mlsanityData to 7 Oct 2026

Asymptotic Properties for Bayesian Neural Network in Besov Space

arXiv 2206.00241 ↗First posted 1 Jun 2022stat.ML cs.LG math.STcited by 7

Not on the map. Why?

Abstract (arXiv)

Neural networks have shown great predictive power when dealing with various unstructured data such as images and natural languages. The Bayesian neural network captures the uncertainty of prediction by putting a prior distribution for the parameter of the model and computing the posterior distribution. In this paper, we show that the Bayesian neural network using spike-and-slab prior has consistency with nearly minimax convergence rate when the true regression function is in the Besov space. Even when the smoothness of the regression function is unknown the same posterior convergence rate holds and thus the spike-and-slab prior is adaptive to the smoothness of the regression function. We also consider the shrinkage prior, which is more feasible than other priors, and show that it has the same convergence rate. In other words, we propose a practical Bayesian neural network with guaranteed asymptotic properties.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Builds on 15 of its 48 references that are in the map. First posted on arXiv 1 Jun 2022.

Builds on

15 of 48 references.

References · 15

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  2. 2015Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learningcited by 4,416
  3. 2017Deep Neural Networks as Gaussian Processescited by 617
  4. 2016Error bounds for approximations with deep ReLU networkscited by 567
  5. 2017Nonparametric regression using deep neural networks with ReLU activation functioncited by 431
  6. 2018Pyro: Deep Universal Probabilistic Programmingcited by 379
  7. 2014Stochastic Gradient Hamiltonian Monte Carlocited by 341
  8. 2018Gaussian Process Behaviour in Wide Deep Neural Networkscited by 314
  9. 2016Benefits of depth in neural networkscited by 248
  10. 2018Adaptivity of deep ReLU network for learning in Besov and mixed smooth Besov spaces: optimal rate and curse of dimensionalitycited by 160
  11. 2015Representation Benefits of Deep Feedforward Networkscited by 84
  12. 2018Posterior Concentration for Sparse Deep Learningcited by 50
3 more
  1. 2014Bayesian linear regression with sparse priorscited by 40
  2. 2019Convergence Rates of Variational Inference in Sparse Deep Learningcited by 27
  3. 2021L'evy Adaptive B-spline Regression via Overcomplete Systemscited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 3; 2025: 1; 2026: 2.

7 papers.

  1. 2023Masked Bayesian Neural Networks : Theoretical Guarantee and its Posterior Inferencecited by 9
  2. 2024Posterior and variational inference for deep neural networks with heavy-tailed weightscited by 9
  3. 2024Misclassification bounds for PAC-Bayesian sparse deep learningcited by 7
  4. 2025Posterior Contraction for Sparse Neural Networks in Besov Spaces with Intrinsic Dimensionalitycited by 2
  5. 2024Variational Bayesian Bow tie Neural Networks with Shrinkagecited by 0
  6. 2026Posterior Concentration of Bayesian Physics-Informed Neural Networks for Elliptic PDEscited by 0
  7. 2026Posterior Contraction of L'evy Adaptive B-spline Regression in Besov Spacescited by 0