Quantitative Universal Approximation Bounds for Deep Belief NetworksDownload PDF

Published: 01 Feb 2023, Last Modified: 13 Feb 2023Submitted to ICLR 2023Readers: Everyone
Keywords: Deep belief network, restricted Boltzmann machine, universal approximation property, expressivity, Kullback-Leibler approximation, probability density
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.
Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.
No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics
Submission Guidelines: Yes
Please Choose The Closest Area That Your Submission Falls Into: Theory (eg, control theory, learning theory, algorithmic game theory)
TL;DR: We prove quantitative approximation results for deep belief networks with binary hidden units.
14 Replies