Monthly
288 pp. per issue
6 x 9, illustrated
ISSN
0899-7667
E-ISSN
1530-888X
2014 Impact factor:
2.21

Neural Computation

July 2014, Vol. 26, No. 7, Pages 1386-1407
(doi: 10.1162/NECO_a_00601)
@ 2014 Massachusetts Institute of Technology
Universal Approximation Depth and Errors of Narrow Belief Networks with Discrete Units
Article PDF (639.17 KB)
Abstract

We generalize recent theoretical work on the minimal number of layers of narrow deep belief networks that can approximate any probability distribution on the states of their visible units arbitrarily well. We relax the setting of binary units (Sutskever & Hinton, 2008; Le Roux & Bengio, 2008, 2010; Montúfar & Ay, 2011) to units with arbitrary finite state spaces and the vanishing approximation error to an arbitrary approximation error tolerance. For example, we show that a q-ary deep belief network with layers of width for some can approximate any probability distribution on without exceeding a Kullback-Leibler divergence of . Our analysis covers discrete restricted Boltzmann machines and naive Bayes models as special cases.