# Training-Free Uncertainty Estimation for Dense Regression: Sensitivity as a Surrogate

arXiv: https://arxiv.org/abs/1910.04858 · HTML: https://mlsanity.com/paper/1910.04858/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Sep 2019.

## Built on by (most cited first, 28 of 28)

- [A Survey on Uncertainty Quantification of Large Language Models: Taxonomy, Open Research Challenges, and Future Directions](https://mlsanity.com/paper/2412.05563/) (2024)
- [Self-Expansion of Pre-trained Models with Mixture of Adapters for Continual Learning](https://mlsanity.com/paper/2403.18886/) (2024)
- [Gradient-based Uncertainty for Monocular Depth Estimation](https://mlsanity.com/paper/2208.02005/) (2022)
- [TokUR: Token-Level Uncertainty Estimation for Large Language Model Reasoning](https://mlsanity.com/paper/2505.11737/) (2025)
- [Diffusion Model Guided Sampling with Pixel-Wise Aleatoric Uncertainty Estimation](https://mlsanity.com/paper/2412.00205/) (2024)
- [Latent Discriminant deterministic Uncertainty](https://mlsanity.com/paper/2207.10130/) (2022)
- [ZigZag: Universal Sampling-free Uncertainty Estimation Through Two-Step Inference](https://mlsanity.com/paper/2211.11435/) (2022)
- [Epistemic Uncertainty Quantification For Pre-trained Neural Network](https://mlsanity.com/paper/2404.10124/) (2024)
- [Self-supervised Remote Sensing Images Change Detection at Pixel-level](https://mlsanity.com/paper/2105.08501/) (2021)
- [Discretization-Induced Dirichlet Posterior for Robust Uncertainty Quantification on Regression](https://mlsanity.com/paper/2308.09065/) (2023)
- [Rate-In: Information-Driven Adaptive Dropout Rates for Improved Inference-Time Uncertainty Estimation](https://mlsanity.com/paper/2412.07169/) (2024)
- [Revisiting Gradient-based Uncertainty for Monocular Depth Estimation](https://mlsanity.com/paper/2502.05964/) (2025)
- [Hyperdimensional Uncertainty Quantification for Multimodal Uncertainty Fusion in Autonomous Vehicles Perception](https://mlsanity.com/paper/2503.20011/) (2025)
- [Knowing What to Label for Few Shot Microscopy Image Cell Segmentation](https://mlsanity.com/paper/2211.10244/) (2022)
- [Surrogate uncertainty estimation for your time series forecasting black-box: learn when to trust](https://mlsanity.com/paper/2302.02834/) (2023)
- [ADU-Depth: Attention-based Distillation with Uncertainty Modeling for Depth Estimation](https://mlsanity.com/paper/2309.14744/) (2023)
- [A Critical Synthesis of Uncertainty Quantification and Foundation Models in Monocular Depth Estimation](https://mlsanity.com/paper/2501.08188/) (2025)
- [Towards Trustworthy Vital Sign Forecasting: Leveraging Uncertainty for Prediction Intervals](https://mlsanity.com/paper/2509.01319/) (2025)
- [Variational Imbalanced Regression: Fair Uncertainty Quantification via Probabilistic Smoothing](https://mlsanity.com/paper/2306.06599/) (2023)
- [Measuring and Modeling Uncertainty Degree for Monocular Depth Estimation](https://mlsanity.com/paper/2307.09929/) (2023)
- [Uncertainty Quantification With Noise Injection in Neural Networks: A Bayesian Perspective](https://mlsanity.com/paper/2501.12314/) (2025)
- [Analysis of Image-and-Text Uncertainty Propagation in Multimodal Large Language Models with Cardiac MR-Based Applications](https://mlsanity.com/paper/2507.12945/) (2025)
- [SmOOD: Smoothness-based Out-of-Distribution Detection Approach for Surrogate Neural Networks in Aircraft Design](https://mlsanity.com/paper/2209.03438/) (2022)
- [Unsupervised Source-Free Ranking of Biomedical Segmentation Models Under Distribution Shift](https://mlsanity.com/paper/2503.00450/) (2025)
- [Robust Uncertainty Estimation under Distribution Shift via Difference Reconstruction](https://mlsanity.com/paper/2601.19341/) (2026)
- [CUPID: A Plug-in Framework for Joint Aleatoric and Epistemic Uncertainty Estimation with a Single Model](https://mlsanity.com/paper/2603.10745/) (2026)
- [CRUISE: Vision-Language Model-Guided Uncertainty-Aware Cross-Modal Sensor Fusion for Robust Autonomous Driving](https://mlsanity.com/paper/2608.09202/) (2026)
- [Explainable Uncertainty Estimation for Reliable Medical AI](https://mlsanity.com/paper/2608.28052/) (2026)

## Abstract (arXiv)

Uncertainty estimation is an essential step in the evaluation of the robustness for deep learning models in computer vision, especially when applied in risk-sensitive areas. However, most state-of-the-art deep learning models either fail to obtain uncertainty estimation or need significant modification (e.g., formulating a proper Bayesian treatment) to obtain it. Most previous methods are not able to take an arbitrary model off the shelf and generate uncertainty estimation without retraining or redesigning it. To address this gap, we perform a systematic exploration into training-free uncertainty estimation for dense regression, an unrecognized yet important problem, and provide a theoretical construction justifying such estimations. We propose three simple and scalable methods to analyze the variance of outputs from a trained network under tolerable perturbations: infer-transformation, infer-noise, and infer-dropout. They operate solely during the inference, without the need to re-train, re-design, or fine-tune the models, as typically required by state-of-the-art uncertainty estimation methods. Surprisingly, even without involving such perturbations in training, our methods produce comparable or even better uncertainty estimation when compared to training-required state-of-the-art methods.