论文标题
方程组隐含的条件独立性和因果关系
Conditional independences and causal relations implied by sets of equations
论文作者
论文摘要
现实世界中的复杂系统通常是由内源性和外源变量的一组方程组建模的。关于在这些方程式出现的变量的因果和概率方面，我们能说什么，而不明确求解方程式？我们利用西蒙的因果秩序算法（Simon，1953）来构建因果订购图，并证明它在某些独特的溶解度假设下表达了柔软而完美的干预措施对方程式的影响。我们进一步构建了马尔可夫订购图，并证明它在类似的唯一溶解度假设下，在具有独立随机外源变量的方程所隐含的分布中编码条件独立性。我们讨论了这种方法如何揭示和解决现有因果建模框架的某些局限性，例如因果贝叶斯网络和结构性因果模型。
Real-world complex systems are often modelled by sets of equations with endogenous and exogenous variables. What can we say about the causal and probabilistic aspects of variables that appear in these equations without explicitly solving the equations? We make use of Simon's causal ordering algorithm (Simon, 1953) to construct a causal ordering graph and prove that it expresses the effects of soft and perfect interventions on the equations under certain unique solvability assumptions. We further construct a Markov ordering graph and prove that it encodes conditional independences in the distribution implied by the equations with independent random exogenous variables, under a similar unique solvability assumption. We discuss how this approach reveals and addresses some of the limitations of existing causal modelling frameworks, such as causal Bayesian networks and structural causal models.
