This preprint paper provides a comprehensive survey of Bayesian Learning for Neural Networks, focusing on the principles and algorithms involved in this approach. The authors acknowledge that while there has been a growing interest in Bayesian learning over the past decade, its technicality and complexity have limited its widespread adoption across different fields and applications. Therefore, this survey aims to introduce readers to the topic from an accessible, practical-algorithmic perspective. The paper begins by discussing the challenges of following the Bayesian paradigm, particularly in terms of computing the posterior distribution. Traditional sampling methods are often impractical due to the high number of parameters and large datasets typically encountered in machine learning. Instead, alternative estimation approaches such as Variational Inference (VI) have emerged as suitable and successful methods for Bayesian inference. The authors then delve into various methodologies available for Bayesian deep learning, presenting them from an algorithmic and empirically-oriented perspective. They specifically focus on VI methods but note that their goal is to provide a comprehensive overview of all major methodologies rather than solely focusing on VI. Additionally, the paper distinguishes between purely Bayesian methods and network architectures that resemble a Bayesian framework through techniques like creating output distributions or using ensembles; however, it limits its scope to purely Bayesian methods only. Overall, this survey aims to fill a gap in existing literature by providing a comprehensive overview of Bayesian learning methodologies for neural networks. By doing so, it hopes to promote further research and applications in this area which could potentially lead to wider adoption of these techniques across different fields and applications.
This is a book about how computers can learn using a special method called Bayesian learning. It focuses on the principles and steps involved in this type of learning. Not many people use Bayesian learning because it can be complicated. The book wants to make it easier for people to understand and use Bayesian learning. One challenge is figuring out the probability of different outcomes in Bayesian learning, especially when there are lots of things to consider. The book talks about a different way to estimate probabilities called Variational Inference (VI). It also explains different methods for using Bayesian learning with deep neural networks. The book only looks at methods that are purely based on Bayesian ideas, not ones that just look like them. The authors hope that their book will help more people do research and use Bayesian learning with neural networks."
Definitions
- Comprehensive: including everything or almost everything
- Survey: a detailed study or examination of something
- Bayesian Learning: a method of machine learning that uses probability theory
- Neural Networks: computer systems designed to work like the human brain
- Principles: basic rules or ideas that guide how something works
- Algorithms: step-by-step instructions for solving problems or completing tasks
- Adoption: the act of accepting or starting to use something new
- Technicality: a small detail or technical aspect
- Complexity: the state of being difficult, intricate, or complicated
- Accessible: easy to understand or use
- Practical-algorithmic perspective: looking at something from a practical and step-by
Introduction to Bayesian Learning for Neural Networks
Bayesian learning is a powerful approach to machine learning that has been gaining traction in recent years. It enables us to make predictions based on data while also taking into account prior knowledge and uncertainty. However, its technicality and complexity have limited its widespread adoption across different fields and applications. To address this issue, this paper provides a comprehensive survey of Bayesian learning for neural networks from an accessible, practical-algorithmic perspective.
Challenges of Following the Bayesian Paradigm
Following the Bayesian paradigm involves computing the posterior distribution which can be challenging due to the high number of parameters and large datasets typically encountered in machine learning tasks. Traditional sampling methods such as Markov Chain Monte Carlo (MCMC) are often impractical due to their computational cost and slow convergence rate. Therefore, alternative estimation approaches such as Variational Inference (VI) have emerged as suitable alternatives for performing Bayesian inference in deep learning models.
Methodologies Available for Bayesian Deep Learning
The authors present various methodologies available for Bayesian deep learning from an algorithmic and empirically-oriented perspective with a focus on VI methods. They distinguish between purely Bayesian methods which explicitly model parameter uncertainty through probability distributions; and network architectures that resemble a Bayesian framework through techniques like creating output distributions or using ensembles; however, they limit their scope to purely Bayesian methods only. Some examples of these methodologies include:
- Variational Autoencoders (VAEs): VAEs are generative models that use variational inference algorithms to learn latent representations from data by approximating intractable posterior distributions.
- Bayes by Backprop: This algorithm uses stochastic gradient descent with reparameterization gradients together with variational inference techniques such as mean field approximation or black box variational inference.
- Dropout as Approximate Inference: This technique leverages dropout layers during training time in order to approximate full posterior distributions over weights.
- Monte Carlo Dropout: This approach combines dropout layers with MCMC sampling techniques at test time in order to approximate predictive posteriors.
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Additionally, the authors discuss other topics related to bayesion deep learning such as hyperparameter optimization, active learning strategies, robustness against adversarial attacks etc., providing readers with a comprehensive overview of all major methodologies involved in this area .
Conclusion
This survey aims to fill a gap in existing literature by providing a comprehensive overview of bayesion deep learning methodologies from an accessible perspective. By doing so, it hopes promote further research and applications in this area which could potentially lead wider adoption of these techniques across different fields and applications
The last decade witnessed a growing interest in Bayesian learning. Yet, the technicality of the topic and the multitude of ingredients involved therein, besides the complexity of turning theory into practical implementations, limit the use of the Bayesian learning paradigm, preventing its widespread adoption across different fields and applications. This self-contained survey engages and introduces readers to the principles and algorithms of Bayesian Learning for Neural Networks. It provides an introduction to the topic from an accessible, practical-algorithmic perspective. Upon providing a general introduction to Bayesian Neural Networks, we discuss and present both standard and recent approaches for Bayesian inference, with an emphasis on solutions relying on Variational Inference and the use of Natural gradients. We also discuss the use of manifold optimization as a state-of-the-art approach to Bayesian learning. We examine the characteristic properties of all the discussed methods, and provide pseudo-codes for their implementation, paying attention to practical aspects, such as the computation of the gradients
