arXiv:2509.13262cs.LG2025-09

无需重训练,单次前向传播即可同时量化模型的两类不确定性。

Post-Hoc Split-Point Self-Consistency Verification for Efficient, Unified Quantification of Aleatoric and Epistemic Uncertainty in Deep Learning

  • 通过拆分点分析分解预测残差,分别计算两侧均值绝对残差。
  • 提出自洽性差异得分,使回归与分类任务的置信区间覆盖更准确。
  • 适用于已有模型的不确定性增强,适合追求高效可信推理的研究者。

不确定性量化(UQ)对可信深度学习至关重要,但现有方法或计算成本高(如贝叶斯或集成方法),或仅提供部分、任务特定估计(如单前向传播技术)。本文提出一种后处理式单前向传播框架,无需修改或重新训练预训练模型,即可联合捕捉偶然性与认知不确定性。该方法采用拆分点分析(SPA)将预测残差分为上下两子集,分别计算均值绝对残差(MAR)。我们证明,在理想条件下,总MAR等于子集MAR的调和平均;偏离程度定义了新的自洽性差异得分(SDS),用于细粒度的认知不确定性估计。在回归任务中,子集特定分位数回归生成具有改进经验覆盖率的预测区间,并通过SDS进一步校准。在分类任务中,若有校准数据,利用SPA校准恒等式调整softmax输出,再基于校准概率计算预测熵。在多种回归与分类基准上的实验表明,本框架性能达到或超过多个前沿UQ方法,且开销极低。代码已开源:https://github.com/zzz0527/SPC-UQ。

原文摘要 · Abstract (English)

Uncertainty quantification (UQ) is vital for trustworthy deep learning, yet existing methods are either computationally intensive, such as Bayesian or ensemble methods, or provide only partial, task-specific estimates, such as single-forward-pass techniques. In this paper, we propose a post-hoc single-forward-pass framework that jointly captures aleatoric and epistemic uncertainty without modifying or retraining pretrained models. Our method applies \emph{Split-Point Analysis} (SPA) to decompose predictive residuals into upper and lower subsets, computing \emph{Mean Absolute Residuals} (MARs) on each side. We prove that, under ideal conditions, the total MAR equals the harmonic mean of subset MARs; deviations define a novel \emph{Self-consistency Discrepancy Score} (SDS) for fine-grained epistemic estimation across regression and classification. For regression, side-specific quantile regression yields prediction intervals with improved empirical coverage, which are further calibrated via SDS. For classification, when calibration data are available, we apply SPA-based calibration identities to adjust the softmax outputs and then compute predictive entropy on these calibrated probabilities. Extensive experiments on diverse regression and classification benchmarks demonstrate that our framework matches or exceeds several state-of-the-art UQ methods while incurring minimal overhead. Our source code is available at https://github.com/zzz0527/SPC-UQ.

不确定性量化单前向传播模型校准回归与分类

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