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Bayesian Neural Networks: An Introduction and Survey

arXiv stat.ML / 4/7/2026

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Key Points

  • The article introduces Bayesian Neural Networks (BNNs) as a way to address the limitation of standard (frequentist) neural networks, particularly their inability to explicitly reason about predictive uncertainty.
  • It surveys seminal work on how to implement BNNs, focusing on principled approaches for approximate Bayesian inference in neural network models.
  • The piece compares different approximate inference methods and evaluates how they affect uncertainty estimation and overall performance.
  • It identifies gaps in current methods and outlines directions for future research to improve Bayesian approximation and inference in neural networks.

Abstract

Neural Networks (NNs) have provided state-of-the-art results for many challenging machine learning tasks such as detection, regression and classification across the domains of computer vision, speech recognition and natural language processing. Despite their success, they are often implemented in a frequentist scheme, meaning they are unable to reason about uncertainty in their predictions. This article introduces Bayesian Neural Networks (BNNs) and the seminal research regarding their implementation. Different approximate inference methods are compared, and used to highlight where future research can improve on current methods.

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