Expressive power and approximation errors of Restricted Boltzmann Machines

Publikationstyp
Conference Paper
Date Issued
2011-12
Sprache
English
Author(s)
Montüfar, Guido F.  
Rauh, Johannes  
Ay, Nihat  
TORE-URI
http://hdl.handle.net/11420/14559
Citation
Advances in Neural Information Processing Systems 24: 25th Annual Conference on Neural Information Processing Systems 2011, NIPS 2011: (2011-12-01)
Contribution to Conference
25th Annual Conference on Neural Information Processing Systems 2011, NIPS 2011  
Publisher DOI
10.48550/arXiv.1406.3140
Scopus ID
2-s2.0-84860629969
ArXiv ID
1406.3140
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 andmhidden 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.
DDC Class
004: Informatik
510: Mathematik