我知我所不知：面向多证据概率推理的潜在后验因子模型
I Know What I Don't Know: Latent Posterior Factor Models for Multi-Evidence Probabilistic Reasoning
March 13, 2026
作者: Aliyu Agboola Alege
cs.AI
摘要
现实世界中的决策（从税务合规评估到医疗诊断）需要聚合多个存在噪声且可能相互矛盾的证据源。现有方法要么缺乏明确的不确定性量化（神经聚合方法），要么依赖人工设计的离散谓词（概率逻辑框架），限制了在非结构化数据上的扩展性。
我们提出隐变量后验因子（LPF）框架，将变分自编码器（VAE）的隐变量后验转化为和积网络（SPN）推理的软似然因子，从而在保持校准化不确定性估计的同时，实现对非结构化证据的可处理概率推理。我们具体实现了LPF-SPN（基于结构化因子的推理）和LPF-Learned（端到端学习式聚合）两种架构，为显式概率推理与学习式聚合在统一不确定性表征下的原理性比较提供了基础。
在八个领域（七个合成数据集和FEVER基准测试）中，LPF-SPN实现了高准确率（最高达97.8%）、低校准误差（ECE为1.4%）和强概率拟合度，在15个随机种子下显著超越证据深度学习、大语言模型和图神经网络基线方法。
核心贡献包括：（1）建立隐变量不确定性表征与结构化概率推理的桥梁；（2）双架构设计实现推理范式的受控比较；（3）包含种子选择的可复现训练方法；（4）与证据深度学习、BERT、R-GCN及大语言模型基线的系统性对比；（5）跨领域验证；（6）在配套论文中提供形式化理论保证。
English
Real-world decision-making, from tax compliance assessment to medical diagnosis, requires aggregating multiple noisy and potentially contradictory evidence sources. Existing approaches either lack explicit uncertainty quantification (neural aggregation methods) or rely on manually engineered discrete predicates (probabilistic logic frameworks), limiting scalability to unstructured data.
We introduce Latent Posterior Factors (LPF), a framework that transforms Variational Autoencoder (VAE) latent posteriors into soft likelihood factors for Sum-Product Network (SPN) inference, enabling tractable probabilistic reasoning over unstructured evidence while preserving calibrated uncertainty estimates. We instantiate LPF as LPF-SPN (structured factor-based inference) and LPF-Learned (end-to-end learned aggregation), enabling a principled comparison between explicit probabilistic reasoning and learned aggregation under a shared uncertainty representation.
Across eight domains (seven synthetic and the FEVER benchmark), LPF-SPN achieves high accuracy (up to 97.8%), low calibration error (ECE 1.4%), and strong probabilistic fit, substantially outperforming evidential deep learning, LLMs and graph-based baselines over 15 random seeds.
Contributions: (1) A framework bridging latent uncertainty representations with structured probabilistic reasoning. (2) Dual architectures enabling controlled comparison of reasoning paradigms. (3) Reproducible training methodology with seed selection. (4) Evaluation against EDL, BERT, R-GCN, and large language model baselines. (5) Cross-domain validation. (6) Formal guarantees in a companion paper.