厘清因果模型中行动与干预的对应关系,揭示现有解释的循环性缺陷。
What is causal about causal models and representations?
- 构建形式化框架,明确行动作为干预的必要条件
- 证明自然解释存在循环性,无法通过数据验证模型
- 提出非循环解释路径,支持因果模型的可证伪性
因果贝叶斯网络因其能预测干预分布而被称为‘因果’模型。要将这些预测与现实结果关联,必须确定世界中的哪些行为对应于模型中的哪些干预。例如,将某行为解释为对治疗变量的干预,需满足:a)改变治疗分布的方式与干预一致;b)不改变结果对治疗的依赖关系,尽管某些变量的边缘分布可能因干预而变化。本文提出一个形式化框架,精确刻画不同行动解释为干预所需的要求。我们证明,看似自然的解释方式具有循环性:只要因果贝叶斯网络正确建模了观测分布,它就自动具备干预有效性,任何行动都无法提供足以证伪该模型的实证数据。进一步证明,不存在既非循环又满足一组自然期望的解释。相反,我们探讨了可能违反部分期望但允许模型被证伪的非循环解释。本工作通过严谨分析因果贝叶斯网络如何真正成为世界的‘因果’模型,而非仅数学对象,为因果表示学习、因果发现和因果抽象提供了概念基础,同时揭示了现有方法的局限。
原文摘要 · Abstract (English)
Causal Bayesian networks are 'causal' models since they make predictions about interventional distributions. To connect such causal model predictions to real-world outcomes, we must determine which actions in the world correspond to which interventions in the model. For example, to interpret an action as an intervention on a treatment variable, the action will presumably have to a) change the distribution of treatment in a way that corresponds to the intervention, and b) not change other aspects, such as how the outcome depends on the treatment; while the marginal distributions of some variables may change as an effect. We introduce a formal framework to make such requirements for different interpretations of actions as interventions precise. We prove that the seemingly natural interpretation of actions as interventions is circular: Under this interpretation, every causal Bayesian network that correctly models the observational distribution is trivially also interventionally valid, and no action yields empirical data that could possibly falsify such a model. We prove an impossibility result: No interpretation exists that is non-circular and simultaneously satisfies a set of natural desiderata. Instead, we examine non-circular interpretations that may violate some desiderata and show how this may in turn enable the falsification of causal models. By rigorously examining how a causal Bayesian network could be a 'causal' model of the world instead of merely a mathematical object, our formal framework contributes to the conceptual foundations of causal representation learning, causal discovery, and causal abstraction, while also highlighting some limitations of existing approaches.
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