用数学框架实现按场景变化的因果发现，更准更高效。
Decentralized Causal Discovery using Judo Calculus
- 基于层叠理论构建可分解的因果推断框架，支持局部验证。
- 在生物与经济数据上，计算效率提升且因果推断更准确。
- 适合需要跨场景推理的科研人员，如医学或社会学研究者。
我们提出一种直觉主义的去中心化因果发现框架，基于犹太极（judo calculus）形式化定义为在层叠拓扑空间中使用j-do-calculus的j-稳定因果推断。现实应用中（如生物、医学、社会科学），因果效应依赖于具体情境（年龄、国家、剂量、基因型或实验协议）。本文将情境依赖性形式化为局部真：因果结论在一组情境覆盖下成立，而非全局一致。Lawvere-Tierney模算子j用于选择相关情境；j-稳定性确保结论在该族情境间构造性且一致成立。我们构建了算法与实现框架，整合标准评分法、约束法与梯度法。在合成及真实世界数据（生物学、经济学）上进行实验，结果表明层叠理论因果发现具有去中心化优势，计算效率更高，性能优于传统方法。
原文摘要 · Abstract (English)
We describe a theory and implementation of an intuitionistic decentralized framework for causal discovery using judo calculus, which is formally defined as j-stable causal inference using j-do-calculus in a topos of sheaves. In real-world applications -- from biology to medicine and social science -- causal effects depend on regime (age, country, dose, genotype, or lab protocol). Our proposed judo calculus formalizes this context dependence formally as local truth: a causal claim is proven true on a cover of regimes, not everywhere at once. The Lawvere-Tierney modal operator j chooses which regimes are relevant; j-stability means the claim holds constructively and consistently across that family. We describe an algorithmic and implementation framework for judo calculus, combining it with standard score-based, constraint-based, and gradient-based causal discovery methods. We describe experimental results on a range of domains, from synthetic to real-world datasets from biology and economics. Our experimental results show the computational efficiency gained by the decentralized nature of sheaf-theoretic causal discovery, as well as improved performance over classical causal discovery methods.
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