I Know What I Don't Know: Latent Posterior Factor Models for Multi-Evidence Probabilistic Reasoning

The multi-evidence aggregation challenge. 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.

Our approach: Latent Posterior Factors (LPF). We introduce LPF, a framework that transforms Variational Autoencoder (VAE) latent posteriors into soft likelihood factors for Sum-Product Network (SPN) inference. This enables tractable probabilistic reasoning over unstructured evidence while preserving calibrated uncertainty estimates.

Two complementary architectures. We instantiate LPF in two forms: LPF-SPN, which performs structured factor-based inference, and LPF-Learned, which learns evidence aggregation end-to-end. This design enables a principled comparison between explicit probabilistic reasoning and learned aggregation under a shared uncertainty representation.

Comprehensive evaluation. 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 as measured by negative log-likelihood, substantially outperforming evidential deep learning and graph-based baselines. Results are averaged over 15 random seeds to ensure statistical reliability.

Key contributions:

1. First general framework bridging latent uncertainty representations with structured probabilistic reasoning
2. Dual architectures enabling controlled comparison of reasoning paradigms
3. A reproducible training methodology with seed selection
4. Extensive evaluation against strong baselines including EDL, BERT, R-GCN, and large language models
5. Cross-domain validation demonstrating broad applicability
6. Formal guarantees (presented in companion paper Aliyu, 2026)