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.

我们开发了一种新的因果推断方法，通过学习随机微分方程 (SDEs) 的稳定密度来模拟系统在干预下的行为，而不需要因果图的结构方程，并且无需考虑无环性的常见假设。我们表明，在若干情况下，这些稳定扩散模型对于变量上的未观测干预进行了推广，通常比传统方法更好。我们的推断方法基于一个新的理论结果，通过在再生核希尔伯特空间中表达扩散的生成器上的稳定条件。由此产生的核函数离稳定性的偏差 (KDS) 是一个独立感兴趣的目标函数。