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Expressive Power and Approximation Errors of Restricted Boltzmann Machines
Guido Montúfar, Johannes Rauh and Nihat Ay
We present explicit classes of probability distributions that can be learned by Restricted Boltzmann Machines (RBMs) depending on the number of units that they contain, and which are representative for the expressive power of the model. We use this to show that the maximal Kullback-Leibler divergence to the RBM model with $n$ visible and $m$ hidden units is bounded from above by $(n-1)-\log(m+1)$.
In this way we can specify the number of hidden units that guarantees a sufficiently rich model containing different classes of distributions and respecting a given error tolerance.
Expressive power and approximation errors of restricted Boltzmann machines
In: Advances in neural information processing systems 24 : NIPS 2011 ; 25th annual conference on neural information processing systems 2011, Granada, Spain December 12th - 15th / John Shawe-Taylor (ed.) La Jolla, CA : Neural Information Processing Systems, 2011. - pp. 415-423