Uncertainty Estimation via Hyperspherical Confidence Mapping

• URL: http://arxiv.org/abs/2605.05964v1
• Date: Thu, 07 May 2026 10:11:01 GMT
• Title: Uncertainty Estimation via Hyperspherical Confidence Mapping
• Abstract summary: Quantifying uncertainty in neural network predictions is essential for high-stakes domains such as autonomous driving, healthcare, and manufacturing.<n>We propose Hyperspherical Confidence Mapping, a principled framework for sampling-free and distribution-free uncertainty estimation.<n> Experiments across diverse benchmarks and real-world industrial tasks demonstrate that HCM matches or surpasses ensemble and evidential approaches.
• Score: 7.467483743345029
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantifying uncertainty in neural network predictions is essential for high-stakes domains such as autonomous driving, healthcare, and manufacturing. While existing approaches often depend on costly sampling or restrictive distributional assumptions, we propose Hyperspherical Confidence Mapping (HCM), a simple yet principled framework for sampling-free and distribution-free uncertainty estimation. HCM decomposes outputs into a magnitude and a normalized direction vector constrained to lie on the unit hypersphere, enabling a novel interpretation of uncertainty as the degree of violation of this geometric constraint. This yields deterministic and interpretable estimates applicable to both regression and classification. Experiments across diverse benchmarks and real-world industrial tasks demonstrate that HCM matches or surpasses ensemble and evidential approaches, with far lower inference cost and stronger confidence-error alignment. Our results highlight the power of geometric structure in uncertainty estimation and position HCM as a versatile alternative to conventional techniques.

Related papers

• It depends: Incorporating correlations for joint aleatoric and epistemic uncertainties of high-dimensional output spaces [23.472868138533926]
  Uncertainty Quantification (UQ) plays a vital role in enhancing the reliability of deep learning model predictions.<n>This paper addresses the dual nature of uncertainty, focusing on their joint integration in high-dimensional regression tasks.<n>We propose a novel approach that approximates the resulting joint uncertainty using a low-rank plus diagonal covariance structure.
  arXiv  Detail & Related papers  (2026-08-25T13:08:17Z)
• Hybrid Uncertainty Sensitivity Analysis Based on the HSIC for High-Dimensional Responses with Aleatory--Epistemic Separation [4.666836674804876]
  A novel double-space tensor-product RKHS framework is proposed for sensitivity analysis under hybrid uncertainty.<n>The resulting dimension-wise sensitivity indices preserve the uncertainty attribution structure across all output dimensions.<n> Numerical studies on a modified multi-output Ishigami function and an aerodynamic pressure-field problem demonstrate the accuracy, scalability, and practical applicability of the proposed framework.
  arXiv  Detail & Related papers  (2026-06-12T02:58:28Z)
• Towards Trustworthy Depression Estimation via Disentangled Evidential Learning [50.22167852149165]
  We propose EviDep, an evidential learning framework that jointly quantifies depression severity.<n>EviDep enforces strict information integrity to guarantee robust evidence synthesis.<n>It achieves state-of-the-art predictive accuracy and superior uncertainty calibration, delivering a robust fail-safe mechanism for trustworthy clinical screening.
  arXiv  Detail & Related papers  (2026-04-17T13:27:11Z)
• Stabilized Maximum-Likelihood Iterative Quantum Amplitude Estimation for Structural CVaR under Correlated Random Fields [0.0]
  Conditional Value-at-Risk (CVaR) is a central tail-risk measure in structural mechanics.<n>We develop a quantum-enhanced inference framework that casts CVaR evaluation as a confidence-constrained maximum-likelihood amplitude estimation problem.
  arXiv  Detail & Related papers  (2026-02-10T14:53:26Z)
• ProbFM: Probabilistic Time Series Foundation Model with Uncertainty Decomposition [0.12489632787815884]
  Time Series Foundation Models (TSFMs) have emerged as a promising approach for zero-shot financial forecasting.<n>Current approaches either rely on restrictive distributional assumptions, conflate different sources of uncertainty, or lack principled calibration mechanisms.<n>We present a novel transformer-based probabilistic framework, ProbFM, that leverages Deep Evidential Regression (DER) to provide principled uncertainty quantification.
  arXiv  Detail & Related papers  (2026-01-15T17:02:06Z)
• Bridging the Gap Between Bayesian Deep Learning and Ensemble Weather Forecasts [100.26854618129039]
  Weather forecasting is fundamentally challenged by the chaotic nature of the atmosphere.<n>Recent advances in Bayesian Deep Learning (BDL) offer a promising but often disconnected alternative.<n>We bridge these paradigms through a unified hybrid BDL framework for ensemble weather forecasting.
  arXiv  Detail & Related papers  (2025-11-18T07:49:52Z)
• Generative Conformal Prediction with Vectorized Non-Conformity Scores [6.059745771017814]
  Conformal prediction provides model-agnostic uncertainty quantification with guaranteed coverage.<n>We propose a generative conformal prediction framework with vectorized non-conformity scores.<n>We construct adaptive uncertainty sets using density-ranked uncertainty balls.
  arXiv  Detail & Related papers  (2024-10-17T16:37:03Z)
• Uncertainty Quantification for Forward and Inverse Problems of PDEs via Latent Global Evolution [110.99891169486366]
  We propose a method that integrates efficient and precise uncertainty quantification into a deep learning-based surrogate model. Our method endows deep learning-based surrogate models with robust and efficient uncertainty quantification capabilities for both forward and inverse problems. Our method excels at propagating uncertainty over extended auto-regressive rollouts, making it suitable for scenarios involving long-term predictions.
  arXiv  Detail & Related papers  (2024-02-13T11:22:59Z)
• Distributional Shift-Aware Off-Policy Interval Estimation: A Unified Error Quantification Framework [8.572441599469597]
  We study high-confidence off-policy evaluation in the context of infinite-horizon Markov decision processes. The objective is to establish a confidence interval (CI) for the target policy value using only offline data pre-collected from unknown behavior policies. We show that our algorithm is sample-efficient, error-robust, and provably convergent even in non-linear function approximation settings.
  arXiv  Detail & Related papers  (2023-09-23T06:35:44Z)
• The Unreasonable Effectiveness of Deep Evidential Regression [72.30888739450343]
  A new approach with uncertainty-aware regression-based neural networks (NNs) shows promise over traditional deterministic methods and typical Bayesian NNs. We detail the theoretical shortcomings and analyze the performance on synthetic and real-world data sets, showing that Deep Evidential Regression is a quantification rather than an exact uncertainty.
  arXiv  Detail & Related papers  (2022-05-20T10:10:32Z)
• Amortized Conditional Normalized Maximum Likelihood: Reliable Out of Distribution Uncertainty Estimation [99.92568326314667]
  We propose the amortized conditional normalized maximum likelihood (ACNML) method as a scalable general-purpose approach for uncertainty estimation. Our algorithm builds on the conditional normalized maximum likelihood (CNML) coding scheme, which has minimax optimal properties according to the minimum description length principle. We demonstrate that ACNML compares favorably to a number of prior techniques for uncertainty estimation in terms of calibration on out-of-distribution inputs.
  arXiv  Detail & Related papers  (2020-11-05T08:04:34Z)
• GenDICE: Generalized Offline Estimation of Stationary Values [108.17309783125398]
  We show that effective estimation can still be achieved in important applications. Our approach is based on estimating a ratio that corrects for the discrepancy between the stationary and empirical distributions. The resulting algorithm, GenDICE, is straightforward and effective.
  arXiv  Detail & Related papers  (2020-02-21T00:27:52Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.