arXiv:2502.06995stat.MLcs.LG2025-02被引 11

让预测区间自动变宽,数据少时更谨慎。

Epistemic Uncertainty in Conformal Scores: A Unified Approach

  • 用贝叶斯方法显式建模认知不确定性,适配任意模型
  • 数据稀疏区自动扩大预测范围,保证覆盖率
  • 兼容任意贝叶斯模型,适合需要可靠置信区间的场景

共形预测方法可提供分布无关的预测带,但未显式捕捉认知不确定性,导致在数据稀疏区域出现过度自信。尽管已有针对特定任务(如回归或分位数回归)的共形得分方法,但它们依赖特定建模假设,适用性受限。本文提出 $ exttt{EPICSCORE}$,一种模型无关的方法,通过集成高斯过程、蒙特卡洛丢弃或贝叶斯加性回归树等贝叶斯技术,显式引入认知不确定性。该方法在数据稀疏区域自适应扩展预测区间,而在数据丰富区域保持紧凑。与所有共形方法一样,$ exttt{EPICSCORE}$ 保证有限样本边际覆盖,且实现渐近条件覆盖。实验表明其性能优于现有方法。该框架兼容任意贝叶斯模型,并具备分布无关保证,为预测问题中的不确定性量化提供了通用解决方案。

原文摘要 · Abstract (English)

Conformal prediction methods create prediction bands with distribution-free guarantees but do not explicitly capture epistemic uncertainty, which can lead to overconfident predictions in data-sparse regions. Although recent conformal scores have been developed to address this limitation, they are typically designed for specific tasks, such as regression or quantile regression. Moreover, they rely on particular modeling choices for epistemic uncertainty, restricting their applicability. We introduce $\texttt{EPICSCORE}$, a model-agnostic approach that enhances any conformal score by explicitly integrating epistemic uncertainty. Leveraging Bayesian techniques such as Gaussian Processes, Monte Carlo Dropout, or Bayesian Additive Regression Trees, $\texttt{EPICSCORE}$ adaptively expands predictive intervals in regions with limited data while maintaining compact intervals where data is abundant. As with any conformal method, it preserves finite-sample marginal coverage. Additionally, it also achieves asymptotic conditional coverage. Experiments demonstrate its good performance compared to existing methods. Designed for compatibility with any Bayesian model, but equipped with distribution-free guarantees, $\texttt{EPICSCORE}$ provides a general-purpose framework for uncertainty quantification in prediction problems.

不确定性量化共形预测贝叶斯方法模型无关

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