field expansions generally give good results.