Probabilistic Neuro-Symbolic Reasoning for Sparse Historical Data: A Framework Integrating Bayesian Inference, Causal Models, and Game-Theoretic Allocation
Saba Kublashvili
TL;DR
<3-5 sentence high-level summary>HistoricalML presents a probabilistic neuro-symbolic framework for analyzing sparse historical data by marrying Bayesian uncertainty, structural causal models, cooperative game theory, and attention-based weighting. The approach enables principled uncertainty quantification, counterfactual reasoning, and axiomatic fair allocation in settings with N<<100. It is validated on two case studies—the colonial partition of Africa and the Second Punic War—producing quantitative insights such as a 107.9% German discrepancy and battle-win probabilities around 0.57, with interpretable drivers like political support and resource mobilization. Theoretical results include identifiability under informative priors, convergence guarantees for Monte Carlo methods, and Shapley-based fairness guarantees, complemented by open-source code.
Abstract
Modeling historical events poses fundamental challenges for machine learning: extreme data scarcity (N << 100), heterogeneous and noisy measurements, missing counterfactuals, and the requirement for human interpretable explanations. We present HistoricalML, a probabilistic neuro-symbolic framework that addresses these challenges through principled integration of (1) Bayesian uncertainty quantification to separate epistemic from aleatoric uncertainty, (2) structural causal models for counterfactual reasoning under confounding, (3) cooperative game theory (Shapley values) for fair allocation modeling, and (4) attention based neural architectures for context dependent factor weighting. We provide theoretical analysis showing that our approach achieves consistent estimation in the sparse data regime when strong priors from domain knowledge are available, and that Shapley based allocation satisfies axiomatic fairness guarantees that pure regression approaches cannot provide. We instantiate the framework on two historical case studies: the 19th century partition of Africa (N = 7 colonial powers) and the Second Punic War (N = 2 factions). Our model identifies Germany's +107.9 percent discrepancy as a quantifiable structural tension preceding World War I, with tension factor 36.43 and 0.79 naval arms race correlation. For the Punic Wars, Monte Carlo battle simulations achieve a 57.3 percent win probability for Carthage at Cannae and 57.8 percent for Rome at Zama, aligning with historical outcomes. Counterfactual analysis reveals that Carthaginian political support (support score 6.4 vs Napoleon's 7.1), rather than military capability, was the decisive factor.