用因果规则解决统计模糊性问题,为因果AI提供理论基础。
Solution of the Hempel's statistical ambiguity problem and Causal AI
- 基于概率提升定义因果规则,通过增量信息更新实现最大特异性
- 证明该方法可导出一致预测,彻底解决赫姆普尔的统计模糊难题
- 适用于因果AI、因果机器学习,推动复杂系统因果推理
本文解决卡尔·赫姆普尔长期存在的归纳-统计推论中的统计模糊性问题,即同一统计律可能导出矛盾预测。赫姆普尔提出最大特异性要求(RMS)以避免此问题,后续学者如萨尔蒙、科法、费茨尔对其进行了修正,最终定义为:‘充分解释的前提必须仅包含对现象发生有影响的属性’。然而此前缺乏基于此定义的解决方案。本文采用南希·卡特赖特的概率提升因果观,引入因果规则概念,并设计一种语义概率推理过程,逐步融合所有统计相关性信息。该过程生成最大特异性因果关系(MSCRs),并证明(定理1)由此导出的预测具有一致性,从而彻底解决统计模糊性问题。该推理机制构成一个概率因果学习系统,可用于因果人工智能与因果机器学习等新领域,从根本上探索因果推断在复杂系统中的作用。类似RMS的性质仍受关注,包括不变特征学习、不变因果预测及虚假关联等概念亦被讨论。
原文摘要 · Abstract (English)
This paper addresses Carl Hempel's longstanding problem of statistical ambiguity in inductive-statistical inference, in which contradictory predictions are derived from statistical laws. To avoid such predictions, Carl Hempel proposed the Requirement of Maximal Specificity (RMS) for the statistical laws used in the inference. An analysis of the RMS refinements made by Wesley Salmon, Alberto Coffa, and James Fetzer led to the following definition of maximally specific statistical laws: "the lawlike premises of an adequate explanation must specify all and only those properties whose presence or absence made a difference to the occurrence of its explanandum-phenomenon." However, there was no proof of a solution to the statistical ambiguity problem based on this definition. We use Nancy Cartwright's definition of causes that raise probabilities across background contexts, and then introduce the concept of Causal Rules. Then we define a special semantic probabilistic inference procedure that incrementally refines these causal rules by incorporating all statistically relevant information. This procedure yields Maximally Specific Causal Relationships (MSCRs), for which we prove (Theorem 1) that predictions derived from them are consistent. This resolves the statistical ambiguity problem. The semantic probabilistic inference procedure provides a probabilistic causal learning system, which may be used in such new areas as Causal AI and Causal Machine Learning. They fundamentally explore causal inference as a tool for understanding cause-and-effect relationships within complex systems. Properties similar to RMS remain under discussion. Several notions related to RMS are considered: invariant feature learning, invariant causal prediction, and spurious association.
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