Expressive Power and Approximation Errors of Restricted Boltzmann Machines

Guido Montúfar, Johannes Rauh, and Nihat Ay

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Submission date: 01. Jun. 2011
Pages: 17
published in: Advances in neural information processing systems 24 : 25th annual conference on neural information processing systems 2011, Granada, Spain December 12th - 15th ; NIPS 2011 / J. Shawe-Taylor (ed.)
La Jolla, CA : Neural Information Processing Systems, 2011. - P. 415 - 423
Bibtex
MSC-Numbers: 68Q32, 68T01, 62-04
Keywords and phrases: Machine Learning, neural networks, Unsupervised Learning, Representational Power, Universal approximator
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Abstract:

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.