# Model uncertainty quantification using feature confidence sets for outcome excursions

arXiv: https://arxiv.org/abs/2504.19464 · HTML: https://mlsanity.com/paper/2504.19464/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 36 references that are in the map.
- First posted on arXiv 28 Apr 2025.

## Builds on (most cited first, 11 of 11)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Shifts: A Dataset of Real Distributional Shift Across Multiple Large-Scale Tasks](https://mlsanity.com/paper/2107.07455/) (2021)
- [Uncertainty Quantification with Statistical Guarantees in End-to-End Autonomous Driving Control](https://mlsanity.com/paper/1909.09884/) (2019)
- [Gradients as a Measure of Uncertainty in Neural Networks](https://mlsanity.com/paper/2008.08030/) (2020)
- [Adversarial Attack for Uncertainty Estimation: Identifying Critical Regions in Neural Networks](https://mlsanity.com/paper/2107.07618/) (2021)
- [A comparative simulation study of data-driven methods for estimating density level sets](https://mlsanity.com/paper/1402.0361/) (2014)
- [Success of Uncertainty-Aware Deep Models Depends on Data Manifold Geometry](https://mlsanity.com/paper/2208.01705/) (2022)
- [Inverse set estimation and inversion of simultaneous confidence intervals](https://mlsanity.com/paper/2210.03933/) (2022)

## Abstract (arXiv)

When implementing prediction models for high-stakes real-world applications such as medicine, finance, and autonomous systems, quantifying prediction uncertainty is critical for effective risk management. Traditional approaches to uncertainty quantification, such as confidence and prediction intervals, provide probability coverage guarantees for the expected outcomes f(boldsymbolx) or the realized outcomes f(boldsymbolx)+ε. Instead, this paper introduces a novel, model-agnostic framework for quantifying uncertainty in continuous and binary outcomes using confidence sets for outcome excursions, where the goal is to identify a subset of the feature space where the expected or realized outcome exceeds a specific value. The proposed method constructs data-dependent inner and outer confidence sets that aim to contain the true feature subset for which the expected or realized outcomes of these features exceed a specified threshold. We establish theoretical guarantees for the probability that these confidence sets contain the true feature subset, both asymptotically and for finite sample sizes. The framework is validated through simulations and applied to real-world datasets, demonstrating its utility in contexts such as housing price prediction and time to sepsis diagnosis in healthcare. This approach provides a unified method for uncertainty quantification that is broadly applicable across various continuous and binary prediction models.