Trustworthy Uncertainty Quantification via Distributionally-Robust Dual Adaptive Conformal Prediction

Abstract Uncertainty quantification (UQ) plays a vital role in ensuring reliable and consistent decision-making, especially in emerging domains such as interactive, data-driven modeling and simulation for digital twins, where challenges such as distribution shifts, dynamic adjustment, and deep uncertainty limit the effectiveness of traditional Bayesian methods that rely on prior distribution assumptions. Conformal prediction (CP) offers a distribution-free framework for UQ with guaranteed marginal coverage. While basic methods like split CP and adaptive CP address some practical concerns, they often suffer from unstable prediction intervals and degraded coverage under distribution shift or dependence among samples. To overcome these limitations, we propose a Dual Adaptive Conformal Prediction method that introduces a dynamic data partitioning mechanism to adaptively adjust conformity scores and interval widths based on observed data characteristics and optimize information allocation for improved predictive uncertainty estimation. This dual adaptation improves the adaptability of uncertainty estimation models, increasing their sensitivity to data variations, and improving the stability of prediction results. To evaluate the effectiveness of the proposed method, experiments were conducted on both exchangeable and non-exchangeable datasets across low- and high-dimensional settings. Experimental results demonstrate superior expected coverage and greater stability in prediction intervals compared to traditional CP and Bayesian methods, especially in enhancing the flexibility of CP methods for non-exchangeable data. The proposed approach significantly strengthens conformal prediction's applicability to real-world, non-ideal conditions—offering a promising direction for future UQ research.