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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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2015 Repository Open Access
Guido Montúfar

Universal approximation of Markov kernels by shallow stochastic feedforward networks