We develop a novel approach towards causal inference. Rather than structural equations over a causal graph, we learn stochastic differential equations (SDEs) whose stationary densities model a system's behavior under interventions. These stationary diffusion models do not require the formalism of causal graphs, let alone the common assumption of acyclicity. We show that in several cases, they generalize to unseen interventions on their variables, often better than classical approaches. Our inference method is based on a new theoretical result that expresses a stationarity condition on the diffusion's generator in a reproducing kernel Hilbert space. The resulting kernel deviation from stationarity (KDS) is an objective function of independent interest.

翻译：我们提出了一种全新的因果推断方法。不同于基于因果图的结构方程，我们学习随机微分方程（SDE），利用其平稳密度来建模系统在干预下的行为。这种平稳扩散模型无需借助因果图的形式化框架，更无需依赖常见的无环性假设。我们证明，在多种情形下，该方法能泛化至变量上未见过的干预场景，其效果通常优于经典方法。我们的推断方法基于一项新的理论结果：该结果在再生核希尔伯特空间中表达了扩散生成元上的平稳性条件。由此导出的核平稳性偏离度（KDS）是一个具有独立研究价值的目标函数。