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

Computer Science > Artificial Intelligence [Submitted on 13 Mar 2026] I Know What I Don't Know: Latent Posterior Factor Models for Multi-Evidence Probabilistic Reasoning Aliyu Agboola Alege 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. Comments: 202 pages, 52 figures, 105 tables. Comprehensive presentation of the Latent Posterior Factors (LPF) framework for multi-evidence probabilistic reasoning, including theoretical analysis, algorithmic design, and extensive empirical evaluation across synthetic and real-world benchmarks Subjects: Artificial Intelligence (cs.AI); Machine Learning (cs.LG) MSC classes: 68T37 (Primary), 68T05, 62F15 ACM classes: I.2.6; I.2.4; G.3 Cite as: arXiv:2603.15670 [cs.AI]   (or arXiv:2603.15670v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2603.15670 Focus to learn more Submission history From: Aliyu Alege [view email] [v1] Fri, 13 Mar 2026 10:05:14 UTC (282 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-03 Change to browse by: cs cs.LG References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)