Abstract We provide a scheme for inferring causal relations from uncontrolled statistical data based on tools from computational algebraic geometry, in particular, the computation of Groebner bases. We focus on causal structures containing just two observed variables, each of which is binary. We consider the consequences of imposing different restrictions on the number and cardinality of latent variables and of assuming different functional dependences of the observed variables on the latent ones (in particular, the noise need not be additive). We provide an inductive scheme for classifying functional causal structures into distinct observational equivalence classes. For each observational equivalence class, we provide a procedure for deriving constraints on the joint distribution that are necessary and sufficient conditions for it to arise from a model in that class. We also demonstrate how this sort of approach provides a means of determining which causal parameters are identifiable and how to solve for these. Prospects for expanding the scope of our scheme, in particular to the problem of quantum causal inference, are also discussed.

中文翻译：

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通过代数几何进行因果推断：具有两个二元观测变量的功能因果结构的可行性测试

摘要 我们提供了一种基于计算代数几何工具，特别是 Groebner 基的计算，从不受控制的统计数据中推断因果关系的方案。我们专注于只包含两个观察变量的因果结构，每个变量都是二元的。我们考虑对潜在变量的数量和基数施加不同限制以及假设观察变量对潜在变量具有不同功能依赖性（特别是噪声不需要相加）的后果。我们提供了一种归纳方案，用于将功能因果结构分类为不同的观察等价类。对于每个观察等价类，我们提供了一个程序来推导出联合分布的约束条件，这些约束条件是从该类中的模型中产生的必要和充分条件。我们还演示了这种方法如何提供一种方法来确定哪些因果参数是可识别的，以及如何解决这些参数。还讨论了扩大我们方案范围的前景，特别是量子因果推理问题。