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Quantitative Universal Approximation Bounds for Deep Belief Networks

arXiv 2208.09033 ↗First posted 18 Aug 2022stat.ML cs.LGcited by 0

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Abstract (arXiv)

We show that deep belief networks with binary hidden units can approximate any multivariate probability density under very mild integrability requirements on the parental density of the visible nodes. The approximation is measured in the Lq-norm for q∈[1,∞] (q=∞ corresponding to the supremum norm) and in Kullback-Leibler divergence. Furthermore, we establish sharp quantitative bounds on the approximation error in terms of the number of hidden units.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 16 of its 66 references that are in the map. First posted on arXiv 18 Aug 2022.

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References · 16

  1. 2017Distributional Reinforcement Learning with Quantile Regressioncited by 464
  2. 2013On the number of response regions of deep feed forward networks with piece-wise linear activationscited by 94
  3. 2018Deep, Skinny Neural Networks are not Universal Approximatorscited by 37
  4. 2021Flexible Model Aggregation for Quantile Regressioncited by 22
  5. 2018Restricted Boltzmann Machines: Introduction and Reviewcited by 14
  6. 2020Constructive Universal High-Dimensional Distribution Generation through Deep ReLU Networkscited by 13
  7. 2018Size-Noise Tradeoffs in Generative Networkscited by 12
  8. 2019Stochastic Feedforward Neural Networks: Universal Approximationcited by 7
  9. 2018An Adaptive Learning Method of Deep Belief Network by Layer Generation Algorithmcited by 6
  10. 2021Restricted Boltzmann Machine and Deep Belief Network: Tutorial and Surveycited by 5
  11. 2013Discrete Restricted Boltzmann Machinescited by 2
  12. 2016DeepQA: Improving the estimation of single protein model quality with deep belief networkscited by 2
4 more
  1. 2019Deep Adversarial Belief Networkscited by 2
  2. 2014Deep Narrow Boltzmann Machines are Universal Approximatorscited by 1
  3. 2015Universal Approximation of Markov Kernels by Shallow Stochastic Feedforward Networkscited by 1
  4. 2019An Object Detection by using Adaptive Structural Learning of Deep Belief Networkcited by 1

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