# Learning Context-conditioned Gaussian Overbounds for Convolution-Based Uncertainty Propagation

arXiv: https://arxiv.org/abs/2605.15789 · HTML: https://mlsanity.com/paper/2605.15789/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 47 references that are in the map.
- First posted on arXiv 15 May 2026.

## Builds on (most cited first, 15 of 15)

- [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)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Uncertainty Quantification and Deep Ensembles](https://mlsanity.com/paper/2007.08792/) (2020)
- [A Survey on Uncertainty Quantification Methods for Deep Learning](https://mlsanity.com/paper/2302.13425/) (2023)
- [Beyond Pinball Loss: Quantile Methods for Calibrated Uncertainty Quantification](https://mlsanity.com/paper/2011.09588/) (2020)
- [Reliable training and estimation of variance networks](https://mlsanity.com/paper/1906.03260/) (2019)
- [Calibrated Reliable Regression using Maximum Mean Discrepancy](https://mlsanity.com/paper/2006.10255/) (2020)
- [Ensemble Conformalized Quantile Regression for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2202.08756/) (2022)
- [Conformal Prediction: A Data Perspective](https://mlsanity.com/paper/2410.06494/) (2024)
- [Conformal Loss-Controlling Prediction](https://mlsanity.com/paper/2301.02424/) (2023)
- [Adaptive Sparse Gaussian Process](https://mlsanity.com/paper/2302.10325/) (2023)
- [Improving Uncertainty Quantification of Variance Networks by Tree-Structured Learning](https://mlsanity.com/paper/2212.12658/) (2022)

## Abstract (arXiv)

Uncertainty quantification is essential in safety-critical settings--from autonomous driving to aviation, finance, and health--where decisions must rely on conservative bounds rather than point estimates. Predictor-level intervals (e.g., from quantile regression, conformal prediction, variance networks, or Bayesian models) generally do not compose: adding two per-variable intervals need not yield a valid interval for their sum or preserve coverage. In aviation, Gaussian overbounding replaces complex error distributions with a conservative Gaussian whose tails dominate the truth, so conservatism propagates through linear operations. Yet classical overbounds are global, often overly conservative, and hard to adapt to feature-conditioned errors. We propose a unified learning framework that trains neural networks to produce context-aware Gaussian overbounds--mean and scale--with provable conservatism on a finite quantile grid and, under three explicit regularity assumptions, continuous-tail conservatism on a certified interval. Our overbounding loss enforces conservativeness at selected quantiles while penalizing distributional distance with a Wasserstein-style term. The learned bounds support conservative linear-combination and convolution analysis on the enforced grid, and on the certified interval when assumptions hold, while being less redundant than traditional methods. We provide a scoped analysis of discrete-to-continuous conservatism and compact-domain objective regularity, and validate on synthetic data and real-world datasets, including multipath, ionospheric, and tropospheric residual errors. Across these settings, the method yields tighter bounds while maintaining conservatism on the enforced grid and in experiments. The framework is modality-agnostic and applicable to learning systems that require conservative, feature-conditioned uncertainty estimates in dynamic environments.