# Tractable Approximate Gaussian Inference for Bayesian Neural Networks

arXiv: https://arxiv.org/abs/2004.09281 · HTML: https://mlsanity.com/paper/2004.09281/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Apr 2020.

## Built on by (most cited first, 7 of 7)

- [Streamlining Prediction in Bayesian Deep Learning](https://mlsanity.com/paper/2411.18425/) (2024)
- [Analytically Tractable Inference in Deep Neural Networks](https://mlsanity.com/paper/2103.05461/) (2021)
- [Analytically Tractable Bayesian Deep Q-Learning](https://mlsanity.com/paper/2106.11086/) (2021)
- [Analytically Tractable Hidden-States Inference in Bayesian Neural Networks](https://mlsanity.com/paper/2107.03759/) (2021)
- [Empowering Bayesian Neural Networks with Functional Priors through Anchored Ensembling for Mechanics Surrogate Modeling Applications](https://mlsanity.com/paper/2409.05234/) (2024)
- [From Overfitting to Reliability: Introducing the Hierarchical Approximate Bayesian Neural Network](https://mlsanity.com/paper/2512.13111/) (2025)
- [Full-Covariance Smoothing of Bayesian Neural Networks for Online Adaptation](https://mlsanity.com/paper/2609.27244/) (2026)

## Abstract (arXiv)

In this paper, we propose an analytical method for performing tractable approximate Gaussian inference (TAGI) in Bayesian neural networks. The method enables the analytical Gaussian inference of the posterior mean vector and diagonal covariance matrix for weights and biases. The method proposed has a computational complexity of O(n) with respect to the number of parameters n, and the tests performed on regression and classification benchmarks confirm that, for a same network architecture, it matches the performance of existing methods relying on gradient backpropagation.