# Multivariate Bayesian Last Layer for Regression with Uncertainty Quantification and Decomposition

arXiv: https://arxiv.org/abs/2405.01761 · HTML: https://mlsanity.com/paper/2405.01761/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 43 references that are in the map.
- First posted on arXiv 2 May 2024.

## Builds on (most cited first, 17 of 17)

- [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)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [Scalable Bayesian Optimization Using Deep Neural Networks](https://mlsanity.com/paper/1502.05700/) (2015)
- [Being Bayesian, Even Just a Bit, Fixes Overconfidence in ReLU Networks](https://mlsanity.com/paper/2002.10118/) (2020)
- [Variational Bayesian Last Layers](https://mlsanity.com/paper/2404.11599/) (2024)
- [Do Bayesian Neural Networks Need To Be Fully Stochastic?](https://mlsanity.com/paper/2211.06291/) (2022)
- [Student-t Processes as Alternatives to Gaussian Processes](https://mlsanity.com/paper/1402.4306/) (2014)
- [The Unreasonable Effectiveness of Deep Evidential Regression](https://mlsanity.com/paper/2205.10060/) (2022)
- [Benchmarking the Neural Linear Model for Regression](https://mlsanity.com/paper/1912.08416/) (2019)
- [Multivariate Deep Evidential Regression](https://mlsanity.com/paper/2104.06135/) (2021)
- [Improved uncertainty quantification for neural networks with Bayesian last layer](https://mlsanity.com/paper/2302.10975/) (2023)
- [Sparse Variational Student-t Processes](https://mlsanity.com/paper/2312.05568/) (2023)

## Abstract (arXiv)

We present new Bayesian Last Layer neural network models in the setting of multivariate regression under heteroscedastic noise, and propose EM algorithms for parameter learning. Bayesian modeling of a neural network's final layer has the attractive property of uncertainty quantification with a single forward pass. The proposed framework is capable of disentangling the aleatoric and epistemic uncertainty, and can be used to enhance a canonically trained deep neural network with uncertainty-aware capabilities.