二分图因果模型的因果推理
Causal Reasoning with Bipartite Graphical Causal Models
- University of Amsterdam（阿姆斯特丹大学）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
针对现有因果推理框架无法表征平衡态循环因果系统的问题，提出二分图因果模型（BGCMs），解决了标准干预的歧义，可泛化CBNs与SCMs并支持域不变性推理。
中文摘要 AI 辅助
因果贝叶斯网络（CBNs）与结构因果模型（SCMs）是图形化因果推理的主流框架，但无法充分表征所有现实世界的因果系统。特别是处于平衡态的系统——其中反馈机制会形成循环因果依赖——其因果语义与上述框架根本不兼容：强制同一变量值的不同干预可能产生不同效果，导致标准的“完美干预”do(X=x)出现歧义。我们提出二分图因果模型（BGCMs），其中方程组的结构由包含变量节点与方程节点的二分图编码。在该框架中，硬干预do(f_j: X_v=ξ_v)指定需替换的方程、目标变量及取值，从而解决了标准概念的歧义。我们通过对一个物理系统的详细案例研究表明，该表征自然对应于不同的现实世界干预。我们基于利用方程组固有函数确定性的新型图形分离准则（B-分离）构建马尔可夫性质，并将其扩展至非随机输入的场景。我们展示了这如何催生用于推理域不变性的do-演算。BGCMs严格泛化了CBNs与SCMs，同时保留了执行图形化因果推理的能力。
英文摘要
Causal Bayesian networks (CBNs) and structural causal models (SCMs) are the dominant frameworks for graphical causal reasoning, but they cannot adequately represent all real-world causal systems. In particular, systems at equilibrium---where feedback mechanisms create cyclic causal dependencies---can exhibit causal semantics that are fundamentally incompatible with these frameworks: different interventions that enforce the same variable value may have different effects, rendering the standard ``perfect intervention'' do($X = x$) ambiguous. We propose bipartite graphical causal models (BGCMs), in which the structure of a system of equations is encoded by a bipartite graph with variable and equation nodes. In this framework, a hard intervention do($f_j : X_v = ξ_v$) specifies which equation is replaced, which variable is targeted, and at what value---resolving the ambiguity of the standard notion. We demonstrate, through a detailed case study of a physical system, that this representation naturally corresponds to distinct real-world interventions. We formulate a Markov property in terms of a new graphical separation criterion (B-separation) that exploits the functional determinism inherent in the equations, and we extend it to settings with non-random inputs. We show how this gives rise to a do-calculus for reasoning about domain invariances. BGCMs strictly generalize CBNs and SCMs while retaining the ability to perform graphical causal reasoning.
