Aliyu Agboola Alege

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.

Aliyu Agboola Alege

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.