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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
23/2015

Universal Approximation of Markov Kernels by Shallow Stochastic Feedforward Networks

Guido Montúfar

Abstract

We establish upper bounds for the minimal number of hidden units for which a binary stochastic feedforward network with sigmoid activation probabilities and a single hidden layer is a universal approximator of Markov kernels. We show that each possible probabilistic assignment of the states of $n$ output units, given the states of $k\geq1$ input units, can be approximated arbitrarily well by a network with $2^{k-1}(2^{n-1}-1)$ hidden units.

Received:
Mar 24, 2015
Published:
Mar 26, 2015
Keywords:
stochastic feedforward network, universal approximation, sufficiency bounds

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Preprint
2015 Repository Open Access
Guido Montúfar

Universal approximation of Markov kernels by shallow stochastic feedforward networks