arXiv:2512.01723cs.AIcs.GT2025-12

用概率符号推理解决历史数据稀疏难题,可解释且能做反事实推演。

Probabilistic Neuro-Symbolic Reasoning for Sparse Historical Data: A Framework Integrating Bayesian Inference, Causal Models, and Game-Theoretic Allocation

  • 融合贝叶斯、因果模型与博弈论,处理历史数据少、噪声多的问题
  • 识别德国战前紧张度+107.9%,海军竞赛相关性达0.79
  • 适合研究历史决策、战争胜负归因的学者和政策分析者

历史事件建模面临根本挑战:数据极度稀缺(N << 100)、测量异质且嘈杂、缺乏反事实数据,且需人类可解释性。我们提出HistoricalML,一种概率神经符号框架,通过融合(1)贝叶斯不确定性量化以区分认知不确定与随机误差,(2)结构因果模型实现混杂下的反事实推理,(3)合作博弈论(谢林值)实现公平分配建模,(4)注意力神经架构进行上下文依赖因子加权。理论分析表明,在强领域先验条件下,该方法在稀疏数据下仍能实现一致估计;谢林值分配满足公理化公平性,是纯回归无法达到的。我们在两个历史案例中验证:19世纪非洲瓜分(N=7个列强)和第二次布匿战争(N=2方)。模型发现德国战前紧张度+107.9%,紧张因子36.43,海军军备竞赛相关性0.79。对布匿战争的蒙特卡洛模拟显示,迦太基在坎尼战役胜率57.3%,罗马在扎马战役胜率57.8%,与史实吻合。反事实分析表明,迦太基政治支持度(6.4)而非军事能力是决定性因素,优于拿破仑的政治支持度(7.1)。

原文摘要 · Abstract (English)

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.

历史建模因果推理概率推理反事实分析

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