用于可识别和可细化预测不确定性的混合概率 zonotope
Hybrid Probabilistic Zonotopes for Identifiable and Refinable Predictive Uncertainty
AI总结：
该研究提出混合概率 zonotope（HProbZ）作为神经网络预测头，分离三种不确定性来源，可细化多步预测分布，具备独特结构特性，在基准测试中优于同编码器混合基线。
AI中文摘要：
神经网络中的概率预测头通常输出高斯混合模型或单个保形区域，两者均无法分离实际预测任务中常存在的不同不确定性来源：模式间的离散选择、所选模式内的有界系统漂移以及不可约的随机噪声。我们提出混合概率 zonotope（HProbZ），这一输出头将上述三种来源表示为 zonotope 的二元、有界和随机生成器，并通过卷积获得闭式似然。在预测步骤间共享有界生成器可代数耦合未来预测，因此观测到一步即可在单次前向传播中细化所有剩余步骤的预测分布。我们证明这三种生成器可通过似然识别（至多排列不同），且 HProbZ 密度在表示上与任何有限高斯混合模型不同。这种共享结构还可在推理时提供解析的单模式风险及无分布多模态保形集。在代表性预测基准上的实证分析表明，与相同编码器的混合基线相比，该设计更有效，同时具备混合或凸保形预测器无法共同提供的结构特性。
英文摘要：
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.
