MiS Preprint Repository
We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
Expressive Power and Approximation Errors of Restricted Boltzmann Machines
Guido Montúfar, Johannes Rauh and Nihat AyAbstract
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
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.
- Received:
- 01.06.11
- Published:
- 01.06.11
- MSC Codes:
- 68Q32, 68T01, 62-04
- Keywords:
- Machine Learning, neural networks, Unsupervised Learning, Representational Power, Universal approximator
Related publications
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