# Masked Bayesian Neural Networks : Computation and Optimality

arXiv: https://arxiv.org/abs/2206.00853 · HTML: https://mlsanity.com/paper/2206.00853/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 69 references that are in the map.
- First posted on arXiv 2 Jun 2022.

## Builds on (most cited first, 30 of 41)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [SNIP: Single-shot Network Pruning based on Connection Sensitivity](https://mlsanity.com/paper/1810.02340/) (2018)
- [Channel Pruning for Accelerating Very Deep Neural Networks](https://mlsanity.com/paper/1707.06168/) (2017)
- [Learning Efficient Convolutional Networks through Network Slimming](https://mlsanity.com/paper/1708.06519/) (2017)
- [Learning Structured Sparsity in Deep Neural Networks](https://mlsanity.com/paper/1608.03665/) (2016)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1402.4102/) (2014)
- [Verified Uncertainty Calibration](https://mlsanity.com/paper/1909.10155/) (2019)
- [What Are Bayesian Neural Network Posteriors Really Like?](https://mlsanity.com/paper/2104.14421/) (2021)
- [Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks](https://mlsanity.com/paper/1502.05336/) (2015)
- [Variational Dropout Sparsifies Deep Neural Networks](https://mlsanity.com/paper/1701.05369/) (2017)
- [Cyclical Stochastic Gradient MCMC for Bayesian Deep Learning](https://mlsanity.com/paper/1902.03932/) (2019)
- [Efficient and Scalable Bayesian Neural Nets with Rank-1 Factors](https://mlsanity.com/paper/2005.07186/) (2020)
- [Multiplicative Normalizing Flows for Variational Bayesian Neural Networks](https://mlsanity.com/paper/1703.01961/) (2017)
- [Uncertainty Quantification and Deep Ensembles](https://mlsanity.com/paper/2007.08792/) (2020)
- [Preconditioned Stochastic Gradient Langevin Dynamics for Deep Neural Networks](https://mlsanity.com/paper/1512.07666/) (2015)
- [Bayesian Compression for Deep Learning](https://mlsanity.com/paper/1705.08665/) (2017)
- [EigenDamage: Structured Pruning in the Kronecker-Factored Eigenbasis](https://mlsanity.com/paper/1905.05934/) (2019)
- [Collaborative Deep Learning for Recommender Systems](https://mlsanity.com/paper/1409.2944/) (2014)
- [Oops I Took A Gradient: Scalable Sampling for Discrete Distributions](https://mlsanity.com/paper/2102.04509/) (2021)
- [A Systematic Comparison of Bayesian Deep Learning Robustness in Diabetic Retinopathy Tasks](https://mlsanity.com/paper/1912.10481/) (2019)

## Built on by (most cited first, 1 of 1)

- [Aerial Image Object Detection With Vision Transformer Detector (ViTDet)](https://mlsanity.com/paper/2301.12058/) (2023)

## Abstract (arXiv)

As data size and computing power increase, the architectures of deep neural networks (DNNs) have been getting more complex and huge, and thus there is a growing need to simplify such complex and huge DNNs. In this paper, we propose a novel sparse Bayesian neural network (BNN) which searches a good DNN with an appropriate complexity. We employ the masking variables at each node which can turn off some nodes according to the posterior distribution to yield a nodewise sparse DNN. We devise a prior distribution such that the posterior distribution has theoretical optimalities (i.e. minimax optimality and adaptiveness), and develop an efficient MCMC algorithm. By analyzing several benchmark datasets, we illustrate that the proposed BNN performs well compared to other existing methods in the sense that it discovers well condensed DNN architectures with similar prediction accuracy and uncertainty quantification compared to large DNNs.