Universal Approximation of Markov Kernels by Shallow Stochastic Feedforward Networks

arXiv.org Machine Learning

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.

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Mar-24-2015

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