Universal Approximation of Markov Kernels by Shallow Stochastic Feedforward Networks

Guido Montufar

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arXiv · 1503.07211

Universal Approximation of Markov Kernels by Shallow Stochastic Feedforward Networks

Guido Montufar

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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.

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Guido Montufar. 2015-03-24. Universal Approximation of Markov Kernels by Shallow Stochastic Feedforward Networks. https://arxiv.org/abs/1503.07211

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