提出可信赖多证据推理的理论框架，确保高风险场景下决策可靠
Theoretical Foundations of Latent Posterior Factors: Formal Guarantees for Multi-Evidence Reasoning
- 用变分自编码器将证据转为高斯后验，再通过蒙特卡洛和网络聚合
- 在4200样本数据上实现0.849的校准相关性，错误率低于0.002%
- 适合医疗、金融等对可靠性要求高的安全关键领域
我们完整刻画了潜在后验因子（LPF）的理论基础，这是一个用于概率预测任务中聚合多种异构证据的严谨框架。多证据推理广泛存在于医疗诊断、金融风险评估、法律分析和合规审查等高风险领域，但现有方法要么缺乏形式化保证，要么架构上无法处理多证据场景。LPF通过变分自编码器将每个证据编码为高斯潜在后验，利用蒙特卡洛边际化转换为软因子，并通过精确的和积网络推理（LPF-SPN）或学习型神经聚合器（LPF-Learned）进行聚合。我们证明了七项形式化保证：校准保持（ECE ≤ ε + C/√K_eff）；蒙特卡洛误差以O(1/√M)衰减；在N=4200时具有0.0085的训练-测试差距的非平凡PAC-Bayes界；运算效率仅比信息论下限高1.12倍；在半数证据被对抗替换时仍保持88%性能，退化呈O(εδ√K)；校准衰减为O(1/√K)，R²=0.849；以及表征认知与随机不确定性分解的误差低于0.002%。所有定理均在控制数据集上验证，最多使用4200个训练样本。该理论框架为安全关键应用中的可信多证据人工智能奠定了基础。
原文摘要 · Abstract (English)
We present a complete theoretical characterization of Latent Posterior Factors (LPF), a principled framework for aggregating multiple heterogeneous evidence items in probabilistic prediction tasks. Multi-evidence reasoning arises pervasively in high-stakes domains including healthcare diagnosis, financial risk assessment, legal case analysis, and regulatory compliance, yet existing approaches either lack formal guarantees or fail to handle multi-evidence scenarios architecturally. LPF encodes each evidence item into a Gaussian latent posterior via a variational autoencoder, converting posteriors to soft factors through Monte Carlo marginalization, and aggregating factors via exact Sum-Product Network inference (LPF-SPN) or a learned neural aggregator (LPF-Learned). We prove seven formal guarantees spanning the key desiderata for trustworthy AI: Calibration Preservation (ECE <= epsilon + C/sqrt(K_eff)); Monte Carlo Error decaying as O(1/sqrt(M)); a non-vacuous PAC-Bayes bound with train-test gap of 0.0085 at N=4200; operation within 1.12x of the information-theoretic lower bound; graceful degradation as O(epsilon*delta*sqrt(K)) under corruption, maintaining 88% performance with half of evidence adversarially replaced; O(1/sqrt(K)) calibration decay with R^2=0.849; and exact epistemic-aleatoric uncertainty decomposition with error below 0.002%. All theorems are empirically validated on controlled datasets spanning up to 4,200 training examples. Our theoretical framework establishes LPF as a foundation for trustworthy multi-evidence AI in safety-critical applications.
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