arXiv:2608.05454cs.LGstat.ML2026-08

提出可区分且可精炼的不确定性表示方法,提升预测可信度

Hybrid Probabilistic Zonotopes for Identifiable and Refinable Predictive Uncertainty

  • 用三种生成器构建混合概率超胞,分离模式选择、系统漂移和随机噪声
  • 单次前向传播即可精炼未来所有步骤的预测分布,效率更高
  • 适合需要高可信度与多模态不确定性的工业级预测任务

神经网络中的概率预测头通常输出高斯混合或单一共形区域,无法区分真实预测任务中常见的三类不确定性:模式间的离散选择、选定模式内的有界系统漂移、以及不可约的随机噪声。本文提出混合概率超胞(HProbZ),将这三类不确定性分别建模为二值、有界和随机生成器,并通过卷积实现闭式似然计算。共享的有界生成器使各预测步之间代数耦合,观测一步即可在一次前向传播中精炼所有剩余步的预测分布。我们证明了三类生成器可从似然中唯一识别(至置换),且其密度形式不同于任何有限高斯混合。相同共享结构还支持解析的每模式风险评估与无分布多模态共形集。在代表性预测基准上的实证分析表明,该设计相较同编码器的混合模型更有效,同时具备混合模型与凸共形预测器无法共同提供的结构性优势。

原文摘要 · Abstract (English)

Probabilistic prediction heads in neural networks typically output either a Gaussian mixture or a single conformal region. Neither separates the distinct sources of uncertainty often present in real prediction tasks: a discrete choice among modes, bounded systematic drift within the chosen mode, and irreducible stochastic noise. We introduce the Hybrid Probabilistic Zonotope (HProbZ), an output head that represents these three sources as binary, bounded, and stochastic generators of a zonotope, and admits a closed-form likelihood by convolution. Sharing the bounded generator across prediction steps couples future predictions algebraically, so observing one step refines the predictive distribution at every remaining step in a single forward pass. We establish that the three generators are identifiable from the likelihood up to permutation, and that an HProbZ density is representationally distinct from any finite Gaussian mixture. The same shared structure provides analytic per-mode risk and distribution-free multi-modal conformal sets at inference time. Empirical analysis on representative prediction benchmarks supports the effectiveness of the design relative to same-encoder mixture baselines, while offering structural properties that mixture or convex-conformal predictors do not jointly provide.

不确定性建模概率预测多模态

Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。