Quantitative Universal Approximation Bounds for Deep Belief NetworksDownload PDF

Published: 01 Feb 2023, 19:30, Last Modified: 13 Feb 2023, 23:27Submitted to ICLR 2023Readers: Everyone
Keywords: Deep belief network, restricted Boltzmann machine, universal approximation property, expressivity, Kullback-Leibler approximation, probability density
TL;DR: We prove quantitative approximation results for deep belief networks with binary hidden units.
Abstract: We show that deep belief networks with binary hidden units can approximate any multivariate probability density under very mild integrability requirements on the parental density of the visible nodes. The approximation is measured in the $L^q$-norm for $q\in[1,\infty]$ ($q=\infty$ corresponding to the supremum norm) and in Kullback-Leibler divergence. Furthermore, we establish sharp quantitative bounds on the approximation error in terms of the number of hidden units.
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