# Uncertainty Decomposition in Bayesian Neural Networks with Latent Variables

arXiv: https://arxiv.org/abs/1706.08495 · HTML: https://mlsanity.com/paper/1706.08495/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jun 2017.

## Built on by (most cited first, 9 of 9)

- [Uncertainty Quantification for In-Context Learning of Large Language Models](https://mlsanity.com/paper/2402.10189/) (2024)
- [Diverse, Global and Amortised Counterfactual Explanations for Uncertainty Estimates](https://mlsanity.com/paper/2112.02646/) (2021)
- [Active Imitation Learning from Multiple Non-Deterministic Teachers: Formulation, Challenges, and Algorithms](https://mlsanity.com/paper/2006.07777/) (2020)
- [RE-MOVE: An Adaptive Policy Design for Robotic Navigation Tasks in Dynamic Environments via Language-Based Feedback](https://mlsanity.com/paper/2303.07622/) (2023)
- [HopCast: Calibration of Autoregressive Dynamics Models](https://mlsanity.com/paper/2501.16587/) (2025)
- [Selective classification using a robust meta-learning approach](https://mlsanity.com/paper/2212.05987/) (2022)
- [Multi-Fidelity Bayesian Neural Network for Uncertainty Quantification in Transonic Aerodynamic Loads](https://mlsanity.com/paper/2407.05684/) (2024)
- [Exploring Efficient Quantification of Modeling Uncertainties with Differentiable Physics-Informed Machine Learning Architectures](https://mlsanity.com/paper/2506.18247/) (2025)
- [An Offline Risk-aware Policy Selection Method for Bayesian Markov Decision Processes](https://mlsanity.com/paper/2105.13431/) (2021)

## Abstract (arXiv)

Bayesian neural networks (BNNs) with latent variables are probabilistic models which can automatically identify complex stochastic patterns in the data. We describe and study in these models a decomposition of predictive uncertainty into its epistemic and aleatoric components. First, we show how such a decomposition arises naturally in a Bayesian active learning scenario by following an information theoretic approach. Second, we use a similar decomposition to develop a novel risk sensitive objective for safe reinforcement learning (RL). This objective minimizes the effect of model bias in environments whose stochastic dynamics are described by BNNs with latent variables. Our experiments illustrate the usefulness of the resulting decomposition in active learning and safe RL settings.