# Probabilistic MIMO U-Net: Efficient and Accurate Uncertainty Estimation for Pixel-wise Regression

arXiv: https://arxiv.org/abs/2308.07477 · HTML: https://mlsanity.com/paper/2308.07477/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 26 references that are in the map.
- First posted on arXiv 14 Aug 2023.

## Builds on (most cited first, 16 of 16)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [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)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Deep Ensembles: A Loss Landscape Perspective](https://mlsanity.com/paper/1912.02757/) (2019)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [BatchEnsemble: An Alternative Approach to Efficient Ensemble and Lifelong Learning](https://mlsanity.com/paper/2002.06715/) (2020)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [Training independent subnetworks for robust prediction](https://mlsanity.com/paper/2010.06610/) (2020)
- [Efficient and Scalable Bayesian Neural Nets with Rank-1 Factors](https://mlsanity.com/paper/2005.07186/) (2020)
- [The Unreasonable Effectiveness of Deep Evidential Regression](https://mlsanity.com/paper/2205.10060/) (2022)
- [Maximum Likelihood Uncertainty Estimation: Robustness to Outliers](https://mlsanity.com/paper/2202.03870/) (2022)

## Abstract (arXiv)

Uncertainty estimation in machine learning is paramount for enhancing the reliability and interpretability of predictive models, especially in high-stakes real-world scenarios. Despite the availability of numerous methods, they often pose a trade-off between the quality of uncertainty estimation and computational efficiency. Addressing this challenge, we present an adaptation of the Multiple-Input Multiple-Output (MIMO) framework -- an approach exploiting the overparameterization of deep neural networks -- for pixel-wise regression tasks. Our MIMO variant expands the applicability of the approach from simple image classification to broader computer vision domains. For that purpose, we adapted the U-Net architecture to train multiple subnetworks within a single model, harnessing the overparameterization in deep neural networks. Additionally, we introduce a novel procedure for synchronizing subnetwork performance within the MIMO framework. Our comprehensive evaluations of the resulting MIMO U-Net on two orthogonal datasets demonstrate comparable accuracy to existing models, superior calibration on in-distribution data, robust out-of-distribution detection capabilities, and considerable improvements in parameter size and inference time. Code available at github.com/antonbaumann/MIMO-Unet