# Single-Model Uncertainties for Deep Learning

arXiv: https://arxiv.org/abs/1811.00908 · HTML: https://mlsanity.com/paper/1811.00908/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Nov 2018.

## Built on by (most cited first, 6 of 6)

- [ZigZag: Universal Sampling-free Uncertainty Estimation Through Two-Step Inference](https://mlsanity.com/paper/2211.11435/) (2022)
- [DEBOSH: Deep Bayesian Shape Optimization](https://mlsanity.com/paper/2109.13337/) (2021)
- [Deep Non-Crossing Quantiles through the Partial Derivative](https://mlsanity.com/paper/2201.12848/) (2022)
- [Function Space Diversity for Uncertainty Prediction via Repulsive Last-Layer Ensembles](https://mlsanity.com/paper/2412.15758/) (2024)
- [Hyperboost: Hyperparameter Optimization by Gradient Boosting surrogate models](https://mlsanity.com/paper/2101.02289/) (2021)
- [Uncertainty separation via ensemble quantile regression](https://mlsanity.com/paper/2412.13738/) (2024)

## Abstract (arXiv)

We provide single-model estimates of aleatoric and epistemic uncertainty for deep neural networks. To estimate aleatoric uncertainty, we propose Simultaneous Quantile Regression (SQR), a loss function to learn all the conditional quantiles of a given target variable. These quantiles can be used to compute well-calibrated prediction intervals. To estimate epistemic uncertainty, we propose Orthonormal Certificates (OCs), a collection of diverse non-constant functions that map all training samples to zero. These certificates map out-of-distribution examples to non-zero values, signaling epistemic uncertainty. Our uncertainty estimators are computationally attractive, as they do not require ensembling or retraining deep models, and achieve competitive performance.